Identifier
-
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
St000877: Binary words ⟶ ℤ
Values
[1,0,1,0] => [2,1] => [1,2] => 0 => 1
[1,1,0,0] => [1,2] => [2,1] => 1 => 0
[1,0,1,0,1,0] => [2,3,1] => [2,1,3] => 10 => 0
[1,0,1,1,0,0] => [2,1,3] => [2,3,1] => 01 => 1
[1,1,0,0,1,0] => [1,3,2] => [3,1,2] => 10 => 0
[1,1,0,1,0,0] => [3,1,2] => [1,3,2] => 01 => 1
[1,1,1,0,0,0] => [1,2,3] => [3,2,1] => 11 => 0
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [3,2,1,4] => 110 => 0
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [3,2,4,1] => 101 => 0
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [3,4,1,2] => 010 => 1
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [3,1,4,2] => 101 => 0
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [3,4,2,1] => 011 => 1
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [4,2,1,3] => 110 => 0
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [4,2,3,1] => 101 => 0
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [2,4,1,3] => 010 => 1
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [2,1,4,3] => 101 => 0
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [2,4,3,1] => 011 => 1
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [4,3,1,2] => 110 => 0
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [4,1,3,2] => 101 => 0
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [1,4,3,2] => 011 => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [4,3,2,1] => 111 => 0
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => [4,3,2,1,5] => 1110 => 0
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [4,3,2,5,1] => 1101 => 0
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [4,3,5,1,2] => 1010 => 0
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [4,3,1,5,2] => 1101 => 0
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [4,3,5,2,1] => 1011 => 0
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [4,5,2,1,3] => 0110 => 1
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [4,5,2,3,1] => 0101 => 1
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [4,2,5,1,3] => 1010 => 0
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [4,2,1,5,3] => 1101 => 0
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [4,2,5,3,1] => 1011 => 0
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [4,5,3,1,2] => 0110 => 1
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [4,5,1,3,2] => 0101 => 1
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [4,1,5,3,2] => 1011 => 0
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [4,5,3,2,1] => 0111 => 1
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [5,3,2,1,4] => 1110 => 0
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [5,3,2,4,1] => 1101 => 0
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [5,3,4,1,2] => 1010 => 0
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [5,3,1,4,2] => 1101 => 0
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [5,3,4,2,1] => 1011 => 0
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [3,5,2,1,4] => 0110 => 1
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [3,5,2,4,1] => 0101 => 1
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [3,2,5,1,4] => 1010 => 0
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [3,2,1,5,4] => 1101 => 0
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [3,2,5,4,1] => 1011 => 0
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [3,5,4,1,2] => 0110 => 1
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [3,5,1,4,2] => 0101 => 1
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [3,1,5,4,2] => 1011 => 0
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [3,5,4,2,1] => 0111 => 1
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [5,4,2,1,3] => 1110 => 0
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [5,4,2,3,1] => 1101 => 0
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [5,2,4,1,3] => 1010 => 0
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [5,2,1,4,3] => 1101 => 0
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [5,2,4,3,1] => 1011 => 0
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [2,5,4,1,3] => 0110 => 1
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [2,5,1,4,3] => 0101 => 1
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [2,1,5,4,3] => 1011 => 0
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [2,5,4,3,1] => 0111 => 1
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [5,4,3,1,2] => 1110 => 0
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [5,4,1,3,2] => 1101 => 0
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [5,1,4,3,2] => 1011 => 0
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [1,5,4,3,2] => 0111 => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [5,4,3,2,1] => 1111 => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => [5,4,3,2,1,6] => 11110 => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [5,4,3,2,6,1] => 11101 => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [5,4,3,6,1,2] => 11010 => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [5,4,3,1,6,2] => 11101 => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [5,4,3,6,2,1] => 11011 => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [5,4,6,2,1,3] => 10110 => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [5,4,6,2,3,1] => 10101 => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [5,4,2,6,1,3] => 11010 => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [5,4,2,1,6,3] => 11101 => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [5,4,2,6,3,1] => 11011 => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [5,4,6,3,1,2] => 10110 => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [5,4,6,1,3,2] => 10101 => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [5,4,1,6,3,2] => 11011 => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [5,4,6,3,2,1] => 10111 => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [5,6,3,2,1,4] => 01110 => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [5,6,3,2,4,1] => 01101 => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => 01010 => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => [5,6,3,1,4,2] => 01101 => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [5,6,3,4,2,1] => 01011 => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [5,3,6,2,1,4] => 10110 => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [5,3,6,2,4,1] => 10101 => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [5,3,2,6,1,4] => 11010 => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [5,3,2,1,6,4] => 11101 => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [5,3,2,6,4,1] => 11011 => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [5,3,6,4,1,2] => 10110 => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [5,3,6,1,4,2] => 10101 => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [5,3,1,6,4,2] => 11011 => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [5,3,6,4,2,1] => 10111 => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [5,6,4,2,1,3] => 01110 => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [5,6,4,2,3,1] => 01101 => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [5,6,2,4,1,3] => 01010 => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => [5,6,2,1,4,3] => 01101 => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [5,6,2,4,3,1] => 01011 => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [5,2,6,4,1,3] => 10110 => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [5,2,6,1,4,3] => 10101 => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [5,2,1,6,4,3] => 11011 => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [5,2,6,4,3,1] => 10111 => 0
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => 01110 => 1
