Identifier
-
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
St000288: Binary words ⟶ ℤ
Values
[1,0,1,0] => [1,2] => [1,2] => 0 => 0
[1,1,0,0] => [2,1] => [2,1] => 1 => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => 00 => 0
[1,0,1,1,0,0] => [1,3,2] => [3,1,2] => 10 => 1
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => 10 => 1
[1,1,0,1,0,0] => [2,3,1] => [1,3,2] => 01 => 1
[1,1,1,0,0,0] => [3,2,1] => [3,2,1] => 11 => 2
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => 000 => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [4,1,2,3] => 100 => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [3,1,2,4] => 100 => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,4,1,3] => 010 => 1
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [4,3,1,2] => 110 => 2
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => 100 => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [1,4,2,3] => 010 => 1
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [1,3,2,4] => 010 => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [1,2,4,3] => 001 => 1
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [4,1,3,2] => 101 => 2
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,2,1,4] => 110 => 2
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [2,1,4,3] => 101 => 2
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [2,4,3,1] => 011 => 2
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => 111 => 3
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => 0000 => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [5,1,2,3,4] => 1000 => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [4,1,2,3,5] => 1000 => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [3,5,1,2,4] => 0100 => 1
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [5,4,1,2,3] => 1100 => 2
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [3,1,2,4,5] => 1000 => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [2,5,1,3,4] => 0100 => 1
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [2,4,1,3,5] => 0100 => 1
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,3,5,1,4] => 0010 => 1
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [5,2,4,1,3] => 1010 => 2
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [4,3,1,2,5] => 1100 => 2
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [3,2,5,1,4] => 1010 => 2
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [3,5,4,1,2] => 0110 => 2
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [5,4,3,1,2] => 1110 => 3
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => 1000 => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [1,5,2,3,4] => 0100 => 1
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [1,4,2,3,5] => 0100 => 1
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [1,3,5,2,4] => 0010 => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [5,1,4,2,3] => 1010 => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [1,3,2,4,5] => 0100 => 1
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [1,2,5,3,4] => 0010 => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [1,2,4,3,5] => 0010 => 1
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [1,2,3,5,4] => 0001 => 1
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [5,1,2,4,3] => 1001 => 2
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [4,1,3,2,5] => 1010 => 2
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [3,1,2,5,4] => 1001 => 2
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [3,5,1,4,2] => 0101 => 2
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [5,4,1,3,2] => 1101 => 3
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,2,1,4,5] => 1100 => 2
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [2,1,5,3,4] => 1010 => 2
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [2,1,4,3,5] => 1010 => 2
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [2,1,3,5,4] => 1001 => 2
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [1,5,2,4,3] => 0101 => 2
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [2,4,3,1,5] => 0110 => 2
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [2,3,1,5,4] => 0101 => 2
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [2,3,5,4,1] => 0011 => 2
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [5,2,4,3,1] => 1011 => 3
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,3,2,1,5] => 1110 => 3
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [3,2,1,5,4] => 1101 => 3
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [3,2,5,4,1] => 1011 => 3
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [2,5,4,3,1] => 0111 => 3
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1] => 1111 => 4
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 00000 => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 10000 => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 10000 => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [4,6,1,2,3,5] => 01000 => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 11000 => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 10000 => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [3,6,1,2,4,5] => 01000 => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [3,5,1,2,4,6] => 01000 => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [3,4,6,1,2,5] => 00100 => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [6,3,5,1,2,4] => 10100 => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => 11000 => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [4,3,6,1,2,5] => 10100 => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [4,6,5,1,2,3] => 01100 => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 11100 => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 10000 => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [2,6,1,3,4,5] => 01000 => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [2,5,1,3,4,6] => 01000 => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [2,4,6,1,3,5] => 00100 => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [6,2,5,1,3,4] => 10100 => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => 01000 => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [2,3,6,1,4,5] => 00100 => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [2,3,5,1,4,6] => 00100 => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,3,4,6,1,5] => 00010 => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [6,2,3,5,1,4] => 10010 => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [5,2,4,1,3,6] => 10100 => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [4,2,3,6,1,5] => 10010 => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [4,6,2,5,1,3] => 01010 => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [6,5,2,4,1,3] => 11010 => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => 11000 => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [3,2,6,1,4,5] => 10100 => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [3,2,5,1,4,6] => 10100 => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [3,2,4,6,1,5] => 10010 => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [2,6,3,5,1,4] => 01010 => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [3,5,4,1,2,6] => 01100 => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [3,4,2,6,1,5] => 01010 => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [3,4,6,5,1,2] => 00110 => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [6,3,5,4,1,2] => 10110 => 3
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => 11100 => 3
>>> Load all 1583 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [4,3,2,6,1,5] => 11010 => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [4,3,6,5,1,2] => 10110 => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [3,6,5,4,1,2] => 01110 => 3
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 11110 => 4
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 10000 => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [1,6,2,3,4,5] => 01000 => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [1,5,2,3,4,6] => 01000 => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [1,4,6,2,3,5] => 00100 => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [6,1,5,2,3,4] => 10100 => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,4,2,3,5,6] => 01000 => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [1,3,6,2,4,5] => 00100 => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [1,3,5,2,4,6] => 00100 => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [1,3,4,6,2,5] => 00010 => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [6,1,3,5,2,4] => 10010 => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [5,1,4,2,3,6] => 10100 => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [4,1,3,6,2,5] => 10010 => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [4,6,1,5,2,3] => 01010 => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [6,5,1,4,2,3] => 11010 => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [1,3,2,4,5,6] => 01000 => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [1,2,6,3,4,5] => 00100 => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [1,2,5,3,4,6] => 00100 => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [1,2,4,6,3,5] => 00010 => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [6,1,2,5,3,4] => 10010 => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [1,2,4,3,5,6] => 00100 => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [1,2,3,6,4,5] => 00010 => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [1,2,3,5,4,6] => 00010 => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [1,2,3,4,6,5] => 00001 => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [6,1,2,3,5,4] => 10001 => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [5,1,2,4,3,6] => 10010 => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [4,1,2,3,6,5] => 10001 => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [4,6,1,2,5,3] => 01001 => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [6,5,1,2,4,3] => 11001 => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,1,3,2,5,6] => 10100 => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,1,2,6,4,5] => 10010 => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [3,1,2,5,4,6] => 10010 => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [3,1,2,4,6,5] => 10001 => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [2,6,1,3,5,4] => 01001 => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [3,5,1,4,2,6] => 01010 => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [3,4,1,2,6,5] => 01001 => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [3,4,6,1,5,2] => 00101 => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [6,3,5,1,4,2] => 10101 => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [5,4,1,3,2,6] => 11010 => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [4,3,1,2,6,5] => 11001 => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [4,3,6,1,5,2] => 10101 => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [3,6,5,1,4,2] => 01101 => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [6,5,4,1,3,2] => 11101 => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 11000 => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [2,1,6,3,4,5] => 10100 => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [2,1,5,3,4,6] => 10100 => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [2,1,4,6,3,5] => 10010 => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [1,6,2,5,3,4] => 01010 => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [2,1,4,3,5,6] => 10100 => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [2,1,3,6,4,5] => 10010 => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [2,1,3,5,4,6] => 10010 => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [2,1,3,4,6,5] => 10001 => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [1,6,2,3,5,4] => 01001 => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [1,5,2,4,3,6] => 01010 => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [1,4,2,3,6,5] => 01001 => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [1,4,6,2,5,3] => 00101 => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [6,1,5,2,4,3] => 10101 => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [2,4,3,1,5,6] => 01100 => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [2,3,1,6,4,5] => 01010 => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [2,3,1,5,4,6] => 01010 => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [2,3,1,4,6,5] => 01001 => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [6,2,1,3,5,4] => 11001 => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [2,3,5,4,1,6] => 00110 => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,4,1,6,5] => 00101 => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [2,3,4,6,5,1] => 00011 => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [6,2,3,5,4,1] => 10011 => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [5,2,4,3,1,6] => 10110 => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [4,2,3,1,6,5] => 10101 => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [4,2,3,6,5,1] => 10011 => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [3,6,2,5,4,1] => 01011 => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [6,5,2,4,3,1] => 11011 => 4
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 11100 => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [3,2,1,6,4,5] => 11010 => 3
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [3,2,1,5,4,6] => 11010 => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [3,2,1,4,6,5] => 11001 => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [2,1,6,3,5,4] => 10101 => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [3,2,5,4,1,6] => 10110 => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,2,4,1,6,5] => 10101 => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [3,2,4,6,5,1] => 10011 => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [2,6,3,5,4,1] => 01011 => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [2,5,4,3,1,6] => 01110 => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [2,4,3,1,6,5] => 01101 => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [2,4,3,6,5,1] => 01011 => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [2,3,6,5,4,1] => 00111 => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [6,2,5,4,3,1] => 10111 => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 11110 => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [4,3,2,1,6,5] => 11101 => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [4,3,2,6,5,1] => 11011 => 4
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [3,2,6,5,4,1] => 10111 => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [3,6,5,4,2,1] => 01111 => 4