>>> Load all 2214 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [5,6,4,1,3,2] => 01101 => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [5,6,1,4,3,2] => 01011 => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [5,1,6,4,3,2] => 10111 => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [5,6,4,3,2,1] => 01111 => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [6,4,3,2,1,5] => 11110 => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [6,4,3,2,5,1] => 11101 => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [6,4,3,5,1,2] => 11010 => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [6,4,3,1,5,2] => 11101 => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [6,4,3,5,2,1] => 11011 => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [6,4,5,2,1,3] => 10110 => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => 10101 => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [6,4,2,5,1,3] => 11010 => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [6,4,2,1,5,3] => 11101 => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [6,4,2,5,3,1] => 11011 => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [6,4,5,3,1,2] => 10110 => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [6,4,5,1,3,2] => 10101 => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [6,4,1,5,3,2] => 11011 => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [6,4,5,3,2,1] => 10111 => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [4,6,3,2,1,5] => 01110 => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [4,6,3,2,5,1] => 01101 => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [4,6,3,5,1,2] => 01010 => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => [4,6,3,1,5,2] => 01101 => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [4,6,3,5,2,1] => 01011 => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [4,3,6,2,1,5] => 10110 => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [4,3,6,2,5,1] => 10101 => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [4,3,2,6,1,5] => 11010 => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [4,3,2,1,6,5] => 11101 => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [4,3,2,6,5,1] => 11011 => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [4,3,6,5,1,2] => 10110 => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [4,3,6,1,5,2] => 10101 => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [4,3,1,6,5,2] => 11011 => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,3,6,5,2,1] => 10111 => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [4,6,5,2,1,3] => 01110 => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [4,6,5,2,3,1] => 01101 => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [4,6,2,5,1,3] => 01010 => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => [4,6,2,1,5,3] => 01101 => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [4,6,2,5,3,1] => 01011 => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [4,2,6,5,1,3] => 10110 => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [4,2,6,1,5,3] => 10101 => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => 11011 => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [4,2,6,5,3,1] => 10111 => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [4,6,5,3,1,2] => 01110 => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [4,6,5,1,3,2] => 01101 => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => [4,6,1,5,3,2] => 01011 => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [4,1,6,5,3,2] => 10111 => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [4,6,5,3,2,1] => 01111 => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [6,5,3,2,1,4] => 11110 => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => [6,5,3,2,4,1] => 11101 => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [6,5,3,4,1,2] => 11010 => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [6,5,3,1,4,2] => 11101 => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => 11011 => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [6,3,5,2,1,4] => 10110 => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [6,3,5,2,4,1] => 10101 => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [6,3,2,5,1,4] => 11010 => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [6,3,2,1,5,4] => 11101 => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [6,3,2,5,4,1] => 11011 => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [6,3,5,4,1,2] => 10110 => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [6,3,5,1,4,2] => 10101 => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [6,3,1,5,4,2] => 11011 => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [6,3,5,4,2,1] => 10111 => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => [3,6,5,2,1,4] => 01110 => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => [3,6,5,2,4,1] => 01101 => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [3,6,2,5,1,4] => 01010 => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => [3,6,2,1,5,4] => 01101 => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => [3,6,2,5,4,1] => 01011 => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => [3,2,6,5,1,4] => 10110 => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => [3,2,6,1,5,4] => 10101 => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => 11011 => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [3,2,6,5,4,1] => 10111 => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => [3,6,5,4,1,2] => 01110 => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => [3,6,5,1,4,2] => 01101 => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => [3,6,1,5,4,2] => 01011 => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [3,1,6,5,4,2] => 10111 => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [3,6,5,4,2,1] => 01111 => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [6,5,4,2,1,3] => 11110 => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [6,5,4,2,3,1] => 11101 => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [6,5,2,4,1,3] => 11010 => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [6,5,2,1,4,3] => 11101 => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [6,5,2,4,3,1] => 11011 => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [6,2,5,4,1,3] => 10110 => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [6,2,5,1,4,3] => 10101 => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [6,2,1,5,4,3] => 11011 => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [6,2,5,4,3,1] => 10111 => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => [2,6,5,4,1,3] => 01110 => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => [2,6,5,1,4,3] => 01101 => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => [2,6,1,5,4,3] => 01011 => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [2,1,6,5,4,3] => 10111 => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [2,6,5,4,3,1] => 01111 => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [6,5,4,3,1,2] => 11110 => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [6,5,4,1,3,2] => 11101 => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [6,5,1,4,3,2] => 11011 => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [6,1,5,4,3,2] => 10111 => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => 01111 => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 11111 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1] => [6,5,4,3,2,1,7] => 111110 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,1,7] => [6,5,4,3,2,7,1] => 111101 => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6] => [6,5,4,3,7,1,2] => 111010 => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => [6,5,4,3,1,7,2] => 111101 => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7] => [6,5,4,3,7,2,1] => 111011 => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5] => [6,5,4,7,2,1,3] => 110110 => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7] => [6,5,4,7,2,3,1] => 110101 => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,6,1,7,5] => [6,5,4,2,7,1,3] => 111010 => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => [6,5,4,2,1,7,3] => 111101 => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,6,1,5,7] => [6,5,4,2,7,3,1] => 111011 => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6] => [6,5,4,7,3,1,2] => 110110 => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,6] => [6,5,4,7,1,3,2] => 110101 => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => [6,5,4,1,7,3,2] => 111011 => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => [6,5,4,7,3,2,1] => 110111 => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4] => [6,5,7,3,2,1,4] => 101110 => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7] => [6,5,7,3,2,4,1] => 101101 => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => [6,5,7,3,4,1,2] => 101010 => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,7,4,6] => [6,5,7,3,1,4,2] => 101101 => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7] => [6,5,7,3,4,2,1] => 101011 => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,5,1,6,7,4] => [6,5,3,7,2,1,4] => 110110 => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,7] => [6,5,3,7,2,4,1] => 110101 => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,5,6,1,7,4] => [6,5,3,2,7,1,4] => 111010 => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,1,4] => [6,5,3,2,1,7,4] => 111101 => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,6,1,4,7] => [6,5,3,2,7,4,1] => 111011 => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,7,6] => [6,5,3,7,4,1,2] => 110110 => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,6] => [6,5,3,7,1,4,2] => 110101 => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,7,1,4,6] => [6,5,3,1,7,4,2] => 111011 => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => [6,5,3,7,4,2,1] => 110111 => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5] => [6,5,7,4,2,1,3] => 101110 => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7] => [6,5,7,4,2,3,1] => 101101 => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => [6,5,7,2,4,1,3] => 101010 => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => [6,5,7,2,1,4,3] => 101101 => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,5,7] => [6,5,7,2,4,3,1] => 101011 => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,6,1,4,7,5] => [6,5,2,7,4,1,3] => 110110 => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,6,1,7,4,5] => [6,5,2,7,1,4,3] => 110101 => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,6,7,1,4,5] => [6,5,2,1,7,4,3] => 111011 => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => [6,5,2,7,4,3,1] => 110111 => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6] => [6,5,7,4,3,1,2] => 101110 => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,7,5,6] => [6,5,7,4,1,3,2] => 101101 => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,5,6] => [6,5,7,1,4,3,2] => 101011 => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => [6,5,1,7,4,3,2] => 110111 => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => [6,5,7,4,3,2,1] => 101111 => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3] => [6,7,4,3,2,1,5] => 011110 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7] => [6,7,4,3,2,5,1] => 011101 => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => [6,7,4,3,5,1,2] => 011010 => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,5,7,3,6] => [6,7,4,3,1,5,2] => 011101 => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7] => [6,7,4,3,5,2,1] => 011011 => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [6,7,4,5,2,1,3] => 010110 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => [6,7,4,5,2,3,1] => 010101 => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [6,7,4,2,5,1,3] => 011010 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,6,7,3,5] => [6,7,4,2,1,5,3] => 011101 => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5,7] => [6,7,4,2,5,3,1] => 011011 => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => [6,7,4,5,3,1,2] => 010110 => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => [6,7,4,5,1,3,2] => 010101 => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,7,3,5,6] => [6,7,4,1,5,3,2] => 011011 => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7] => [6,7,4,5,3,2,1] => 010111 => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,6,7,3] => [6,4,7,3,2,1,5] => 101110 => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,6,3,7] => [6,4,7,3,2,5,1] => 101101 => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6] => [6,4,7,3,5,1,2] => 101010 => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,7,3,6] => [6,4,7,3,1,5,2] => 101101 => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,6,7] => [6,4,7,3,5,2,1] => 101011 => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => [6,4,3,7,2,1,5] => 110110 => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,7] => [6,4,3,7,2,5,1] => 110101 => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,1,7,3] => [6,4,3,2,7,1,5] => 111010 => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,1,3] => [6,4,3,2,1,7,5] => 111101 => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,1,3,7] => [6,4,3,2,7,5,1] => 111011 => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,1,3,7,6] => [6,4,3,7,5,1,2] => 110110 => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,6] => [6,4,3,7,1,5,2] => 110101 => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,7,1,3,6] => [6,4,3,1,7,5,2] => 111011 => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,1,3,6,7] => [6,4,3,7,5,2,1] => 110111 => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,6,7,5] => [6,4,7,5,2,1,3] => 101110 => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5,7] => [6,4,7,5,2,3,1] => 101101 => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5] => [6,4,7,2,5,1,3] => 101010 => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,7,3,5] => [6,4,7,2,1,5,3] => 101101 => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5,7] => [6,4,7,2,5,3,1] => 101011 => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,6,1,3,7,5] => [6,4,2,7,5,1,3] => 110110 => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,6,1,7,3,5] => [6,4,2,7,1,5,3] => 110101 => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,6,7,1,3,5] => [6,4,2,1,7,5,3] => 111011 => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,7] => [6,4,2,7,5,3,1] => 110111 => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,4,1,3,5,7,6] => [6,4,7,5,3,1,2] => 101110 => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,4,1,3,7,5,6] => [6,4,7,5,1,3,2] => 101101 => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,5,6] => [6,4,7,1,5,3,2] => 101011 => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,7,1,3,5,6] => [6,4,1,7,5,3,2] => 110111 => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => [6,4,7,5,3,2,1] => 101111 => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4] => [6,7,5,3,2,1,4] => 011110 => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7] => [6,7,5,3,2,4,1] => 011101 => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => [6,7,5,3,4,1,2] => 011010 => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,3,5,7,4,6] => [6,7,5,3,1,4,2] => 011101 => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7] => [6,7,5,3,4,2,1] => 011011 => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [6,7,3,5,2,1,4] => 010110 => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => [6,7,3,5,2,4,1] => 010101 => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [6,7,3,2,5,1,4] => 011010 => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,6,7,3,4] => [6,7,3,2,1,5,4] => 011101 => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,6,3,4,7] => [6,7,3,2,5,4,1] => 011011 => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => [6,7,3,5,4,1,2] => 010110 => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => [6,7,3,5,1,4,2] => 010101 => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,7,3,4,6] => [6,7,3,1,5,4,2] => 