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 11111 => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 100000 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 100000 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [5,7,1,2,3,4,6] => 010000 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => 110000 => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 100000 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [4,7,1,2,3,5,6] => 010000 => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [4,6,1,2,3,5,7] => 010000 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [4,5,7,1,2,3,6] => 001000 => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [7,4,6,1,2,3,5] => 101000 => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [6,5,1,2,3,4,7] => 110000 => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [5,4,7,1,2,3,6] => 101000 => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [5,7,6,1,2,3,4] => 011000 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => 111000 => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 100000 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [3,7,1,2,4,5,6] => 010000 => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [3,6,1,2,4,5,7] => 010000 => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [3,5,7,1,2,4,6] => 001000 => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [7,3,6,1,2,4,5] => 101000 => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [3,5,1,2,4,6,7] => 010000 => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [3,4,7,1,2,5,6] => 001000 => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [3,4,6,1,2,5,7] => 001000 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [3,4,5,7,1,2,6] => 000100 => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [7,3,4,6,1,2,5] => 100100 => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [6,3,5,1,2,4,7] => 101000 => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [5,3,4,7,1,2,6] => 100100 => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [5,7,3,6,1,2,4] => 010100 => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [7,6,3,5,1,2,4] => 110100 => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => 110000 => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [4,3,7,1,2,5,6] => 101000 => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [4,3,6,1,2,5,7] => 101000 => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [4,3,5,7,1,2,6] => 100100 => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [3,7,4,6,1,2,5] => 010100 => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [4,6,5,1,2,3,7] => 011000 => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [4,5,3,7,1,2,6] => 010100 => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [4,5,7,6,1,2,3] => 001100 => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [7,4,6,5,1,2,3] => 101100 => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [6,5,4,1,2,3,7] => 111000 => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [5,4,3,7,1,2,6] => 110100 => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [5,4,7,6,1,2,3] => 101100 => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [4,7,6,5,1,2,3] => 011100 => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => 111100 => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 100000 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [2,7,1,3,4,5,6] => 010000 => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [2,6,1,3,4,5,7] => 010000 => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [2,5,7,1,3,4,6] => 001000 => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [7,2,6,1,3,4,5] => 101000 => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [2,5,1,3,4,6,7] => 010000 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [2,4,7,1,3,5,6] => 001000 => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [2,4,6,1,3,5,7] => 001000 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [2,4,5,7,1,3,6] => 000100 => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [7,2,4,6,1,3,5] => 100100 => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [6,2,5,1,3,4,7] => 101000 => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [5,2,4,7,1,3,6] => 100100 => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [5,7,2,6,1,3,4] => 010100 => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [7,6,2,5,1,3,4] => 110100 => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => 010000 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [2,3,7,1,4,5,6] => 001000 => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [2,3,6,1,4,5,7] => 001000 => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [2,3,5,7,1,4,6] => 000100 => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [7,2,3,6,1,4,5] => 100100 => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [2,3,5,1,4,6,7] => 001000 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [2,3,4,7,1,5,6] => 000100 => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [2,3,4,6,1,5,7] => 000100 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [2,3,4,5,7,1,6] => 000010 => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [7,2,3,4,6,1,5] => 100010 => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [6,2,3,5,1,4,7] => 100100 => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [5,2,3,4,7,1,6] => 100010 => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [5,7,2,3,6,1,4] => 010010 => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [7,6,2,3,5,1,4] => 110010 => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [5,2,4,1,3,6,7] => 101000 => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [4,2,3,7,1,5,6] => 100100 => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [4,2,3,6,1,5,7] => 100100 => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [4,2,3,5,7,1,6] => 100010 => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [3,7,2,4,6,1,5] => 010010 => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [4,6,2,5,1,3,7] => 010100 => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [4,5,2,3,7,1,6] => 010010 => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [4,5,7,2,6,1,3] => 001010 => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [7,4,6,2,5,1,3] => 101010 => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [6,5,2,4,1,3,7] => 110100 => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [5,4,2,3,7,1,6] => 110010 => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [5,4,7,2,6,1,3] => 101010 => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [4,7,6,2,5,1,3] => 011010 => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [7,6,5,2,4,1,3] => 111010 => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [4,3,1,2,5,6,7] => 110000 => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [3,2,7,1,4,5,6] => 101000 => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [3,2,6,1,4,5,7] => 101000 => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [3,2,5,7,1,4,6] => 100100 => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [2,7,3,6,1,4,5] => 010100 => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [3,2,5,1,4,6,7] => 101000 => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [3,2,4,7,1,5,6] => 100100 => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [3,2,4,6,1,5,7] => 100100 => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [3,2,4,5,7,1,6] => 100010 => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [2,7,3,4,6,1,5] => 010010 => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [2,6,3,5,1,4,7] => 010100 => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [2,5,3,4,7,1,6] => 010010 => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [2,5,7,3,6,1,4] => 001010 => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [7,2,6,3,5,1,4] => 101010 => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [3,5,4,1,2,6,7] => 011000 => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [3,4,2,7,1,5,6] => 010100 => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [3,4,2,6,1,5,7] => 010100 => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [3,4,2,5,7,1,6] => 010010 => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [7,3,2,4,6,1,5] => 110010 => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [3,4,6,5,1,2,7] => 001100 => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [3,4,5,2,7,1,6] => 001010 => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [3,4,5,7,6,1,2] => 000110 => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [7,3,4,6,5,1,2] => 100110 => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [6,3,5,4,1,2,7] => 101100 => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [5,3,4,2,7,1,6] => 101010 => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [5,3,4,7,6,1,2] => 100110 => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [4,7,3,6,5,1,2] => 010110 => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [7,6,3,5,4,1,2] => 110110 => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [5,4,3,1,2,6,7] => 111000 => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [4,3,2,7,1,5,6] => 110100 => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [4,3,2,6,1,5,7] => 110100 => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [4,3,2,5,7,1,6] => 110010 => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [3,2,7,4,6,1,5] => 101010 => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [4,3,6,5,1,2,7] => 101100 => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [4,3,5,2,7,1,6] => 101010 => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [4,3,5,7,6,1,2] => 100110 => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [3,7,4,6,5,1,2] => 010110 => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [3,6,5,4,1,2,7] => 011100 => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [3,5,4,2,7,1,6] => 011010 => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [3,5,4,7,6,1,2] => 010110 => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [3,4,7,6,5,1,2] => 001110 => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [7,3,6,5,4,1,2] => 101110 => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [6,5,4,3,1,2,7] => 111100 => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [5,4,3,2,7,1,6] => 111010 => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [5,4,3,7,6,1,2] => 110110 => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [4,3,7,6,5,1,2] => 101110 => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [4,7,6,5,3,1,2] => 011110 => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [7,6,5,4,3,1,2] => 111110 => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 100000 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [1,7,2,3,4,5,6] => 010000 => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [1,6,2,3,4,5,7] => 010000 => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [1,5,7,2,3,4,6] => 001000 => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [7,1,6,2,3,4,5] => 101000 => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [1,5,2,3,4,6,7] => 010000 => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [1,4,7,2,3,5,6] => 001000 => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [1,4,6,2,3,5,7] => 001000 => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [1,4,5,7,2,3,6] => 000100 => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [7,1,4,6,2,3,5] => 100100 => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [6,1,5,2,3,4,7] => 101000 => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [5,1,4,7,2,3,6] => 100100 => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [5,7,1,6,2,3,4] => 010100 => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [7,6,1,5,2,3,4] => 110100 => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,4,2,3,5,6,7] => 010000 => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [1,3,7,2,4,5,6] => 001000 => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [1,3,6,2,4,5,7] => 001000 => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [1,3,5,7,2,4,6] => 000100 => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [7,1,3,6,2,4,5] => 100100 => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [1,3,5,2,4,6,7] => 001000 => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [1,3,4,7,2,5,6] => 000100 => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [1,3,4,6,2,5,7] => 000100 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [1,3,4,5,7,2,6] => 000010 => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [7,1,3,4,6,2,5] => 100010 => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [6,1,3,5,2,4,7] => 100100 => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [5,1,3,4,7,2,6] => 100010 => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [5,7,1,3,6,2,4] => 010010 => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [7,6,1,3,5,2,4] => 110010 => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [5,1,4,2,3,6,7] => 101000 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [4,1,3,7,2,5,6] => 100100 => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [4,1,3,6,2,5,7] => 100100 => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [4,1,3,5,7,2,6] => 100010 => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [3,7,1,4,6,2,5] => 010010 => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [4,6,1,5,2,3,7] => 010100 => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [4,5,1,3,7,2,6] => 010010 => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [4,5,7,1,6,2,3] => 001010 => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [7,4,6,1,5,2,3] => 101010 => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [6,5,1,4,2,3,7] => 110100 => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [5,4,1,3,7,2,6] => 110010 => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [5,4,7,1,6,2,3] => 101010 => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [4,7,6,1,5,2,3] => 011010 => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [7,6,5,1,4,2,3] => 111010 => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [1,3,2,4,5,6,7] => 010000 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [1,2,7,3,4,5,6] => 001000 => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [1,2,6,3,4,5,7] => 001000 => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [1,2,5,7,3,4,6] => 000100 => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [7,1,2,6,3,4,5] => 100100 => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [1,2,5,3,4,6,7] => 001000 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [1,2,4,7,3,5,6] => 000100 => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [1,2,4,6,3,5,7] => 000100 => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [1,2,4,5,7,3,6] => 000010 => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [7,1,2,4,6,3,5] => 100010 => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [6,1,2,5,3,4,7] => 100100 => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [5,1,2,4,7,3,6] => 100010 => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [5,7,1,2,6,3,4] => 010010 => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [7,6,1,2,5,3,4] => 110010 => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [1,2,4,3,5,6,7] => 001000 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [1,2,3,7,4,5,6] => 000100 => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [1,2,3,6,4,5,7] => 000100 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [1,2,3,5,7,4,6] => 000010 => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [7,1,2,3,6,4,5] => 100010 => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [1,2,3,5,4,6,7] => 000100 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [1,2,3,4,7,5,6] => 000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [1,2,3,4,6,5,7] => 000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [1,2,3,4,5,7,6] => 000001 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [7,1,2,3,4,6,5] => 100001 => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [6,1,2,3,5,4,7] => 100010 => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [5,1,2,3,4,7,6] => 100001 => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [5,7,1,2,3,6,4] => 010001 => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [7,6,1,2,3,5,4] => 110001 => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [5,1,2,4,3,6,7] => 100100 => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [4,1,2,3,7,5,6] => 100010 => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [4,1,2,3,6,5,7] => 100010 => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [4,1,2,3,5,7,6] => 100001 => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [3,7,1,2,4,6,5] => 010001 => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [4,6,1,2,5,3,7] => 010010 => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [4,5,1,2,3,7,6] => 010001 => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [4,5,7,1,2,6,3] => 001001 => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [7,4,6,1,2,5,3] => 101001 => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [6,5,1,2,4,3,7] => 110010 => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [5,4,1,2,3,7,6] => 110001 => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [5,4,7,1,2,6,3] => 101001 => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [4,7,6,1,2,5,3] => 011001 => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [7,6,5,1,2,4,3] => 111001 => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [4,1,3,2,5,6,7] => 101000 => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [3,1,2,7,4,5,6] => 100100 => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [3,1,2,6,4,5,7] => 100100 => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [3,1,2,5,7,4,6] => 100010 => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [2,7,1,3,6,4,5] => 010010 => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [3,1,2,5,4,6,7] => 100100 => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [3,1,2,4,7,5,6] => 100010 => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [3,1,2,4,6,5,7] => 100010 => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [3,1,2,4,5,7,6] => 100001 => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [2,7,1,3,4,6,5] => 010001 => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [2,6,1,3,5,4,7] => 010010 => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [2,5,1,3,4,7,6] => 010001 => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [2,5,7,1,3,6,4] => 001001 => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [7,2,6,1,3,5,4] => 101001 => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [3,5,1,4,2,6,7] => 010100 => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [3,4,1,2,7,5,6] => 010010 => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [3,4,1,2,6,5,7] => 010010 => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [3,4,1,2,5,7,6] => 010001 => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [7,3,1,2,4,6,5] => 110001 => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [3,4,6,1,5,2,7] => 001010 => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [3,4,5,1,2,7,6] => 001001 => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [3,4,5,7,1,6,2] => 000101 => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [7,3,4,6,1,5,2] => 100101 => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [6,3,5,1,4,2,7] => 101010 => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [5,3,4,1,2,7,6] => 101001 => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [5,3,4,7,1,6,2] => 100101 => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [4,7,3,6,1,5,2] => 010101 => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [7,6,3,5,1,4,2] => 110101 => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [5,4,1,3,2,6,7] => 110100 => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [4,3,1,2,7,5,6] => 110010 => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [4,3,1,2,6,5,7] => 110010 => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [4,3,1,2,5,7,6] => 110001 => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [3,2,7,1,4,6,5] => 101001 => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [4,3,6,1,5,2,7] => 101010 => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [4,3,5,1,2,7,6] => 101001 => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [4,3,5,7,1,6,2] => 100101 => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [3,7,4,6,1,5,2] => 010101 => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [3,6,5,1,4,2,7] => 011010 => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [3,5,4,1,2,7,6] => 011001 => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [3,5,4,7,1,6,2] => 010101 => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [3,4,7,6,1,5,2] => 001101 => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [7,3,6,5,1,4,2] => 101101 => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [6,5,4,1,3,2,7] => 111010 => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [5,4,3,1,2,7,6] => 111001 => 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [5,4,3,7,1,6,2] => 110101 => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [4,3,7,6,1,5,2] => 101101 => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [4,7,6,5,1,3,2] => 011101 => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [7,6,5,4,1,3,2] => 111101 => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 110000 => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [2,1,7,3,4,5,6] => 101000 => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [2,1,6,3,4,5,7] => 101000 => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [2,1,5,7,3,4,6] => 100100 => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [1,7,2,6,3,4,5] => 010100 => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [2,1,5,3,4,6,7] => 101000 => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [2,1,4,7,3,5,6] => 100100 => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [2,1,4,6,3,5,7] => 100100 => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [2,1,4,5,7,3,6] => 100010 => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [1,7,2,4,6,3,5] => 010010 => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [1,6,2,5,3,4,7] => 010100 => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [1,5,2,4,7,3,6] => 010010 => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [1,5,7,2,6,3,4] => 001010 => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [7,1,6,2,5,3,4] => 101010 => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [2,1,4,3,5,6,7] => 101000 => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [2,1,3,7,4,5,6] => 100100 => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [2,1,3,6,4,5,7] => 100100 => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [2,1,3,5,7,4,6] => 100010 => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [1,7,2,3,6,4,5] => 010010 => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [2,1,3,5,4,6,7] => 100100 => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [2,1,3,4,7,5,6] => 100010 => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [2,1,3,4,6,5,7] => 100010 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [2,1,3,4,5,7,6] => 100001 => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [1,7,2,3,4,6,5] => 010001 => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [1,6,2,3,5,4,7] => 010010 => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [1,5,2,3,4,7,6] => 010001 => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [1,5,7,2,3,6,4] => 001001 => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [7,1,6,2,3,5,4] => 101001 => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [1,5,2,4,3,6,7] => 010100 => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [1,4,2,3,7,5,6] => 010010 => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [1,4,2,3,6,5,7] => 010010 => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [1,4,2,3,5,7,6] => 010001 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [1,3,7,2,4,6,5] => 001001 => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [1,4,6,2,5,3,7] => 001010 => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [1,4,5,2,3,7,6] => 001001 => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [1,4,5,7,2,6,3] => 000101 => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [7,1,4,6,2,5,3] => 100101 => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [6,1,5,2,4,3,7] => 101010 => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [5,1,4,2,3,7,6] => 101001 => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [5,1,4,7,2,6,3] => 100101 => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [4,7,1,6,2,5,3] => 010101 => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [7,6,1,5,2,4,3] => 110101 => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [2,4,3,1,5,6,7] => 011000 => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [2,3,1,7,4,5,6] => 010100 => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [2,3,1,6,4,5,7] => 010100 => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [2,3,1,5,7,4,6] => 010010 => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [7,2,1,3,6,4,5] => 110010 => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [2,3,1,5,4,6,7] => 010100 => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [2,3,1,4,7,5,6] => 010010 => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [2,3,1,4,6,5,7] => 010010 => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [2,3,1,4,5,7,6] => 010001 => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [7,2,1,3,4,6,5] => 110001 => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [6,2,1,3,5,4,7] => 110010 => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [5,2,1,3,4,7,6] => 110001 => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [5,1,7,2,3,6,4] => 101001 => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [1,7,6,2,3,5,4] => 011001 => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [2,3,5,4,1,6,7] => 001100 => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [2,3,4,1,7,5,6] => 001010 => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [2,3,4,1,6,5,7] => 001010 => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [2,3,4,1,5,7,6] => 001001 => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [7,2,3,1,4,6,5] => 101001 => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [2,3,4,6,5,1,7] => 000110 => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [2,3,4,5,1,7,6] => 000101 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [2,3,4,5,7,6,1] => 000011 => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [7,2,3,4,6,5,1] => 100011 => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [6,2,3,5,4,1,7] => 100110 => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [5,2,3,4,1,7,6] => 100101 => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [5,2,3,4,7,6,1] => 100011 => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [4,7,2,3,6,5,1] => 010011 => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [7,6,2,3,5,4,1] => 110011 => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [5,2,4,3,1,6,7] => 101100 => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [4,2,3,1,7,5,6] => 101010 => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [4,2,3,1,6,5,7] => 101010 => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [4,2,3,1,5,7,6] => 101001 => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [3,7,2,1,4,6,5] => 011001 => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [4,2,3,6,5,1,7] => 100110 => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [4,2,3,5,1,7,6] => 100101 => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [4,2,3,5,7,6,1] => 100011 => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [3,7,2,4,6,5,1] => 010011 => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [3,6,2,5,4,1,7] => 010110 => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [3,5,2,4,1,7,6] => 010101 => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [3,5,2,4,7,6,1] => 010011 => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [3,4,7,2,6,5,1] => 001011 => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [7,3,6,2,5,4,1] => 101011 => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [6,5,2,4,3,1,7] => 110110 => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [5,4,2,3,1,7,6] => 110101 => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [5,4,2,3,7,6,1] => 110011 => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [4,3,7,2,6,5,1] => 101011 => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [4,7,6,2,5,3,1] => 011011 => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [7,6,5,2,4,3,1] => 111011 => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 111000 => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [3,2,1,7,4,5,6] => 110100 => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [3,2,1,6,4,5,7] => 110100 => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [3,2,1,5,7,4,6] => 110010 => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [2,1,7,3,6,4,5] => 101010 => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [3,2,1,5,4,6,7] => 110100 => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [3,2,1,4,7,5,6] => 110010 => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [3,2,1,4,6,5,7] => 110010 => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [3,2,1,4,5,7,6] => 110001 => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [2,1,7,3,4,6,5] => 101001 => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [2,1,6,3,5,4,7] => 101010 => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [2,1,5,3,4,7,6] => 101001 => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [2,1,5,7,3,6,4] => 100101 => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [1,7,2,6,3,5,4] => 010101 => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [3,2,5,4,1,6,7] => 101100 => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [3,2,4,1,7,5,6] => 101010 => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [3,2,4,1,6,5,7] => 101010 => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [3,2,4,1,5,7,6] => 101001 => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [2,7,3,1,4,6,5] => 011001 => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [3,2,4,6,5,1,7] => 100110 => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [3,2,4,5,1,7,6] => 100101 => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [3,2,4,5,7,6,1] => 100011 => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [2,7,3,4,6,5,1] => 010011 => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [2,6,3,5,4,1,7] => 010110 => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [2,5,3,4,1,7,6] => 010101 => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [2,5,3,4,7,6,1] => 010011 => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [2,4,7,3,6,5,1] => 001011 => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [7,2,6,3,5,4,1] => 101011 => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [2,5,4,3,1,6,7] => 011100 => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [2,4,3,1,7,5,6] => 011010 => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [2,4,3,1,6,5,7] => 011010 => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [2,4,3,1,5,7,6] => 011001 => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [2,3,1,7,4,6,5] => 010101 => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [2,4,3,6,5,1,7] => 010110 => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [2,4,3,5,1,7,6] => 010101 => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [2,4,3,5,7,6,1] => 010011 => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [2,3,7,4,6,5,1] => 001011 => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [2,3,6,5,4,1,7] => 001110 => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [2,3,5,4,1,7,6] => 001101 => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [2,3,5,4,7,6,1] => 001011 => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [2,3,4,7,6,5,1] => 000111 => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [7,2,3,6,5,4,1] => 100111 => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [6,2,5,4,3,1,7] => 101110 => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [5,2,4,3,1,7,6] => 101101 => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [5,2,4,3,7,6,1] => 101011 => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [4,2,3,7,6,5,1] => 100111 => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [4,7,2,6,5,3,1] => 010111 => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [7,6,2,5,4,3,1] => 110111 => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 111100 => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [4,3,2,1,7,5,6] => 111010 => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [4,3,2,1,6,5,7] => 111010 => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [4,3,2,1,5,7,6] => 111001 => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [3,2,1,7,4,6,5] => 110101 => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [4,3,2,6,5,1,7] => 110110 => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [4,3,2,5,1,7,6] => 110101 => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [4,3,2,5,7,6,1] => 110011 => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [3,2,7,4,6,5,1] => 101011 => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [3,2,6,5,4,1,7] => 101110 => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [3,2,5,4,1,7,6] => 101101 => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [3,2,5,4,7,6,1] => 101011 => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [3,2,4,7,6,5,1] => 100111 => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [2,7,3,6,5,4,1] => 010111 => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [3,6,5,4,2,1,7] => 011110 => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [3,5,4,2,1,7,6] => 011101 => 4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [3,5,4,2,7,6,1] => 011011 => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [3,4,2,7,6,5,1] => 010111 => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [3,4,7,6,5,2,1] => 001111 => 4
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [7,3,6,5,4,2,1] => 101111 => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 111110 => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [5,4,3,2,1,7,6] => 111101 => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [5,4,3,2,7,6,1] => 111011 => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [4,3,2,7,6,5,1] => 110111 => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [4,3,7,6,5,2,1] => 101111 => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [3,7,6,5,4,2,1] => 011111 => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 111111 => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 1000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [6,8,1,2,3,4,5,7] => 0100000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [8,7,1,2,3,4,5,6] => 1100000 => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => 1000000 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [5,8,1,2,3,4,6,7] => 0100000 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [5,7,1,2,3,4,6,8] => 0100000 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [5,6,8,1,2,3,4,7] => 0010000 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [8,5,7,1,2,3,4,6] => 1010000 => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [7,6,1,2,3,4,5,8] => 1100000 => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [6,5,8,1,2,3,4,7] => 1010000 => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => [6,8,7,1,2,3,4,5] => 0110000 => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [8,7,6,1,2,3,4,5] => 1110000 => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1000000 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [4,8,1,2,3,5,6,7] => 0100000 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [4,7,1,2,3,5,6,8] => 0100000 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [4,6,8,1,2,3,5,7] => 0010000 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [8,4,7,1,2,3,5,6] => 1010000 => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [4,6,1,2,3,5,7,8] => 0100000 => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [4,5,8,1,2,3,6,7] => 0010000 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [4,5,6,8,1,2,3,7] => 0001000 => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [7,4,6,1,2,3,5,8] => 1010000 => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [6,4,5,8,1,2,3,7] => 1001000 => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [8,7,4,6,1,2,3,5] => 1101000 => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [5,4,8,1,2,3,6,7] => 1010000 => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [5,4,7,1,2,3,6,8] => 1010000 => 2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [4,8,5,7,1,2,3,6] => 0101000 => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => [5,7,6,1,2,3,4,8] => 0110000 => 2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => [5,6,8,7,1,2,3,4] => 0011000 => 2