011011 => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,4,6,7] => [6,7,3,5,4,2,1] => 010111 => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,5,1,3,6,7,4] => [6,3,7,5,2,1,4] => 101110 => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,5,1,3,6,4,7] => [6,3,7,5,2,4,1] => 101101 => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4] => [6,3,7,2,5,1,4] => 101010 => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,5,1,6,7,3,4] => [6,3,7,2,1,5,4] => 101101 => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,4,7] => [6,3,7,2,5,4,1] => 101011 => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,6,1,3,7,4] => [6,3,2,7,5,1,4] => 110110 => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,5,6,1,7,3,4] => [6,3,2,7,1,5,4] => 110101 => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,1,3,4] => [6,3,2,1,7,5,4] => 111011 => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,5,6,1,3,4,7] => [6,3,2,7,5,4,1] => 110111 => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1,3,4,7,6] => [6,3,7,5,4,1,2] => 101110 => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,5,1,3,7,4,6] => [6,3,7,5,1,4,2] => 101101 => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,4,6] => [6,3,7,1,5,4,2] => 101011 => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => [6,3,1,7,5,4,2] => 110111 => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => [6,3,7,5,4,2,1] => 101111 => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5] => [6,7,5,4,2,1,3] => 011110 => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7] => [6,7,5,4,2,3,1] => 011101 => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [6,7,5,2,4,1,3] => 011010 => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => [6,7,5,2,1,4,3] => 011101 => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,6,4,5,7] => [6,7,5,2,4,3,1] => 011011 => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => [6,7,2,5,4,1,3] => 010110 => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => [6,7,2,5,1,4,3] => 010101 => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,7,3,4,5] => [6,7,2,1,5,4,3] => 011011 => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => [6,7,2,5,4,3,1] => 010111 => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,6,1,3,4,7,5] => [6,2,7,5,4,1,3] => 101110 => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6,1,3,7,4,5] => [6,2,7,5,1,4,3] => 101101 => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => [6,2,7,1,5,4,3] => 101011 => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => [6,2,1,7,5,4,3] => 110111 => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => [6,2,7,5,4,3,1] => 101111 => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [6,7,5,4,3,1,2] => 011110 => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => [6,7,5,4,1,3,2] => 011101 => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => [6,7,5,1,4,3,2] => 011011 => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => [6,7,1,5,4,3,2] => 010111 => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => [6,1,7,5,4,3,2] => 101111 => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [6,7,5,4,3,2,1] => 011111 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => [7,5,4,3,2,1,6] => 111110 => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => [7,5,4,3,2,6,1] => 111101 => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => [7,5,4,3,6,1,2] => 111010 => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => [7,5,4,3,1,6,2] => 111101 => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => [7,5,4,3,6,2,1] => 111011 => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [7,5,4,6,2,1,3] => 110110 => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [7,5,4,6,2,3,1] => 110101 => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => [7,5,4,2,6,1,3] => 111010 => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => [7,5,4,2,1,6,3] => 111101 => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => [7,5,4,2,6,3,1] => 111011 => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [7,5,4,6,3,1,2] => 110110 => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [7,5,4,6,1,3,2] => 110101 => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => [7,5,4,1,6,3,2] => 111011 => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [7,5,4,6,3,2,1] => 110111 => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [7,5,6,3,2,1,4] => 101110 => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [7,5,6,3,2,4,1] => 101101 => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [7,5,6,3,4,1,2] => 101010 => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [7,5,6,3,1,4,2] => 101101 => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [7,5,6,3,4,2,1] => 101011 => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => [7,5,3,6,2,1,4] => 110110 => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => [7,5,3,6,2,4,1] => 110101 => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => [7,5,3,2,6,1,4] => 111010 => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => [7,5,3,2,1,6,4] => 111101 => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => [7,5,3,2,6,4,1] => 111011 => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => [7,5,3,6,4,1,2] => 110110 => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => [7,5,3,6,1,4,2] => 110101 => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => [7,5,3,1,6,4,2] => 111011 => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => [7,5,3,6,4,2,1] => 110111 => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [7,5,6,4,2,1,3] => 101110 => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [7,5,6,4,2,3,1] => 101101 => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [7,5,6,2,4,1,3] => 101010 => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [7,5,6,2,1,4,3] => 101101 => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [7,5,6,2,4,3,1] => 101011 => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => [7,5,2,6,4,1,3] => 110110 => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => [7,5,2,6,1,4,3] => 110101 => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => [7,5,2,1,6,4,3] => 111011 => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => [7,5,2,6,4,3,1] => 110111 => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [7,5,6,4,3,1,2] => 101110 => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [7,5,6,4,1,3,2] => 101101 => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [7,5,6,1,4,3,2] => 101011 => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => [7,5,1,6,4,3,2] => 110111 => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [7,5,6,4,3,2,1] => 101111 => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,2] => [5,7,4,3,2,1,6] => 011110 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,2,7] => [5,7,4,3,2,6,1] => 011101 => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6] => [5,7,4,3,6,1,2] => 011010 => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,5,7,2,6] => [5,7,4,3,1,6,2] => 011101 => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,5,2,6,7] => [5,7,4,3,6,2,1] => 011011 => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [5,7,4,6,2,1,3] => 010110 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => [5,7,4,6,2,3,1] => 010101 => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [5,7,4,2,6,1,3] => 011010 => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,6,7,2,5] => [5,7,4,2,1,6,3] => 011101 => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,6,2,5,7] => [5,7,4,2,6,3,1] => 011011 => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => [5,7,4,6,3,1,2] => 010110 => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => [5,7,4,6,1,3,2] => 010101 => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,7,2,5,6] => [5,7,4,1,6,3,2] => 011011 => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,5,6,7] => [5,7,4,6,3,2,1] => 