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => [8,5,7,6,1,2,3,4] => 1011000 => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [7,6,5,1,2,3,4,8] => 1110000 => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [6,5,4,8,1,2,3,7] => 1101000 => 3
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => [6,5,8,7,1,2,3,4] => 1011000 => 3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => [5,8,7,6,1,2,3,4] => 0111000 => 3
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [8,7,6,5,1,2,3,4] => 1111000 => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => 1000000 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [3,8,1,2,4,5,6,7] => 0100000 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [3,7,1,2,4,5,6,8] => 0100000 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [3,6,8,1,2,4,5,7] => 0010000 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [8,3,7,1,2,4,5,6] => 1010000 => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [3,6,1,2,4,5,7,8] => 0100000 => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [3,5,7,1,2,4,6,8] => 0010000 => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [3,5,6,8,1,2,4,7] => 0001000 => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [8,3,5,7,1,2,4,6] => 1001000 => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [6,3,5,8,1,2,4,7] => 1001000 => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => [6,8,3,7,1,2,4,5] => 0101000 => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [8,7,3,6,1,2,4,5] => 1101000 => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [3,5,1,2,4,6,7,8] => 0100000 => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [3,4,6,8,1,2,5,7] => 0001000 => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [3,4,5,8,1,2,6,7] => 0001000 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [3,4,5,7,1,2,6,8] => 0001000 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [3,4,5,6,8,1,2,7] => 0000100 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [8,3,4,5,7,1,2,6] => 1000100 => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [8,7,3,4,6,1,2,5] => 1100100 => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [6,3,5,1,2,4,7,8] => 1010000 => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,5,7,3,8] => [5,3,4,7,1,2,6,8] => 1001000 => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [4,8,3,5,7,1,2,6] => 0100100 => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [8,7,6,3,5,1,2,4] => 1110100 => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [5,4,1,2,3,6,7,8] => 1100000 => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [4,3,6,8,1,2,5,7] => 1001000 => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [3,8,4,7,1,2,5,6] => 0101000 => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [4,3,5,7,1,2,6,8] => 1001000 => 2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [3,8,4,5,7,1,2,6] => 0100100 => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [8,3,7,4,6,1,2,5] => 1010100 => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => [4,6,5,1,2,3,7,8] => 0110000 => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => [4,5,3,6,8,1,2,7] => 0100100 => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => [4,5,6,3,8,1,2,7] => 0010100 => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => [4,5,6,8,7,1,2,3] => 0001100 => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [6,5,4,1,2,3,7,8] => 1110000 => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [5,4,3,6,8,1,2,7] => 1100100 => 3
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,8,5,4,7,6,3] => [4,8,5,7,6,1,2,3] => 0101100 => 3
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,8,5,6,4,7,3] => [4,6,5,8,7,1,2,3] => 0101100 => 3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => [4,5,8,7,6,1,2,3] => 0011100 => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [7,6,5,4,1,2,3,8] => 1111000 => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [6,5,4,3,8,1,2,7] => 1110100 => 4
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => [6,5,4,8,7,1,2,3] => 1101100 => 4
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => [5,4,8,7,6,1,2,3] => 1011100 => 4
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => [5,8,7,6,4,1,2,3] => 0111100 => 4
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [8,7,6,5,4,1,2,3] => 1111100 => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => 1000000 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [2,8,1,3,4,5,6,7] => 0100000 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [2,7,1,3,4,5,6,8] => 0100000 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [2,6,8,1,3,4,5,7] => 0010000 => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [2,6,1,3,4,5,7,8] => 0100000 => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [2,5,8,1,3,4,6,7] => 0010000 => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [2,5,6,8,1,3,4,7] => 0001000 => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [8,2,5,7,1,3,4,6] => 1001000 => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [6,2,5,8,1,3,4,7] => 1001000 => 2
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => [6,8,2,7,1,3,4,5] => 0101000 => 2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [8,7,2,6,1,3,4,5] => 1101000 => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [2,5,1,3,4,6,7,8] => 0100000 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [2,4,6,8,1,3,5,7] => 0001000 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [8,2,4,7,1,3,5,6] => 1001000 => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [2,4,6,1,3,5,7,8] => 0010000 => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [2,4,5,8,1,3,6,7] => 0001000 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [2,4,5,6,8,1,3,7] => 0000100 => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [7,2,4,6,1,3,5,8] => 1001000 => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [6,2,4,5,8,1,3,7] => 1000100 => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [5,2,4,8,1,3,6,7] => 1001000 => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [5,2,4,7,1,3,6,8] => 1001000 => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [5,2,4,6,8,1,3,7] => 1000100 => 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [4,8,2,5,7,1,3,6] => 0100100 => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => [5,6,2,4,8,1,3,7] => 0100100 => 2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [8,5,7,2,6,1,3,4] => 1010100 => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [6,5,2,4,8,1,3,7] => 1100100 => 3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => [5,8,7,2,6,1,3,4] => 0110100 => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [8,7,6,2,5,1,3,4] => 1110100 => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [2,4,1,3,5,6,7,8] => 0100000 => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [2,3,8,1,4,5,6,7] => 0010000 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [2,3,7,1,4,5,6,8] => 0010000 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [2,3,6,8,1,4,5,7] => 0001000 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => [8,2,3,7,1,4,5,6] => 1001000 => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [2,3,5,8,1,4,6,7] => 0001000 => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [2,3,5,7,1,4,6,8] => 0001000 => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [2,3,5,6,8,1,4,7] => 0000100 => 1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [8,2,3,5,7,1,4,6] => 1000100 => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [6,2,3,5,8,1,4,7] => 1000100 => 2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => [6,8,2,3,7,1,4,5] => 0100100 => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [8,7,2,3,6,1,4,5] => 1100100 => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [2,3,5,1,4,6,7,8] => 0010000 => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,5,2,6,8,7] => [2,3,4,8,1,5,6,7] => 0001000 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [2,3,4,7,1,5,6,8] => 0001000 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [2,3,4,6,8,1,5,7] => 0000100 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [8,2,3,4,7,1,5,6] => 1000100 => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [2,3,4,6,1,5,7,8] => 0001000 => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [2,3,4,5,8,1,6,7] => 0000100 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [2,3,4,5,7,1,6,8] => 0000100 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [2,3,4,5,6,8,1,7] => 0000010 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [8,2,3,4,5,7,1,6] => 1000010 => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [6,2,3,4,5,8,1,7] => 1000010 => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [6,8,2,3,4,7,1,5] => 0100010 => 2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [8,7,2,3,4,6,1,5] => 1100010 => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => [5,2,3,4,7,1,6,8] => 1000100 => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [5,2,3,4,6,8,1,7] => 1000010 => 2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => [5,6,8,2,3,7,1,4] => 0010010 => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [6,5,2,3,4,8,1,7] => 1100010 => 3
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,8,6,5,7,2] => [6,5,8,2,3,7,1,4] => 1010010 => 3
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,8,6,7,5,2] => [5,8,7,2,3,6,1,4] => 0110010 => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => [5,2,4,1,3,6,7,8] => 1010000 => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [4,2,3,8,1,5,6,7] => 1001000 => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [4,2,3,6,8,1,5,7] => 1000100 => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => [4,2,3,5,6,8,1,7] => 1000010 => 2
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [8,3,7,2,4,6,1,5] => 1010010 => 3
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => [8,4,2,3,5,7,1,6] => 1100010 => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => [4,5,6,2,3,8,1,7] => 0010010 => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,8,4,6,7,5,2] => [5,8,4,7,2,6,1,3] => 0101010 => 3
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [4,3,8,2,5,7,1,6] => 1010010 => 3
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => [5,4,6,8,2,7,1,3] => 1001010 => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => [4,8,5,7,2,6,1,3] => 0101010 => 3
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => [4,5,8,7,2,6,1,3] => 0011010 => 3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => [8,4,7,6,2,5,1,3] => 1011010 => 4
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [5,4,8,7,2,6,1,3] => 1011010 => 4
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => [5,8,7,6,2,4,1,3] => 0111010 => 4
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [8,7,6,5,2,4,1,3] => 1111010 => 5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [4,3,1,2,5,6,7,8] => 1100000 => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [3,2,8,1,4,5,6,7] => 1010000 => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [3,2,6,8,1,4,5,7] => 1001000 => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [2,8,3,7,1,4,5,6] => 0101000 => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [3,2,5,7,1,4,6,8] => 1001000 => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [3,2,5,6,8,1,4,7] => 1000100 => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [2,7,3,6,1,4,5,8] => 0101000 => 2
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,8,6,7,5] => [2,6,8,3,7,1,4,5] => 0010100 => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [8,2,7,3,6,1,4,5] => 1010100 => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,3,5,2,6,7,8] => [3,2,5,1,4,6,7,8] => 1010000 => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3,5,2,7,8,6] => [3,2,4,6,8,1,5,7] => 1000100 => 2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3,5,2,8,7,6] => [2,8,3,4,7,1,5,6] => 0100100 => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [3,2,4,6,1,5,7,8] => 1001000 => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [3,2,4,5,6,8,1,7] => 1000010 => 2
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [2,6,8,3,4,7,1,5] => 0010010 => 2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [8,2,7,3,4,6,1,5] => 1010010 => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [2,5,3,4,6,8,1,7] => 0100010 => 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [2,4,8,3,5,7,1,6] => 0010010 => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => [6,2,5,8,3,7,1,4] => 1001010 => 3
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => [5,8,2,7,3,6,1,4] => 0101010 => 3
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [8,7,2,6,3,5,1,4] => 1101010 => 4
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => [8,3,2,4,7,1,5,6] => 1100100 => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [3,4,2,5,6,8,1,7] => 0100010 => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,5,3,4,7,6,2,8] => [7,3,2,4,6,1,5,8] => 1100100 => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => [3,4,6,5,1,2,7,8] => 0011000 => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => [3,4,5,6,2,8,1,7] => 0001010 => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [3,4,5,6,8,7,1,2] => 0000110 => 2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => [8,7,3,4,6,5,1,2] => 1100110 => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => [5,3,4,7,6,1,2,8] => 1001100 => 3
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,8,3,5,4,7,6,2] => [4,8,3,5,7,6,1,2] => 0100110 => 3
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => [4,6,3,5,8,7,1,2] => 0100110 => 3
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8,3,5,6,7,4,2] => [4,5,8,3,7,6,1,2] => 0010110 => 3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => [8,4,7,3,6,5,1,2] => 1010110 => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => [6,5,3,4,2,8,1,7] => 1101010 => 4
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => [6,5,3,4,8,7,1,2] => 1100110 => 4
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => [8,7,6,3,5,4,1,2] => 1110110 => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [5,4,3,1,2,6,7,8] => 1110000 => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [4,3,2,7,1,5,6,8] => 1101000 => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [4,3,2,6,1,5,7,8] => 1101000 => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [4,3,2,5,7,1,6,8] => 1100100 => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [4,3,2,5,6,8,1,7] => 1100010 => 3
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [3,2,8,4,5,7,1,6] => 1010010 => 3
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [2,8,3,7,4,6,1,5] => 0101010 => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => [4,3,6,5,1,2,7,8] => 1011000 => 3
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => [3,8,4,2,5,7,1,6] => 0110010 => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [4,3,5,6,8,7,1,2] => 1000110 => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => [3,6,4,5,2,8,1,7] => 0101010 => 3
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => [3,6,4,5,8,7,1,2] => 0100110 => 3
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,8,4,3,6,7,5,2] => [3,5,8,4,7,6,1,2] => 0010110 => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => [3,6,5,4,1,2,7,8] => 0111000 => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => [3,5,4,2,8,1,6,7] => 0110100 => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7,4,5,3,6,8,2] => [3,5,4,6,2,8,1,7] => 0101010 => 3
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [3,5,4,6,8,7,1,2] => 0100110 => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,7,4,5,6,3,2,8] => [3,4,7,6,5,1,2,8] => 0011100 => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => [3,4,6,5,2,8,1,7] => 0011010 => 3
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,8,4,5,6,3,7,2] => [3,4,6,5,8,7,1,2] => 0010110 => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [3,4,5,8,7,6,1,2] => 0001110 => 3
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => [6,3,5,4,8,7,1,2] => 1010110 => 4
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => [5,3,4,8,7,6,1,2] => 1001110 => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [6,5,4,3,1,2,7,8] => 1111000 => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [5,4,3,2,8,1,6,7] => 1110100 => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [5,4,3,2,6,8,1,7] => 1110010 => 4
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [4,3,2,8,5,7,1,6] => 1101010 => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,7,5,4,3,6,2,8] => [5,4,3,7,6,1,2,8] => 1101100 => 4
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => [5,4,3,6,8,7,1,2] => 1100110 => 4
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8,5,4,3,7,6,2] => [4,3,8,5,7,6,1,2] => 1010110 => 4