010111 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,6,7,2] => [5,4,7,3,2,1,6] => 101110 => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,6,2,7] => [5,4,7,3,2,6,1] => 101101 => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6] => [5,4,7,3,6,1,2] => 101010 => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,7,2,6] => [5,4,7,3,1,6,2] => 101101 => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,6,7] => [5,4,7,3,6,2,1] => 101011 => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,1,6,7,2] => [5,4,3,7,2,1,6] => 110110 => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,7] => [5,4,3,7,2,6,1] => 110101 => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,1,7,2] => [5,4,3,2,7,1,6] => 111010 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,2] => [5,4,3,2,1,7,6] => 111101 => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,1,2,7] => [5,4,3,2,7,6,1] => 111011 => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,1,2,7,6] => [5,4,3,7,6,1,2] => 110110 => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,6] => [5,4,3,7,1,6,2] => 110101 => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,7,1,2,6] => [5,4,3,1,7,6,2] => 111011 => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6,7] => [5,4,3,7,6,2,1] => 110111 => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,1,2,6,7,5] => [5,4,7,6,2,1,3] => 101110 => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5,7] => [5,4,7,6,2,3,1] => 101101 => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5] => [5,4,7,2,6,1,3] => 101010 => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,7,2,5] => [5,4,7,2,1,6,3] => 101101 => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5,7] => [5,4,7,2,6,3,1] => 101011 => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,6,1,2,7,5] => [5,4,2,7,6,1,3] => 110110 => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,6,1,7,2,5] => [5,4,2,7,1,6,3] => 110101 => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,6,7,1,2,5] => [5,4,2,1,7,6,3] => 111011 => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5,7] => [5,4,2,7,6,3,1] => 110111 => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,1,2,5,7,6] => [5,4,7,6,3,1,2] => 101110 => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,2,7,5,6] => [5,4,7,6,1,3,2] => 101101 => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,5,6] => [5,4,7,1,6,3,2] => 101011 => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,7,1,2,5,6] => [5,4,1,7,6,3,2] => 110111 => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [5,4,7,6,3,2,1] => 101111 => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,5,6,7,4] => [5,7,6,3,2,1,4] => 011110 => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,5,6,4,7] => [5,7,6,3,2,4,1] => 011101 => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => [5,7,6,3,4,1,2] => 011010 => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,7,4,6] => [5,7,6,3,1,4,2] => 011101 => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,5,4,6,7] => [5,7,6,3,4,2,1] => 011011 => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [5,7,3,6,2,1,4] => 010110 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,7] => [5,7,3,6,2,4,1] => 010101 => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [5,7,3,2,6,1,4] => 011010 => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,6,7,2,4] => [5,7,3,2,1,6,4] => 011101 => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,6,2,4,7] => [5,7,3,2,6,4,1] => 011011 => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,7,6] => [5,7,3,6,4,1,2] => 010110 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,6] => [5,7,3,6,1,4,2] => 010101 => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,7,2,4,6] => [5,7,3,1,6,4,2] => 011011 => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,4,6,7] => [5,7,3,6,4,2,1] => 010111 => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,5,1,2,6,7,4] => [5,3,7,6,2,1,4] => 101110 => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,6,4,7] => [5,3,7,6,2,4,1] => 101101 => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => [5,3,7,2,6,1,4] => 101010 => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,5,1,6,7,2,4] => [5,3,7,2,1,6,4] => 101101 => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,4,7] => [5,3,7,2,6,4,1] => 101011 => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,5,6,1,2,7,4] => [5,3,2,7,6,1,4] => 110110 => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,5,6,1,7,2,4] => [5,3,2,7,1,6,4] => 110101 => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,1,2,4] => [5,3,2,1,7,6,4] => 111011 => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => [5,3,2,7,6,4,1] => 110111 => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,7,6] => [5,3,7,6,4,1,2] => 101110 => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,7,4,6] => [5,3,7,6,1,4,2] => 101101 => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,4,6] => [5,3,7,1,6,4,2] => 101011 => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,5,7,1,2,4,6] => [5,3,1,7,6,4,2] => 110111 => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,5,1,2,4,6,7] => [5,3,7,6,4,2,1] => 101111 => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,2,4,6,7,5] => [5,7,6,4,2,1,3] => 011110 => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,2,4,6,5,7] => [5,7,6,4,2,3,1] => 011101 => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [5,7,6,2,4,1,3] => 011010 => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,2,6,7,4,5] => [5,7,6,2,1,4,3] => 011101 => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,2,6,4,5,7] => [5,7,6,2,4,3,1] => 011011 => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,4,7,5] => [5,7,2,6,4,1,3] => 010110 => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,5] => [5,7,2,6,1,4,3] => 010101 => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,7,2,4,5] => [5,7,2,1,6,4,3] => 011011 => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,4,5,7] => [5,7,2,6,4,3,1] => 010111 => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1,2,4,7,5] => [5,2,7,6,4,1,3] => 101110 => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [3,6,1,2,7,4,5] => [5,2,7,6,1,4,3] => 101101 => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,6,1,7,2,4,5] => [5,2,7,1,6,4,3] => 101011 => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => [5,2,1,7,6,4,3] => 110111 => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,6,1,2,4,5,7] => [5,2,7,6,4,3,1] => 101111 => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [5,7,6,4,3,1,2] => 011110 => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,2,4,7,5,6] => [5,7,6,4,1,3,2] => 011101 => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,2,7,4,5,6] => [5,7,6,1,4,3,2] => 011011 => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,4,5,6] => [5,7,1,6,4,3,2] => 010111 => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,7,1,2,4,5,6] => [5,1,7,6,4,3,2] => 101111 => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => [5,7,6,4,3,2,1] => 011111 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [7,6,4,3,2,1,5] => 111110 => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [7,6,4,3,2,5,1] => 111101 => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [7,6,4,3,5,1,2] => 111010 => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [7,6,4,3,1,5,2] => 111101 => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [7,6,4,3,5,2,1] => 111011 => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [7,6,4,5,2,1,3] => 110110 => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [7,6,4,5,2,3,1] => 110101 => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [7,6,4,2,5,1,3] => 111010 => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [7,6,4,2,1,5,3] => 111101 => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [7,6,4,2,5,3,1] => 111011 => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [7,6,4,5,3,1,2] => 