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => [4,3,6,5,8,7,1,2] => 1010110 => 4
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [4,3,5,8,7,6,1,2] => 1001110 => 4
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => [3,8,4,7,6,5,1,2] => 0101110 => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => [4,7,6,5,3,1,2,8] => 0111100 => 4
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => [4,6,5,3,8,7,1,2] => 0110110 => 4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => [4,5,3,8,7,6,1,2] => 0101110 => 4
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => [4,5,8,7,6,3,1,2] => 0011110 => 4
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => [8,4,7,6,5,3,1,2] => 1011110 => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [7,6,5,4,3,1,2,8] => 1111100 => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [6,5,4,3,2,8,1,7] => 1111010 => 5
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [6,5,4,3,8,7,1,2] => 1110110 => 5
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [5,4,3,8,7,6,1,2] => 1101110 => 5
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => [5,4,8,7,6,3,1,2] => 1011110 => 5
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [4,8,7,6,5,3,1,2] => 0111110 => 5
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [8,7,6,5,4,3,1,2] => 1111110 => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => 1000000 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [1,8,2,3,4,5,6,7] => 0100000 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [1,7,2,3,4,5,6,8] => 0100000 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [1,6,8,2,3,4,5,7] => 0010000 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [8,1,7,2,3,4,5,6] => 1010000 => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [1,6,2,3,4,5,7,8] => 0100000 => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [1,5,8,2,3,4,6,7] => 0010000 => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,4,6,7,5,8] => [1,5,7,2,3,4,6,8] => 0010000 => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [1,5,6,8,2,3,4,7] => 0001000 => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [6,1,5,8,2,3,4,7] => 1001000 => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [8,7,1,6,2,3,4,5] => 1101000 => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [1,5,2,3,4,6,7,8] => 0100000 => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [1,4,8,2,3,5,6,7] => 0010000 => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [1,4,6,8,2,3,5,7] => 0001000 => 1
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [8,1,4,7,2,3,5,6] => 1001000 => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [1,4,5,8,2,3,6,7] => 0001000 => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [1,4,5,6,8,2,3,7] => 0000100 => 1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => [6,8,1,4,7,2,3,5] => 0100100 => 2
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [4,8,1,5,7,2,3,6] => 0100100 => 2
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => [5,6,8,1,7,2,3,4] => 0010100 => 2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => [8,5,7,1,6,2,3,4] => 1010100 => 3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => [5,8,7,1,6,2,3,4] => 0110100 => 3
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [8,7,6,1,5,2,3,4] => 1110100 => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 0100000 => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [1,3,8,2,4,5,6,7] => 0010000 => 1
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [8,1,3,7,2,4,5,6] => 1001000 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [1,3,6,2,4,5,7,8] => 0010000 => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [1,3,5,8,2,4,6,7] => 0001000 => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [1,3,5,7,2,4,6,8] => 0001000 => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [1,3,5,6,8,2,4,7] => 0000100 => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [8,1,3,5,7,2,4,6] => 1000100 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [6,1,3,5,8,2,4,7] => 1000100 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [6,8,1,3,7,2,4,5] => 0100100 => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [8,7,1,3,6,2,4,5] => 1100100 => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [1,3,5,2,4,6,7,8] => 0010000 => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [1,3,4,8,2,5,6,7] => 0001000 => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [1,3,4,5,8,2,6,7] => 0000100 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [1,3,4,5,7,2,6,8] => 0000100 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [1,3,4,5,6,8,2,7] => 0000010 => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [6,8,1,3,4,7,2,5] => 0100010 => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [8,7,1,3,4,6,2,5] => 1100010 => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [5,1,3,4,8,2,6,7] => 1000100 => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [5,6,8,1,3,7,2,4] => 0010010 => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [6,5,1,3,4,8,2,7] => 1100010 => 3
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => [5,8,7,1,3,6,2,4] => 0110010 => 3
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [8,7,6,1,3,5,2,4] => 1110010 => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [5,1,4,2,3,6,7,8] => 1010000 => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [4,1,3,8,2,5,6,7] => 1001000 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [3,8,1,4,7,2,5,6] => 0100100 => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [4,1,3,5,8,2,6,7] => 1000100 => 2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [3,8,1,4,5,7,2,6] => 0100010 => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [3,6,1,4,5,8,2,7] => 0100010 => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [8,3,7,1,4,6,2,5] => 1010010 => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [4,5,1,3,8,2,6,7] => 0100100 => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => [4,5,1,3,6,8,2,7] => 0100010 => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [6,4,5,8,1,7,2,3] => 1001010 => 3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => [5,8,4,7,1,6,2,3] => 0101010 => 3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => [8,7,4,6,1,5,2,3] => 1101010 => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [5,4,1,3,8,2,6,7] => 1100100 => 3
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [4,3,8,1,5,7,2,6] => 1010010 => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,7,5,4,6,8,3] => [5,4,6,1,3,8,2,7] => 1010010 => 3
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => [5,4,6,8,1,7,2,3] => 1001010 => 3
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [4,8,5,7,1,6,2,3] => 0101010 => 3
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [4,6,5,8,1,7,2,3] => 0101010 => 3
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => [4,5,8,7,1,6,2,3] => 0011010 => 3
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [8,4,7,6,1,5,2,3] => 1011010 => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [7,6,5,1,4,2,3,8] => 1110100 => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [6,5,4,1,3,8,2,7] => 1110010 => 4
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [6,5,4,8,1,7,2,3] => 1101010 => 4
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [5,4,8,7,1,6,2,3] => 1011010 => 4
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [5,8,7,6,1,4,2,3] => 0111010 => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [8,7,6,5,1,4,2,3] => 1111010 => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 0100000 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [1,2,8,3,4,5,6,7] => 0010000 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [1,2,7,3,4,5,6,8] => 0010000 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [1,2,6,8,3,4,5,7] => 0001000 => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [1,2,5,8,3,4,6,7] => 0001000 => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [1,2,5,7,3,4,6,8] => 0001000 => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [6,1,2,5,8,3,4,7] => 1000100 => 2
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [8,7,1,2,6,3,4,5] => 1100100 => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [1,2,5,3,4,6,7,8] => 0010000 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [1,2,4,7,3,5,6,8] => 0001000 => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [1,2,4,6,3,5,7,8] => 0001000 => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [1,2,4,5,7,3,6,8] => 0000100 => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [1,2,4,5,6,8,3,7] => 0000010 => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,8,6,7,4] => [6,8,1,2,4,7,3,5] => 0100010 => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [6,1,2,5,3,4,7,8] => 1001000 => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [5,1,2,4,8,3,6,7] => 1000100 => 2
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [4,8,1,2,5,7,3,6] => 0100010 => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,7,5,6,4,8] => [5,7,1,2,6,3,4,8] => 0100100 => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [6,5,1,2,4,8,3,7] => 1100010 => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [5,8,7,1,2,6,3,4] => 0110010 => 3
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [8,7,6,1,2,5,3,4] => 1110010 => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [1,2,4,3,5,6,7,8] => 0010000 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [1,2,3,8,4,5,6,7] => 0001000 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [1,2,3,7,4,5,6,8] => 0001000 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [1,2,3,6,8,4,5,7] => 0000100 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [8,1,2,3,7,4,5,6] => 1000100 => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [1,2,3,6,4,5,7,8] => 0001000 => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [1,2,3,5,8,4,6,7] => 0000100 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [1,2,3,5,7,4,6,8] => 0000100 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [1,2,3,5,6,8,4,7] => 0000010 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [8,1,2,3,5,7,4,6] => 1000010 => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [7,1,2,3,6,4,5,8] => 1000100 => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [6,1,2,3,5,8,4,7] => 1000010 => 2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [6,8,1,2,3,7,4,5] => 0100010 => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [8,7,1,2,3,6,4,5] => 1100010 => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [1,2,3,5,4,6,7,8] => 0001000 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [1,2,3,4,8,5,6,7] => 0000100 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [1,2,3,4,7,5,6,8] => 0000100 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [1,2,3,4,6,8,5,7] => 0000010 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [8,1,2,3,4,7,5,6] => 1000010 => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [1,2,3,4,6,5,7,8] => 0000100 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [1,2,3,4,5,8,6,7] => 0000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [1,2,3,4,5,7,6,8] => 0000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,8,7] => 0000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [8,1,2,3,4,5,7,6] => 1000001 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [7,1,2,3,4,6,5,8] => 1000010 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [6,1,2,3,4,5,8,7] => 1000001 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => [6,8,1,2,3,4,7,5] => 0100001 => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [8,7,1,2,3,4,6,5] => 1100001 => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [6,1,2,3,5,4,7,8] => 1000100 => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [5,1,2,3,4,6,8,7] => 1000001 => 2
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [4,8,1,2,3,5,7,6] => 0100001 => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,7,5,6,8,1] => [5,6,1,2,3,4,8,7] => 0100001 => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => [5,6,8,1,2,3,7,4] => 0010001 => 2
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => [8,5,7,1,2,3,6,4] => 1010001 => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [7,6,1,2,3,5,4,8] => 1100010 => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [6,5,1,2,3,4,8,7] => 1100001 => 3
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [8,7,6,1,2,3,5,4] => 1110001 => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [5,1,2,4,3,6,7,8] => 1001000 => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [4,1,2,3,7,5,6,8] => 1000100 => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [4,1,2,3,6,5,7,8] => 1000100 => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [4,1,2,3,5,7,6,8] => 1000010 => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [4,1,2,3,5,6,8,7] => 1000001 => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [3,6,1,2,4,5,8,7] => 0100001 => 2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => [3,6,8,1,2,4,7,5] => 0010001 => 2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [8,3,7,1,2,4,6,5] => 1010001 => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => [4,6,1,2,5,3,7,8] => 0100100 => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [4,5,1,2,3,8,6,7] => 0100010 => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => [4,5,6,1,2,3,8,7] => 0010001 => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [4,5,6,8,1,2,7,3] => 0001001 => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => [6,4,5,1,2,3,8,7] => 1010001 => 3
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => [5,8,4,7,1,2,6,3] => 0101001 => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [5,4,1,2,3,8,6,7] => 1100010 => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,7,5,4,6,8,1] => [5,4,6,1,2,3,8,7] => 1010001 => 3
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => [5,4,6,8,1,2,7,3] => 1001001 => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => [4,6,5,1,2,3,8,7] => 0110001 => 3
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,8,5,6,4,7,1] => [4,6,5,8,1,2,7,3] => 0101001 => 3
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => [4,5,8,7,1,2,6,3] => 0011001 => 3
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,8,5,7,6,4,1] => [8,4,7,6,1,2,5,3] => 1011001 => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [7,6,5,1,2,4,3,8] => 1110010 => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [6,5,4,1,2,3,8,7] => 1110001 => 4
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => [6,5,4,8,1,2,7,3] => 1101001 => 4
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [8,7,6,5,1,2,4,3] => 1111001 => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [4,1,3,2,5,6,7,8] => 1010000 => 2
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [2,8,1,3,7,4,5,6] => 0100100 => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [3,1,2,5,8,4,6,7] => 1000100 => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [3,1,2,5,6,8,4,7] => 1000010 => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [2,8,1,3,5,7,4,6] => 0100010 => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [2,6,1,3,5,8,4,7] => 0100010 => 2
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,8,6,7,5] => [2,6,8,1,3,7,4,5] => 0010010 => 2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [8,2,7,1,3,6,4,5] => 1010010 => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [3,1,2,4,8,5,6,7] => 1000100 => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [3,1,2,4,7,5,6,8] => 1000100 => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [3,1,2,4,6,8,5,7] => 1000010 => 2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [2,8,1,3,4,7,5,6] => 0100010 => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,3,5,6,7,1,8] => [3,1,2,4,5,7,6,8] => 1000010 => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [3,1,2,4,5,6,8,7] => 1000001 => 2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [2,8,1,3,4,5,7,6] => 0100001 => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [2,6,1,3,4,5,8,7] => 0100001 => 2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,4,3,5,8,7,6,1] => [8,2,7,1,3,4,6,5] => 1010001 => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [2,6,1,3,5,4,7,8] => 0100100 => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [2,4,8,1,3,5,7,6] => 0010001 => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => [2,5,6,1,3,4,8,7] => 0010001 => 2
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => [2,5,6,8,1,3,7,4] => 0001001 => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,8,5,7,6,1] => [8,2,5,7,1,3,6,4] => 1001001 => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [6,2,5,1,3,4,8,7] => 1010001 => 3
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,3,8,6,7,5,1] => [5,8,2,7,1,3,6,4] => 0101001 => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => [3,5,1,4,2,6,7,8] => 0101000 => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => [8,3,1,2,4,7,5,6] => 1100010 => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => [3,4,1,2,5,7,6,8] => 0100010 => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => [3,4,1,2,5,6,8,7] => 0100001 => 2
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => [8,3,1,2,4,5,7,6] => 1100001 => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,3,4,7,6,8,1] => [6,3,1,2,4,5,8,7] => 1100001 => 3
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => [6,2,8,1,3,4,7,5] => 1010001 => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => [3,4,6,1,5,2,7,8] => 0010100 => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => [3,4,5,1,2,6,8,7] => 0010001 => 2
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => [8,3,4,1,2,5,7,6] => 1010001 => 3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => [3,4,5,6,8,1,7,2] => 0000101 => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,8,3,4,5,7,6,1] => [8,3,4,5,7,1,6,2] => 1000101 => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => [5,3,4,1,2,8,6,7] => 1010010 => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,6,3,5,4,7,8,1] => [5,3,4,1,2,6,8,7] => 1010001 => 3
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => [4,8,3,5,7,1,6,2] => 0100101 => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,7,3,5,6,4,8,1] => [4,6,3,5,1,2,8,7] => 0101001 => 3
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => [8,4,7,3,6,1,5,2] => 1010101 => 4
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,8,3,7,5,6,4,1] => [5,8,7,3,6,1,4,2] => 0110101 => 4
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => [8,7,6,3,5,1,4,2] => 1110101 => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [5,4,1,3,2,6,7,8] => 1101000 => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [4,3,1,2,8,5,6,7] => 1100100 => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [4,3,1,2,6,8,5,7] => 1100010 => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [4,3,1,2,5,7,6,8] => 1100010 => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [4,3,1,2,5,6,8,7] => 1100001 => 3
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [3,2,8,1,4,5,7,6] => 1010001 => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [3,2,6,1,4,5,8,7] => 1010001 => 3
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [2,8,3,7,1,4,6,5] => 0101001 => 3
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,6,4,3,5,8,7,1] => [3,8,4,1,2,5,7,6] => 0110001 => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => [4,3,5,6,1,2,8,7] => 1001001 => 3
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => [4,3,5,6,8,1,7,2] => 1000101 => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => [3,6,4,5,1,2,8,7] => 0101001 => 3
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => [3,5,8,4,7,1,6,2] => 0010101 => 3
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => [8,3,7,4,6,1,5,2] => 1010101 => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,4,5,3,1,7,8] => [3,6,5,1,4,2,7,8] => 0110100 => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,4,5,3,1,8,7] => [3,5,4,1,2,8,6,7] => 0110010 => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => [3,4,6,5,1,2,8,7] => 0011001 => 3
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => [3,4,6,5,8,1,7,2] => 0010101 => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,7,4,6,5,3,8,1] => [6,3,5,4,1,2,8,7] => 1011001 => 4
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => [6,3,5,4,8,1,7,2] => 1010101 => 4
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => [8,7,3,6,5,1,4,2] => 1101101 => 5
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [5,4,3,1,2,8,6,7] => 1110010 => 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => [5,4,3,6,1,2,8,7] => 1101001 => 4
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => [5,4,3,6,8,1,7,2] => 1100101 => 4
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,8,5,4,3,7,6,1] => [4,3,8,5,7,1,6,2] => 1010101 => 4
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => [3,8,4,7,6,1,5,2] => 0101101 => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,6,4,5,3,8,1] => [4,6,5,3,1,2,8,7] => 0111001 => 4
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,8,7,4,5,6,3,1] => [4,5,8,7,6,1,3,2] => 0011101 => 4
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => [8,4,7,6,5,1,3,2] => 1011101 => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [7,6,5,4,1,3,2,8] => 1111010 => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [6,5,4,3,1,2,8,7] => 1111001 => 5
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => [5,4,8,7,6,1,3,2] => 1011101 => 5
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => [4,8,7,6,5,1,3,2] => 0111101 => 5
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [8,7,6,5,4,1,3,2] => 1111101 => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => 1100000 => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [2,1,8,3,4,5,6,7] => 1010000 => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [2,1,7,3,4,5,6,8] => 1010000 => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [2,1,6,8,3,4,5,7] => 1001000 => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [1,8,2,7,3,4,5,6] => 0101000 => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [2,1,5,6,8,3,4,7] => 1000100 => 2
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [1,8,2,5,7,3,4,6] => 0100100 => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [1,7,2,6,3,4,5,8] => 0101000 => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [1,6,2,5,8,3,4,7] => 0100100 => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [1,6,8,2,7,3,4,5] => 0010100 => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [8,1,7,2,6,3,4,5] => 1010100 => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [2,1,5,3,4,6,7,8] => 1010000 => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [2,1,4,6,3,5,7,8] => 1001000 => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [2,1,4,5,6,8,3,7] => 1000010 => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [1,7,2,4,6,3,5,8] => 0100100 => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [1,6,2,4,5,8,3,7] => 0100010 => 2
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [8,1,7,2,4,6,3,5] => 1010010 => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [1,6,2,5,3,4,7,8] => 0101000 => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [1,5,2,4,8,3,6,7] => 0100100 => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [1,5,2,4,6,8,3,7] => 0100010 => 2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [1,4,8,2,5,7,3,6] => 0010010 => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => [1,5,6,2,4,8,3,7] => 0010010 => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [7,1,6,2,5,3,4,8] => 1010100 => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [6,1,5,2,4,8,3,7] => 1010010 => 3
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => [6,1,5,8,2,7,3,4] => 1001010 => 3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => [5,8,1,7,2,6,3,4] => 0101010 => 3
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [8,7,1,6,2,5,3,4] => 1101010 => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [2,1,4,3,5,6,7,8] => 1010000 => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [2,1,3,8,4,5,6,7] => 1001000 => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [2,1,3,6,4,5,7,8] => 1001000 => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [2,1,3,5,8,4,6,7] => 1000100 => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [1,8,2,3,5,7,4,6] => 0100010 => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [1,7,2,3,6,4,5,8] => 0100100 => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [1,6,2,3,5,8,4,7] => 0100010 => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [1,6,8,2,3,7,4,5] => 0010010 => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [8,1,7,2,3,6,4,5] => 1010010 => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [1,8,2,3,4,7,5,6] => 0100010 => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [2,1,3,4,6,5,7,8] => 1000100 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [2,1,3,4,5,7,6,8] => 1000010 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [2,1,3,4,5,6,8,7] => 1000001 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [1,8,2,3,4,5,7,6] => 0100001 => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [1,6,2,3,4,5,8,7] => 0100001 => 2
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => [1,6,8,2,3,4,7,5] => 0010001 => 2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [1,4,8,2,3,5,7,6] => 0010001 => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,7,5,6,8,1] => [1,5,6,2,3,4,8,7] => 0010001 => 2
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => [1,5,6,8,2,3,7,4] => 0001001 => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [6,1,5,2,3,4,8,7] => 1010001 => 3
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [8,7,1,6,2,3,5,4] => 1101001 => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [1,5,2,4,3,6,7,8] => 0101000 => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [1,4,2,3,8,5,6,7] => 0100100 => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [1,4,2,3,7,5,6,8] => 0100100 => 2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [1,3,8,2,4,7,5,6] => 0010010 => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [1,4,2,3,5,8,6,7] => 0100010 => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [1,4,2,3,5,6,8,7] => 0100001 => 2
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [1,3,8,2,4,5,7,6] => 0010001 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [1,3,7,2,4,6,5,8] => 0010010 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [1,3,6,2,4,5,8,7] => 0010001 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => [1,3,6,8,2,4,7,5] => 0001001 => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,2,6,4,5,1,7,8] => [1,4,6,2,5,3,7,8] => 0010100 => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [1,4,5,2,3,8,6,7] => 0010010 => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,2,6,4,5,7,1,8] => [1,4,5,2,3,7,6,8] => 0010010 => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => [1,4,5,7,2,6,3,8] => 0001010 => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => [1,4,5,6,8,2,7,3] => 0000101 => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [5,1,4,2,3,8,6,7] => 1010010 => 3
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => [5,1,4,6,8,2,7,3] => 1000101 => 3
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => [4,8,1,5,7,2,6,3] => 0100101 => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [4,7,1,6,2,5,3,8] => 0101010 => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => [4,6,1,5,2,3,8,7] => 0101001 => 3
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => [4,6,1,5,8,2,7,3] => 0100101 => 3
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => [8,4,7,1,6,2,5,3] => 1010101 => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [7,6,1,5,2,4,3,8] => 1101010 => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [6,5,1,4,2,3,8,7] => 1101001 => 4
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,8,6,5,7,4,1] => [5,4,8,1,7,2,6,3] => 1010101 => 4
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,8,7,5,6,4,1] => [5,8,7,1,6,2,4,3] => 0110101 => 4
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [8,7,6,1,5,2,4,3] => 1110101 => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => [2,4,3,1,5,6,7,8] => 0110000 => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,2,3,1,5,7,8,6] => [2,3,1,6,8,4,5,7] => 0100100 => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,3,1,6,5,7,8] => [2,3,1,6,4,5,7,8] => 0101000 => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [2,3,1,5,6,8,4,7] => 0100010 => 2
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [8,2,1,3,5,7,4,6] => 1100010 => 3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [6,1,8,2,3,7,4,5] => 1010010 => 3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [1,8,7,2,3,6,4,5] => 0110010 => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => [2,3,1,5,4,6,7,8] => 0101000 => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,2,3,5,1,6,8,7] => [2,3,1,4,8,5,6,7] => 0100100 => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => [8,2,1,3,4,7,5,6] => 1100010 => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => [2,3,1,4,5,8,6,7] => 0100010 => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => [2,3,1,4,5,7,6,8] => 0100010 => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => [2,3,1,4,5,6,8,7] => 0100001 => 2
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => [8,2,1,3,4,5,7,6] => 1100001 => 3
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,2,3,5,8,7,6,1] => [1,8,7,2,3,4,6,5] => 0110001 => 3
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => [4,1,8,2,3,5,7,6] => 1010001 => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [5,1,6,2,3,4,8,7] => 1010001 => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,2,3,7,6,5,8,1] => [1,6,5,2,3,4,8,7] => 0110001 => 3
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,2,3,8,6,7,5,1] => [1,5,8,7,2,3,6,4] => 0011001 => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [2,3,5,4,1,6,7,8] => 0011000 => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => [2,3,4,1,8,5,6,7] => 0010100 => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [2,3,4,1,6,8,5,7] => 0010010 => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => [2,3,4,1,6,5,7,8] => 0010100 => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2,3,4,6,1,8,7] => [2,3,4,1,5,8,6,7] => 0010010 => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => [2,3,4,1,5,7,6,8] => 0010010 => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [2,3,4,1,5,6,8,7] => 0010001 => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => [7,2,3,1,4,6,5,8] => 1010010 => 3
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => [6,8,2,1,3,4,7,5] => 0110001 => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => [2,3,4,6,5,1,7,8] => 0001100 => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => [2,3,4,5,1,8,6,7] => 0001010 => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => [2,3,4,5,1,7,6,8] => 0001010 => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => [2,3,4,5,1,6,8,7] => 0001001 => 2
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => [8,2,3,4,1,5,7,6] => 1001001 => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [2,3,4,5,7,6,1,8] => 0000110 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [2,3,4,5,6,1,8,7] => 0000101 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,8,7,1] => 0000011 => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => [8,2,3,4,5,7,6,1] => 1000011 => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,2,3,4,6,5,1,8] => [7,2,3,4,6,5,1,8] => 1000110 => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => [6,2,3,5,4,1,7,8] => 1001100 => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => [5,2,3,4,1,8,6,7] => 1001010 => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,2,3,5,4,7,8,1] => [5,2,3,4,1,6,8,7] => 1001001 => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => [5,2,3,4,7,6,1,8] => 1000110 => 3
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8,2,3,5,4,7,6,1] => [4,8,2,3,5,7,6,1] => 0100011 => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => [4,7,2,3,6,5,1,8] => 0100110 => 3
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8,2,3,5,6,7,4,1] => [4,5,8,2,3,7,6,1] => 0010011 => 3
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8,2,3,5,7,6,4,1] => [8,4,7,2,3,6,5,1] => 1010011 => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => [7,6,2,3,5,4,1,8] => 1100110 => 4
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => [5,8,7,2,3,6,4,1] => 0110011 => 4
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8,2,3,7,6,5,4,1] => [8,7,6,2,3,5,4,1] => 1110011 => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => [5,2,4,3,1,6,7,8] => 1011000 => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => [4,2,3,1,8,5,6,7] => 1010100 => 3
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => [3,8,2,1,4,7,5,6] => 0110010 => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [4,2,3,1,5,8,6,7] => 1010010 => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [5,2,4,3,6,7,1,8] => [4,2,3,1,5,7,6,8] => 1010010 => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => [3,6,2,1,4,5,8,7] => 0110001 => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [4,2,3,5,1,8,6,7] => 1001010 => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => [3,7,2,4,6,5,1,8] => 0100110 => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [3,6,2,4,5,1,8,7] => 0100101 => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [3,6,2,4,5,8,7,1] => 0100011 => 3
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => [3,5,8,2,4,7,6,1] => 0010011 => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,2,4,5,3,1,7,8] => [3,6,2,5,4,1,7,8] => 0101100 => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2,4,5,3,1,8,7] => [3,5,2,4,1,8,6,7] => 0101010 => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,2,4,5,3,8,7,1] => [3,4,8,2,1,5,7,6] => 0011001 => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => [3,5,2,4,7,6,1,8] => 0100110 => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => [3,5,2,4,6,1,8,7] => 0100101 => 3
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [3,4,8,2,5,7,6,1] => 0010011 => 3