110110 => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [7,6,4,5,1,3,2] => 110101 => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [7,6,4,1,5,3,2] => 111011 => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [7,6,4,5,3,2,1] => 110111 => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => [7,4,6,3,2,1,5] => 101110 => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => [7,4,6,3,2,5,1] => 101101 => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => [7,4,6,3,5,1,2] => 101010 => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => [7,4,6,3,1,5,2] => 101101 => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => [7,4,6,3,5,2,1] => 101011 => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => [7,4,3,6,2,1,5] => 110110 => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => [7,4,3,6,2,5,1] => 110101 => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => [7,4,3,2,6,1,5] => 111010 => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => [7,4,3,2,1,6,5] => 111101 => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => [7,4,3,2,6,5,1] => 111011 => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => [7,4,3,6,5,1,2] => 110110 => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => [7,4,3,6,1,5,2] => 110101 => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => [7,4,3,1,6,5,2] => 111011 => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => [7,4,3,6,5,2,1] => 110111 => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [7,4,6,5,2,1,3] => 101110 => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [7,4,6,5,2,3,1] => 101101 => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => [7,4,6,2,5,1,3] => 101010 => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => [7,4,6,2,1,5,3] => 101101 => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => [7,4,6,2,5,3,1] => 101011 => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => [7,4,2,6,5,1,3] => 110110 => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => [7,4,2,6,1,5,3] => 110101 => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => [7,4,2,1,6,5,3] => 111011 => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => [7,4,2,6,5,3,1] => 110111 => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [7,4,6,5,3,1,2] => 101110 => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [7,4,6,5,1,3,2] => 101101 => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => [7,4,6,1,5,3,2] => 101011 => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => [7,4,1,6,5,3,2] => 110111 => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [7,4,6,5,3,2,1] => 101111 => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,6,7,3] => [4,7,6,3,2,1,5] => 011110 => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2,5,6,3,7] => [4,7,6,3,2,5,1] => 011101 => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6] => [4,7,6,3,5,1,2] => 011010 => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,5,7,3,6] => [4,7,6,3,1,5,2] => 011101 => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,3,6,7] => [4,7,6,3,5,2,1] => 011011 => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [4,7,3,6,2,1,5] => 010110 => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,7] => [4,7,3,6,2,5,1] => 010101 => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [4,7,3,2,6,1,5] => 011010 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,6,7,2,3] => [4,7,3,2,1,6,5] => 011101 => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,6,2,3,7] => [4,7,3,2,6,5,1] => 011011 => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,3,7,6] => [4,7,3,6,5,1,2] => 010110 => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,6] => [4,7,3,6,1,5,2] => 010101 => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,7,2,3,6] => [4,7,3,1,6,5,2] => 011011 => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,3,6,7] => [4,7,3,6,5,2,1] => 010111 => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,1,2,6,7,3] => [4,3,7,6,2,1,5] => 101110 => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,6,3,7] => [4,3,7,6,2,5,1] => 101101 => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => [4,3,7,2,6,1,5] => 101010 => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,1,6,7,2,3] => [4,3,7,2,1,6,5] => 101101 => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,3,7] => [4,3,7,2,6,5,1] => 101011 => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,1,2,7,3] => [4,3,2,7,6,1,5] => 110110 => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,1,7,2,3] => [4,3,2,7,1,6,5] => 110101 => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,1,2,3] => [4,3,2,1,7,6,5] => 111011 => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [4,3,2,7,6,5,1] => 110111 => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,1,2,3,7,6] => [4,3,7,6,5,1,2] => 101110 => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,1,2,7,3,6] => [4,3,7,6,1,5,2] => 101101 => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,3,6] => [4,3,7,1,6,5,2] => 101011 => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => [4,3,1,7,6,5,2] => 110111 => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7] => [4,3,7,6,5,2,1] => 101111 => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,6,7,5] => [4,7,6,5,2,1,3] => 011110 => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5,7] => [4,7,6,5,2,3,1] => 011101 => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [4,7,6,2,5,1,3] => 011010 => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [4,1,2,6,7,3,5] => [4,7,6,2,1,5,3] => 011101 => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5,7] => [4,7,6,2,5,3,1] => 011011 => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,3,7,5] => [4,7,2,6,5,1,3] => 010110 => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => [4,7,2,6,1,5,3] => 010101 => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,7,2,3,5] => [4,7,2,1,6,5,3] => 011011 => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5,7] => [4,7,2,6,5,3,1] => 010111 => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => [4,2,7,6,5,1,3] => 101110 => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,6,1,2,7,3,5] => [4,2,7,6,1,5,3] => 101101 => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,6,1,7,2,3,5] => [4,2,7,1,6,5,3] => 101011 => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => [4,2,1,7,6,5,3] => 110111 => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5,7] => [4,2,7,6,5,3,1] => 101111 => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [4,7,6,5,3,1,2] => 011110 => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [4,1,2,3,7,5,6] => [4,7,6,5,1,3,2] => 011101 => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,2,7,3,5,6] => [4,7,6,1,5,3,2] => 011011 => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,3,5,6] => [4,7,1,6,5,3,2] => 010111 => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,7,1,2,3,5,6] => [4,1,7,6,5,3,2] => 101111 => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => [4,7,6,5,3,2,1] => 011111 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [7,6,5,3,2,1,4] => 111110 => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [7,6,5,3,2,4,1] => 111101 => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [7,6,5,3,4,1,2] => 111010 => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [7,6,5,3,1,4,2] => 111101 => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [7,6,5,3,4,2,1] => 111011 => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [7,6,3,5,2,1,4] => 110110 => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [7,6,3,5,2,4,1] => 110101 => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [7,6,3,2,5,1,4] => 111010 => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [7,6,3,2,1,5,4] => 111101 => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [7,6,3,2,5,4,1] => 111011 => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [7,6,3,5,4,1,2] => 110110 => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [7,6,3,5,1,4,2] => 110101 => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [7,6,3,1,5,4,2] => 111011 => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [7,6,3,5,4,2,1] => 110111 => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => [7,3,6,5,2,1,4] => 101110 => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => [7,3,6,5,2,4,1] => 101101 => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => [7,3,6,2,5,1,4] => 101010 => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => [7,3,6,2,1,5,4] => 101101 => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => [7,3,6,2,5,4,1] => 101011 => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => [7,3,2,6,5,1,4] => 110110 => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => [7,3,2,6,1,5,4] => 110101 => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => [7,3,2,1,6,5,4] => 111011 => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => [7,3,2,6,5,4,1] => 110111 => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => [7,3,6,5,4,1,2] => 101110 => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => [7,3,6,5,1,4,2] => 101101 => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => [7,3,6,1,5,4,2] => 101011 => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => [7,3,1,6,5,4,2] => 110111 => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => [7,3,6,5,4,2,1] => 101111 => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,2,3,6,7,4] => [3,7,6,5,2,1,4] => 011110 => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,1,2,3,6,4,7] => [3,7,6,5,2,4,1] => 011101 => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [3,7,6,2,5,1,4] => 011010 => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,1,2,6,7,3,4] => [3,7,6,2,1,5,4] => 011101 => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,1,2,6,3,4,7] => [3,7,6,2,5,4,1] => 011011 => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => [3,7,2,6,5,1,4] => 010110 => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => [3,7,2,6,1,5,4] => 010101 => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,1,6,7,2,3,4] => [3,7,2,1,6,5,4] => 011011 => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,3,4,7] => [3,7,2,6,5,4,1] => 010111 => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => [3,2,7,6,5,1,4] => 101110 => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,6,1,2,7,3,4] => [3,2,7,6,1,5,4] => 101101 => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,6,1,7,2,3,4] => [3,2,7,1,6,5,4] => 101011 => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,1,2,3,4] => [3,2,1,7,6,5,4] => 110111 => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => [3,2,7,6,5,4,1] => 101111 => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [3,7,6,5,4,1,2] => 011110 => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,2,3,7,4,6] => [3,7,6,5,1,4,2] => 011101 => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,1,2,7,3,4,6] => [3,7,6,1,5,4,2] => 011011 => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,3,4,6] => [3,7,1,6,5,4,2] => 010111 => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => [3,1,7,6,5,4,2] => 101111 => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7] => [3,7,6,5,4,2,1] => 011111 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [7,6,5,4,2,1,3] => 111110 => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [7,6,5,4,2,3,1] => 111101 => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [7,6,5,2,4,1,3] => 111010 => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [7,6,5,2,1,4,3] => 111101 => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [7,6,5,2,4,3,1] => 111011 => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [7,6,2,5,4,1,3] => 110110 => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [7,6,2,5,1,4,3] => 110101 => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [7,6,2,1,5,4,3] => 111011 => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [7,6,2,5,4,3,1] => 110111 => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => [7,2,6,5,4,1,3] => 101110 => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => [7,2,6,5,1,4,3] => 101101 => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => [7,2,6,1,5,4,3] => 101011 => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => [7,2,1,6,5,4,3] => 110111 => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => [7,2,6,5,4,3,1] => 101111 => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [2,7,6,5,4,1,3] => 011110 => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,1,2,3,7,4,5] => [2,7,6,5,1,4,3] => 011101 => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,1,2,7,3,4,5] => [2,7,6,1,5,4,3] => 011011 => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [6,1,7,2,3,4,5] => [2,7,1,6,5,4,3] => 010111 => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [6,7,1,2,3,4,5] => [2,1,7,6,5,4,3] => 101111 => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5,7] => [2,7,6,5,4,3,1] => 011111 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [7,6,5,4,3,1,2] => 111110 => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [7,6,5,4,1,3,2] => 111101 => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [7,6,5,1,4,3,2] => 111011 => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [7,6,1,5,4,3,2] => 110111 => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => [7,1,6,5,4,3,2] => 101111 => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [1,7,6,5,4,3,2] => 011111 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => 111111 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,1] => [7,6,5,4,3,2,1,8] => 1111110 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,1,8] => [7,6,5,4,3,2,8,1] => 1111101 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7] => [7,6,5,4,3,8,1,2] => 1111010 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,8,1,7] => [7,6,5,4,3,1,8,2] => 1111101 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,1,7,8] => [7,6,5,4,3,8,2,1] => 1111011 => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,8,6] => [7,6,5,4,8,2,1,3] => 1110110 => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,8] => [7,6,5,4,8,2,3,1] => 1110101 => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,7,1,8,6] => [7,6,5,4,2,8,1,3] => 1111010 => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,7,8,1,6] => [7,6,5,4,2,1,8,3] => 1111101 => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6,8] => [7,6,5,4,2,8,3,1] => 1111011 => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,5,1,6,8,7] => [7,6,5,4,8,3,1,2] => 1110110 => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,1,8,6,7] => [7,6,5,4,8,1,3,2] => 1110101 => 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,8,1,6,7] => [7,6,5,4,1,8,3,2] => 1111011 => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [7,6,5,4,8,3,2,1] => 1110111 => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,5] => [7,6,5,8,3,2,1,4] => 1101110 => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,4,1,6,7,5,8] => [7,6,5,8,3,2,4,1] => 1101101 => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7] => [7,6,5,8,3,4,1,2] => 1101010 => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,8,5,7] => [7,6,5,8,3,1,4,2] => 1101101 => 0
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,1,6,5,7,8] => [7,6,5,8,3,4,2,1] => 1101011 => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,4,6,1,7,5,8] => [7,6,5,3,8,2,4,1] => 1110101 => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,1,5] => [7,6,5,3,2,1,8,4] => 1111101 => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,4,6,7,1,5,8] => [7,6,5,3,2,8,4,1] => 1111011 => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,8,7] => [7,6,5,3,8,4,1,2] => 1110110 => 0
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,4,6,8,1,5,7] => [7,6,5,3,1,8,4,2] => 1111011 => 0