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8,2,4,5,6,3,7,1] => [3,4,6,2,5,8,7,1] => 0010011 => 3
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8,2,4,5,7,6,3,1] => [8,3,4,7,2,6,5,1] => 1001011 => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => [7,3,6,2,5,4,1,8] => 1010110 => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,2,4,6,5,3,8,1] => [6,3,5,2,4,1,8,7] => 1010101 => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8,2,4,7,5,6,3,1] => [5,8,3,7,2,6,4,1] => 0101011 => 4
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => [8,7,3,6,2,5,4,1] => 1101011 => 5
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => [5,4,2,3,1,8,6,7] => 1101010 => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,2,5,4,3,7,8,1] => [5,4,2,3,1,6,8,7] => 1101001 => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => [5,4,2,3,7,6,1,8] => 1100110 => 4
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => [4,3,8,2,5,7,6,1] => 1010011 => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,2,5,4,6,3,8,1] => [4,3,6,2,5,1,8,7] => 1010101 => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => [4,6,5,2,3,1,8,7] => 0110101 => 4
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => [4,6,5,2,3,8,7,1] => 0110011 => 4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => [4,5,3,8,2,7,6,1] => 0101011 => 4
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => [4,5,8,7,2,6,3,1] => 0011011 => 4
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => [8,4,7,6,2,5,3,1] => 1011011 => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,6,5,4,3,8,1] => [6,5,4,2,3,1,8,7] => 1110101 => 5
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => [5,4,3,8,2,7,6,1] => 1101011 => 5
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => [5,4,8,7,2,6,3,1] => 1011011 => 5
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => [4,8,7,6,2,5,3,1] => 0111011 => 5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => [8,7,6,5,2,4,3,1] => 1111011 => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => 1110000 => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [3,2,1,8,4,5,6,7] => 1101000 => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [3,2,1,6,8,4,5,7] => 1100100 => 3
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [2,1,8,3,7,4,5,6] => 1010100 => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [3,2,1,5,8,4,6,7] => 1100100 => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [3,2,1,5,7,4,6,8] => 1100100 => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [3,2,1,5,6,8,4,7] => 1100010 => 3
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [2,1,8,3,5,7,4,6] => 1010010 => 3
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [2,1,6,8,3,7,4,5] => 1001010 => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [1,8,2,7,3,6,4,5] => 0101010 => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [3,2,1,5,4,6,7,8] => 1101000 => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [3,2,1,4,6,8,5,7] => 1100010 => 3
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [2,1,8,3,4,7,5,6] => 1010010 => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [3,2,1,4,5,8,6,7] => 1100010 => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [3,2,1,4,5,6,8,7] => 1100001 => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [2,1,6,3,4,5,8,7] => 1010001 => 3
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [1,8,2,7,3,4,6,5] => 0101001 => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [2,1,5,3,4,6,8,7] => 1010001 => 3
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [2,1,4,8,3,5,7,6] => 1001001 => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => [2,1,5,6,3,4,8,7] => 1001001 => 3
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => [2,1,5,6,8,3,7,4] => 1000101 => 3
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => [1,8,2,5,7,3,6,4] => 0100101 => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [1,6,2,5,3,4,8,7] => 0101001 => 3
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => [1,5,8,2,7,3,6,4] => 0010101 => 3
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [8,1,7,2,6,3,5,4] => 1010101 => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => [3,2,5,4,1,6,7,8] => 1011000 => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => [3,2,4,1,8,5,6,7] => 1010100 => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => [3,2,4,1,7,5,6,8] => 1010100 => 3
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => [2,8,3,1,4,7,5,6] => 0110010 => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => [3,2,4,1,6,5,7,8] => 1010100 => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => [3,2,4,1,5,8,6,7] => 1010010 => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => [3,2,4,1,5,6,8,7] => 1010001 => 3
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [3,2,4,5,6,8,7,1] => 1000011 => 3
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8,3,2,4,6,5,7,1] => [2,6,3,4,5,8,7,1] => 0100011 => 3
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8,3,2,4,7,6,5,1] => [8,2,7,3,4,6,5,1] => 1010011 => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,3,2,5,4,1,7,8] => [2,6,3,5,4,1,7,8] => 0101100 => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [2,5,3,4,1,8,6,7] => 0101010 => 3
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,3,2,5,4,8,7,1] => [2,4,8,3,1,5,7,6] => 0011001 => 3
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [2,4,8,3,5,7,6,1] => 0010011 => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,3,2,5,6,4,8,1] => [2,4,6,3,5,1,8,7] => 0010101 => 3
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8,3,2,5,6,4,7,1] => [2,4,6,3,5,8,7,1] => 0010011 => 3
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => [8,2,4,7,3,6,5,1] => 1001011 => 4
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => [5,8,2,7,3,6,4,1] => 0101011 => 4
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [8,7,2,6,3,5,4,1] => 1101011 => 5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => [2,5,4,3,1,6,7,8] => 0111000 => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => [2,4,3,1,8,5,6,7] => 0110100 => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [2,4,3,1,6,8,5,7] => 0110010 => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => [2,3,1,8,4,7,5,6] => 0101010 => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => [2,4,3,1,5,8,6,7] => 0110010 => 3
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => [2,3,1,6,8,4,7,5] => 0100101 => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => [2,4,3,5,1,8,6,7] => 0101010 => 3
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [2,4,3,5,6,8,7,1] => 0100011 => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => [2,3,6,4,5,1,8,7] => 0010101 => 3
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8,3,4,2,6,5,7,1] => [2,3,6,4,5,8,7,1] => 0010011 => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,3,4,5,2,1,7,8] => [2,3,6,5,4,1,7,8] => 0011100 => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => [2,3,5,4,1,8,6,7] => 0011010 => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [2,3,5,4,1,7,6,8] => 0011010 => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => [2,3,5,4,1,6,8,7] => 0011001 => 3
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [2,3,4,8,5,7,6,1] => 0001011 => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => [2,3,4,7,6,5,1,8] => 0001110 => 3
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => [2,3,4,6,5,8,7,1] => 0001011 => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [2,3,4,5,8,7,6,1] => 0000111 => 3
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => [8,2,3,4,7,6,5,1] => 1000111 => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,3,4,6,5,2,1,8] => [7,2,3,6,5,4,1,8] => 1001110 => 4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => [8,7,2,3,6,5,4,1] => 1100111 => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => [5,2,4,3,1,7,6,8] => 1011010 => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,3,5,4,2,7,8,1] => [5,2,4,3,1,6,8,7] => 1011001 => 4
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,3,5,4,2,8,7,1] => [4,2,3,1,8,5,7,6] => 1010101 => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => [5,2,4,3,7,6,1,8] => 1010110 => 4
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8,3,5,4,2,7,6,1] => [4,2,3,8,5,7,6,1] => 1001011 => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => [4,2,3,6,5,1,8,7] => 1001101 => 4
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,5,4,6,7,2,1] => [4,2,3,5,8,7,6,1] => 1000111 => 4
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [3,8,2,4,7,6,5,1] => 0100111 => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => [4,7,2,6,5,3,1,8] => 0101110 => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => [4,6,2,5,3,1,8,7] => 0101101 => 4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [4,6,2,5,3,8,7,1] => 0101011 => 4
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => [8,4,7,2,6,5,3,1] => 1010111 => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => [7,6,2,5,4,3,1,8] => 1101110 => 5
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => [6,5,2,4,3,8,7,1] => 1101011 => 5
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8,3,7,5,4,6,2,1] => [5,4,8,2,7,6,3,1] => 1010111 => 5
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => [4,8,7,2,6,5,3,1] => 0110111 => 5
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => [8,7,6,2,5,4,3,1] => 1110111 => 6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => 1111000 => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [4,3,2,1,8,5,6,7] => 1110100 => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [4,3,2,1,7,5,6,8] => 1110100 => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [4,3,2,1,6,8,5,7] => 1110010 => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [3,2,1,8,4,7,5,6] => 1101010 => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [4,3,2,1,6,5,7,8] => 1110100 => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [4,3,2,1,5,8,6,7] => 1110010 => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [4,3,2,1,5,7,6,8] => 1110010 => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [4,3,2,1,5,6,8,7] => 1110001 => 4
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [3,2,1,8,4,5,7,6] => 1101001 => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [3,2,1,7,4,6,5,8] => 1101010 => 4
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [2,1,8,3,7,4,6,5] => 1010101 => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => [4,3,2,6,5,1,7,8] => 1101100 => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => [4,3,2,5,1,8,6,7] => 1101010 => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [4,3,2,5,6,1,8,7] => 1100101 => 4
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => [4,3,2,5,6,8,7,1] => 1100011 => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,4,3,2,6,5,1,8] => [3,2,7,4,6,5,1,8] => 1010110 => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => [3,2,6,4,5,1,8,7] => 1010101 => 4
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => [2,8,3,7,4,6,5,1] => 0101011 => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => [3,2,5,4,1,8,6,7] => 1011010 => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [3,2,5,4,6,1,8,7] => 1010101 => 4
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => [3,2,4,6,5,8,7,1] => 1001011 => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => [2,7,3,6,5,4,1,8] => 0101110 => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => [2,6,3,5,4,1,8,7] => 0101101 => 4
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => [2,5,8,3,7,6,4,1] => 0010111 => 4
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8,4,3,7,6,5,2,1] => [8,2,7,3,6,5,4,1] => 1010111 => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => [3,6,5,4,2,1,7,8] => 0111100 => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,3,4,2,7,8,1] => [3,5,4,2,1,6,8,7] => 0111001 => 4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => [3,5,4,2,7,6,1,8] => 0110110 => 4
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => [3,4,2,8,5,7,6,1] => 0101011 => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [3,4,2,6,5,1,8,7] => 0101101 => 4
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => [3,4,2,5,8,7,6,1] => 0100111 => 4
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => [8,3,2,4,7,6,5,1] => 1100111 => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => [3,4,7,6,5,2,1,8] => 0011110 => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => [3,4,6,5,2,1,8,7] => 0011101 => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => [3,4,5,8,7,6,2,1] => 0001111 => 4
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => [8,3,4,7,6,5,2,1] => 1001111 => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => [7,3,6,5,4,2,1,8] => 1011110 => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => [6,3,5,4,2,1,8,7] => 1011101 => 5
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8,6,3,5,4,2,7,1] => [6,3,5,4,2,8,7,1] => 1011011 => 5
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [5,3,4,8,7,6,2,1] => 1001111 => 5
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [4,8,3,7,6,5,2,1] => 0101111 => 5
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => [8,7,3,6,5,4,2,1] => 1101111 => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => 1111100 => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [5,4,3,2,1,8,6,7] => 1111010 => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [5,4,3,2,1,7,6,8] => 1111010 => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [5,4,3,2,1,6,8,7] => 1111001 => 5
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [4,3,2,1,8,5,7,6] => 1110101 => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => [5,4,3,2,7,6,1,8] => 1110110 => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [5,4,3,2,6,1,8,7] => 1110101 => 5
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => [5,4,3,2,6,8,7,1] => 1110011 => 5
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [4,3,2,8,5,7,6,1] => 1101011 => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [4,3,2,6,5,1,8,7] => 1101101 => 5
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => [4,3,2,6,5,8,7,1] => 1101011 => 5
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => [4,3,2,5,8,7,6,1] => 1100111 => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => [4,3,7,6,5,2,1,8] => 1011110 => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => [4,3,6,5,2,1,8,7] => 1011101 => 5
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => [4,3,6,5,2,8,7,1] => 1011011 => 5
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [3,8,4,7,6,5,2,1] => 0101111 => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => [3,6,5,4,2,1,8,7] => 0111101 => 5
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => [3,6,5,4,2,8,7,1] => 0111011 => 5
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [3,4,8,7,6,5,2,1] => 0011111 => 5
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => [8,3,7,6,5,4,2,1] => 1011111 => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 1111110 => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [6,5,4,3,2,1,8,7] => 1111101 => 6
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => [6,5,4,3,2,8,7,1] => 1111011 => 6
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => [5,4,3,2,8,7,6,1] => 1110111 => 6
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => [5,4,3,8,7,6,2,1] => 1101111 => 6
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => [4,3,8,7,6,5,2,1] => 1011111 => 6
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [4,8,7,6,5,3,2,1] => 0111111 => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 1111111 => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => 11111110 => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [9,8,7,6,5,4,3,1,2] => 11111110 => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => 111111110 => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,7,6,4,5,3,2,1,9] => [4,8,7,6,5,3,2,1,9] => 01111110 => 6
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,9,8,7,5,6,4,3,2] => [5,9,8,7,6,4,3,1,2] => 01111110 => 6
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [10,9,8,7,6,5,4,3,1,2] => 111111110 => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110 => 9
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [11,10,9,8,7,6,5,4,3,1,2] => 1111111110 => 9
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1,12] => [11,10,9,8,7,6,5,4,3,2,1,12] => 11111111110 => 10
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,6,5,4,3,2,8,1,9] => [6,5,4,3,2,1,8,7,9] => 11111010 => 6
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [9,8,7,6,5,2,4,1,3] => 11111010 => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => 11111100 => 6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [8,7,6,5,4,3,1,2,9] => 11111100 => 6
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [9,8,7,6,5,4,1,2,3] => 11111100 => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,7,6,5,4,3,2,9,1,10] => [7,6,5,4,3,2,1,9,8,10] => 111111010 => 7
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,10,9,8,7,6,5,4,2] => [10,9,8,7,6,5,2,4,1,3] => 111111010 => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => 111111100 => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [9,8,7,6,5,4,3,1,2,10] => 111111100 => 7
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [10,9,8,7,6,5,4,1,2,3] => 111111100 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [1,2,3,4,5,6,7,9,8] => 00000001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [9,1,2,3,4,5,6,8,7] => 10000001 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [7,1,2,3,4,5,6,9,8] => 10000001 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,5,8,6,7,9,1] => [6,7,1,2,3,4,5,9,8] => 01000001 => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => [3,1,2,4,5,6,7,9,8] => 10000001 => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,9,3,4,5,6,7,8,1] => [3,4,5,6,7,9,1,8,2] => 00000101 => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => [7,6,5,4,3,1,2,9,8] => 11111001 => 6
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,9,8,6,5,7,4,3,1] => [5,4,9,8,7,6,1,3,2] => 10111101 => 6
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [9,8,7,6,5,4,1,3,2] => 11111101 => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [2,1,3,4,5,6,7,9,8] => 10000001 => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,1] => [2,3,1,4,5,6,7,9,8] => 01000001 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [2,3,4,5,6,7,1,9,8] => 00000101 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,9,8,1] => 00000011 => 2
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9,2,8,7,6,5,4,3,1] => [9,8,7,6,5,2,4,3,1] => 11111011 => 7
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [9,3,4,5,6,2,8,7,1] => [2,3,4,5,9,6,8,7,1] => 00001011 => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,3,4,5,6,7,8,2,1] => [2,3,4,5,6,9,8,7,1] => 00000111 => 3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [9,8,4,7,6,5,3,2,1] => [9,8,3,7,6,5,4,2,1] => 11011111 => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [7,6,5,4,3,2,1,9,8] => 11111101 => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9,7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,9,8,1] => 11111011 => 7
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,8,7,5,6,4,3,2,1] => [4,9,8,7,6,5,3,2,1] => 01111111 => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111 => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [9,1,2,3,4,5,6,7,8] => 10000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [7,9,1,2,3,4,5,6,8] => 01000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [6,7,9,1,2,3,4,5,8] => 00100000 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [5,6,7,9,1,2,3,4,8] => 00010000 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [4,5,6,7,9,1,2,3,8] => 00001000 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [2,3,4,5,6,7,9,1,8] => 00000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [10,1,2,3,4,5,6,7,8,9] => 100000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [9,8,1,2,3,4,5,6,7] => 11000000 => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [8,10,1,2,3,4,5,6,7,9] => 010000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [7,8,10,1,2,3,4,5,6,9] => 001000000 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [5,6,7,8,10,1,2,3,4,9] => 000010000 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [4,5,6,7,8,10,1,2,3,9] => 000001000 => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [3,2,4,5,6,7,9,1,8] => 10000010 => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [2,3,4,5,6,7,8,10,1,9] => 000000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [1,2,3,4,5,6,7,8,10,9] => 000000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [11,1,2,3,4,5,6,7,8,9,10] => 1000000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [10,9,1,2,3,4,5,6,7,8] => 110000000 => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [9,11,1,2,3,4,5,6,7,8,10] => 0100000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [9,8,7,1,2,3,4,5,6] => 11100000 => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => [2,3,4,5,6,7,8,9,11,1,10] => 0000000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [1,2,3,4,5,6,7,8,9,11,10] => 0000000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [10,9,8,1,2,3,4,5,6,7] => 111000000 => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,12,2] => [2,3,4,5,6,7,8,9,10,12,1,11] => 00000000010 => 1
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [9,8,7,6,1,2,3,4,5] => 11110000 => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [10,9,8,7,1,2,3,4,5,6] => 111100000 => 4
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [9,8,7,6,5,1,2,3,4] => 11111000 => 5
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [10,9,8,7,6,1,2,3,4,5] => 111110000 => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [2,3,4,5,6,7,8,1,10,9] => 000000101 => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [8,1,2,3,4,5,6,7,9] => 10000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [7,1,2,3,4,5,6,8,9] => 10000000 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [6,1,2,3,4,5,7,8,9] => 10000000 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => 10000000 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => 10000000 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => 10000000 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [2,9,1,3,4,5,6,7,8] => 01000000 => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [4,3,1,2,5,6,7,8,9] => 11000000 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,6,5,4,3,2,9,8] => [6,5,4,3,2,9,1,7,8] => 11110100 => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => 10000000 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [1,9,2,3,4,5,6,7,8] => 01000000 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [1,8,2,3,4,5,6,7,9] => 01000000 => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [1,4,2,3,5,6,7,8,9] => 01000000 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => 11000000 => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => 11100000 => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [9,1,8,2,7,3,6,4,5] => 10101010 => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => 11110000 => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => 11111000 => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [9,1,2,3,4,5,6,7,8,10] => 100000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => 100000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => 100000000 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => 100000000 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => 100000000 => 1
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [10,9,8,7,6,5,1,2,3,4] => 111111000 => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => 100000000 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => 100000000 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => 100000000 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [1,10,2,3,4,5,6,7,8,9] => 010000000 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => 110000000 => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => 111000000 => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => 111100000 => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => 111110000 => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10] => 111111000 => 6
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 111111111 => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => 01000000 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => 00100000 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => 00010000 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [1,2,3,4,6,5,7,8,9] => 00001000 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [1,2,3,4,5,7,6,8,9] => 00000100 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [1,2,3,4,5,6,8,7,9] => 00000010 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => 010000000 => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => [4,1,3,2,5,6,7,8,9] => 10100000 => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => 001000000 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => 000100000 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => 000010000 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => 000001000 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [8,1,2,3,4,5,7,6,9] => 10000010 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [1,2,3,4,5,6,8,7,9,10] => 000000100 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [1,2,3,4,5,6,7,9,8,10] => 000000010 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [1,7,9,2,3,4,5,6,8] => 00100000 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [1,2,9,3,4,5,6,7,8] => 00100000 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,2,3,4,5,6,7,1,9] => [2,3,4,5,6,8,7,1,9] => 00000110 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,2,3,4,5,6,1,8,9] => [2,3,4,5,7,6,1,8,9] => 00001100 => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,2,3,4,5,1,7,8,9] => [2,3,4,6,5,1,7,8,9] => 00011000 => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8,9] => [2,3,5,4,1,6,7,8,9] => 00110000 => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8,9] => [2,4,3,1,5,6,7,8,9] => 01100000 => 2
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [10,9,8,7,6,5,4,1,3,2] => 111111101 => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [8,7,6,5,4,3,2,1,10,9] => 111111101 => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [9,8,7,6,5,4,3,2,1,11,10] => 1111111101 => 9
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,5,4,3,2,7,1,8,9] => [5,4,3,2,1,7,6,8,9] => 11110100 => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,4,3,2,6,1,7,8,9] => [4,3,2,1,6,5,7,8,9] => 11101000 => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8,9] => [3,2,1,5,4,6,7,8,9] => 11010000 => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => 10100000 => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,9,8,7,5,6,4,3,2,1] => [5,10,9,8,7,6,4,3,2,1] => 011111111 => 8
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,2,3,4,5,6,1,9,8] => [2,3,4,5,6,1,9,7,8] => 00001010 => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,10,3,4,5,6,7,8,9,1] => [3,4,5,6,7,8,10,1,9,2] => 000000101 => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => [2,3,5,1,4,6,7,8,9] => 00100000 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6,7,9,8] => [1,2,3,4,9,5,6,7,8] => 00001000 => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8,9] => [1,3,5,2,4,6,7,8,9] => 00100000 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [2,1,3,4,5,6,8,7,9] => 10000010 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [1,2,3,4,5,6,9,7,8] => 00000010 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [1,3,4,5,6,7,9,2,8] => 00000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => [9,1,2,3,4,5,8,6,7] => 10000010 => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10,3,4,5,6,7,8,9,2,1] => [2,3,4,5,6,7,10,9,8,1] => 000000111 => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,10,9,1] => 000000011 => 2
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [9,8,7,6,3,5,1,2,4] => 11110100 => 5
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => [9,8,7,4,6,1,2,3,5] => 11101000 => 4
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => [9,8,5,7,1,2,3,4,6] => 11010000 => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [9,6,8,1,2,3,4,5,7] => 10100000 => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,9,4] => [2,1,4,5,6,7,9,3,8] => 10000010 => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => 01000000 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => [1,3,4,5,6,7,8,10,2,9] => 000000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [10,1,2,3,4,5,6,7,8,9,11] => 1000000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [6,8,1,2,3,4,5,7,9] => 01000000 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,7,2,9,8] => [2,3,4,5,6,9,1,7,8] => 00000100 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => [1,2,3,4,5,6,7,8,10,9,11] => 0000000010 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [2,3,4,5,6,8,1,7,9] => 00000100 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [1,2,3,4,5,6,7,10,8,9] => 000000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => [1,2,3,4,5,7,9,6,8] => 00000010 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,2,3,4,5,6,7,8,9,11,1] => [2,3,4,5,6,7,8,9,1,11,10] => 0000000101 => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => [2,4,1,3,5,6,7,8,9,10] => 010000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,6,8,10,9,7] => [10,7,9,1,2,3,4,5,6,8] => 101000000 => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,6,8,7,9,2] => [7,2,3,4,5,6,9,1,8] => 10000010 => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [2,4,6,8,10,1,3,5,7,9] => 000010000 => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9,10] => [4,1,3,2,5,6,7,8,9,10] => 101000000 => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9,10] => [2,1,4,3,5,6,7,8,9,10] => 101000000 => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => [2,3,4,5,7,1,6,8,9] => 00001000 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,7,9,8,1,10] => [9,1,2,3,4,5,6,8,7,10] => 100000010 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,11,10] => [1,2,3,4,5,6,7,8,11,9,10] => 0000000010 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,1,7,8,9,6] => [1,2,3,4,6,7,9,5,8] => 00000010 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,7,8,10,9,1] => [1,10,2,3,4,5,6,7,9,8] => 010000001 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,7,1,9,10,8] => [1,2,3,4,5,6,8,10,7,9] => 000000010 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,9,8] => [1,2,3,4,6,9,5,7,8] => 00000100 => 1
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,10,9,8,7,6,5,3] => [10,9,8,7,6,3,5,1,2,4] => 111110100 => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,12,10] => [2,4,6,8,10,12,1,3,5,7,9,11] => 00000100000 => 1
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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 1,3,1 1,7,5,1 1,15,18,7,1 1,31,56,34,9,1 1,63,161,140,52,11,1
F2=1+q
F3=1+3 q+q2
F4=1+7 q+5 q2+q3
F5=1+15 q+18 q2+7 q3+q4
F6=1+31 q+56 q2+34 q3+9 q4+q5
F7=1+63 q+161 q2+140 q3+52 q4+11 q5+q6
Description
The number of ones in a binary word.
This is also known as the Hamming weight of the word.
This is also known as the Hamming weight of the word.
Map
Lehmer-code to major-code bijection
Description
Sends a permutation to the unique permutation such that the Lehmer code is sent to the major code.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation σ is given by L(σ)=l1…ln with li=#{j>i:σj<σi}. In particular, li is the number of boxes in the i-th column of the Rothe diagram. For example, the Lehmer code of σ=[4,3,1,5,2] is 32010. The Lehmer code L:Sn ˜⟶ Sn is a bijection between permutations of size n and sequences l1…ln∈Nn with li≤i.
* The major code M(σ) of a permutation σ∈Sn is a way to encode a permutation as a sequence m1m2…mn with mi≥i. To define mi, let deli(σ) be the normalized permutation obtained by removing all σj<i from the one-line notation of σ. The i-th index is then given by
mi=maj(deli(σ))−maj(deli−1(σ)).
For example, the permutation [9,3,5,7,2,1,4,6,8] has major code [5,0,1,0,1,2,0,1,0] since
maj([8,2,4,6,1,3,5,7])=5,maj([7,1,3,5,2,4,6])=5,maj([6,2,4,1,3,5])=4,
maj([5,1,3,2,4])=4,maj([4,2,1,3])=3,maj([3,1,2])=1,maj([2,1])=1.
Observe that the sum of the major code of σ equals the major index of σ.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation σ is given by L(σ)=l1…ln with li=#{j>i:σj<σi}. In particular, li is the number of boxes in the i-th column of the Rothe diagram. For example, the Lehmer code of σ=[4,3,1,5,2] is 32010. The Lehmer code L:Sn ˜⟶ Sn is a bijection between permutations of size n and sequences l1…ln∈Nn with li≤i.
* The major code M(σ) of a permutation σ∈Sn is a way to encode a permutation as a sequence m1m2…mn with mi≥i. To define mi, let deli(σ) be the normalized permutation obtained by removing all σj<i from the one-line notation of σ. The i-th index is then given by
mi=maj(deli(σ))−maj(deli−1(σ)).
For example, the permutation [9,3,5,7,2,1,4,6,8] has major code [5,0,1,0,1,2,0,1,0] since
maj([8,2,4,6,1,3,5,7])=5,maj([7,1,3,5,2,4,6])=5,maj([6,2,4,1,3,5])=4,
maj([5,1,3,2,4])=4,maj([4,2,1,3])=3,maj([3,1,2])=1,maj([2,1])=1.
Observe that the sum of the major code of σ equals the major index of σ.
Map
to non-crossing permutation
Description
Sends a Dyck path D with valley at positions {(i1,j1),…,(ik,jk)} to the unique non-crossing permutation π having descents {i1,…,ik} and whose inverse has descents {j1,…,jk}.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to n(n−1) minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to n(n−1) minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation π of n letters and each 1≤i≤n−1 such that π(i)>π(i+1) we set wi=1, otherwise wi=0.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation π of n letters and each 1≤i≤n−1 such that π(i)>π(i+1) we set wi=1, otherwise wi=0.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
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