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8] => [7,6,5,3,8,4,2,1] => 1110111 => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,4,1,5,7,8,6] => [7,6,5,8,4,2,1,3] => 1101110 => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,4,1,5,7,6,8] => [7,6,5,8,4,2,3,1] => 1101101 => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,1,7,5,8,6] => [7,6,5,8,2,4,1,3] => 1101010 => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,1,7,8,5,6] => [7,6,5,8,2,1,4,3] => 1101101 => 0
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,4,1,7,5,6,8] => [7,6,5,8,2,4,3,1] => 1101011 => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,4,7,1,5,8,6] => [7,6,5,2,8,4,1,3] => 1110110 => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,4,7,1,8,5,6] => [7,6,5,2,8,1,4,3] => 1110101 => 0
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,7,8,1,5,6] => [7,6,5,2,1,8,4,3] => 1111011 => 0
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => [7,6,5,2,8,4,3,1] => 1110111 => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,4,1,5,6,8,7] => [7,6,5,8,4,3,1,2] => 1101110 => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,4,1,5,8,6,7] => [7,6,5,8,4,1,3,2] => 1101101 => 0
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [7,6,5,8,1,4,3,2] => 1101011 => 0
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [7,6,5,1,8,4,3,2] => 1110111 => 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [7,6,5,8,4,3,2,1] => 1101111 => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,4] => [7,6,8,4,3,2,1,5] => 1011110 => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,5,6,7,4,8] => [7,6,8,4,3,2,5,1] => 1011101 => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,5,6,8,4,7] => [7,6,8,4,3,1,5,2] => 1011101 => 0
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,5,6,4,7,8] => [7,6,8,4,3,5,2,1] => 1011011 => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,7,8,6] => [7,6,8,4,5,2,1,3] => 1010110 => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8] => [7,6,8,4,5,2,3,1] => 1010101 => 0
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6,8] => [7,6,8,4,2,5,3,1] => 1011011 => 0
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,5,8,4,6,7] => [7,6,8,4,1,5,3,2] => 1011011 => 0
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,5,4,6,7,8] => [7,6,8,4,5,3,2,1] => 1010111 => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,4] => [7,6,4,8,3,2,1,5] => 1101110 => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,5,1,6,7,4,8] => [7,6,4,8,3,2,5,1] => 1101101 => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,5,1,6,8,4,7] => [7,6,4,8,3,1,5,2] => 1101101 => 0
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,5,1,6,4,7,8] => [7,6,4,8,3,5,2,1] => 1101011 => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,5,6,1,7,8,4] => [7,6,4,3,8,2,1,5] => 1110110 => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,5,6,1,7,4,8] => [7,6,4,3,8,2,5,1] => 1110101 => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,5,6,7,1,8,4] => [7,6,4,3,2,8,1,5] => 1111010 => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,1,4] => [7,6,4,3,2,1,8,5] => 1111101 => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,6,7,1,4,8] => [7,6,4,3,2,8,5,1] => 1111011 => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,6,1,4,8,7] => [7,6,4,3,8,5,1,2] => 1110110 => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,6,1,8,4,7] => [7,6,4,3,8,1,5,2] => 1110101 => 0
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,8,1,4,7] => [7,6,4,3,1,8,5,2] => 1111011 => 0
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => [7,6,4,3,8,5,2,1] => 1110111 => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,7,8,6] => [7,6,4,8,5,2,1,3] => 1101110 => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6,8] => [7,6,4,8,5,2,3,1] => 1101101 => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,7,4,8,6] => [7,6,4,8,2,5,1,3] => 1101010 => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,7,8,4,6] => [7,6,4,8,2,1,5,3] => 1101101 => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,7,1,4,8,6] => [7,6,4,2,8,5,1,3] => 1110110 => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,7,1,8,4,6] => [7,6,4,2,8,1,5,3] => 1110101 => 0
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6,8] => [7,6,4,2,8,5,3,1] => 1110111 => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,3,5,1,4,6,8,7] => [7,6,4,8,5,3,1,2] => 1101110 => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,5,1,4,8,6,7] => [7,6,4,8,5,1,3,2] => 1101101 => 0
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,8,4,6,7] => [7,6,4,8,1,5,3,2] => 1101011 => 0
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,8,1,4,6,7] => [7,6,4,1,8,5,3,2] => 1110111 => 0
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,1,4,6,7,8] => [7,6,4,8,5,3,2,1] => 1101111 => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,5] => [7,6,8,5,3,2,1,4] => 1011110 => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,4,6,7,5,8] => [7,6,8,5,3,2,4,1] => 1011101 => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,1,4,6,5,8,7] => [7,6,8,5,3,4,1,2] => 1011010 => 0
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,1,4,6,5,7,8] => [7,6,8,5,3,4,2,1] => 1011011 => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,3,1,6,4,7,8,5] => [7,6,8,3,5,2,1,4] => 1010110 => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,8] => [7,6,8,3,5,2,4,1] => 1010101 => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,3,1,6,7,4,8,5] => [7,6,8,3,2,5,1,4] => 1011010 => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,4,5] => [7,6,8,3,2,1,5,4] => 1011101 => 0
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,1,6,7,4,5,8] => [7,6,8,3,2,5,4,1] => 1011011 => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,4,8,5,7] => [7,6,8,3,5,1,4,2] => 1010101 => 0
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,1,6,8,4,5,7] => [7,6,8,3,1,5,4,2] => 1011011 => 0
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,1,6,4,5,7,8] => [7,6,8,3,5,4,2,1] => 1010111 => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,1,4,7,8,5] => [7,6,3,8,5,2,1,4] => 1101110 => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,3,6,1,7,4,8,5] => [7,6,3,8,2,5,1,4] => 1101010 => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,1,7,8,4,5] => [7,6,3,8,2,1,5,4] => 1101101 => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,3,6,7,1,4,8,5] => [7,6,3,2,8,5,1,4] => 1110110 => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,6,7,1,8,4,5] => [7,6,3,2,8,1,5,4] => 1110101 => 0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,6,7,8,1,4,5] => [7,6,3,2,1,8,5,4] => 1111011 => 0
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,6,7,1,4,5,8] => [7,6,3,2,8,5,4,1] => 1110111 => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,8,7] => [7,6,3,8,5,4,1,2] => 1101110 => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,6,1,4,8,5,7] => [7,6,3,8,5,1,4,2] => 1101101 => 0
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,6,1,8,4,5,7] => [7,6,3,8,1,5,4,2] => 1101011 => 0
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,6,1,4,5,7,8] => [7,6,3,8,5,4,2,1] => 1101111 => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,4,5,7,8,6] => [7,6,8,5,4,2,1,3] => 1011110 => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,1,4,5,7,6,8] => [7,6,8,5,4,2,3,1] => 1011101 => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,1,4,7,5,8,6] => [7,6,8,5,2,4,1,3] => 1011010 => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,4,7,8,5,6] => [7,6,8,5,2,1,4,3] => 1011101 => 0
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,1,4,7,5,6,8] => [7,6,8,5,2,4,3,1] => 1011011 => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,7,4,8,5,6] => [7,6,8,2,5,1,4,3] => 1010101 => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,1,4,8,5,6] => [7,6,2,8,5,1,4,3] => 1101101 => 0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [7,6,2,1,8,5,4,3] => 1110111 => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,1,4,5,6,8,7] => [7,6,8,5,4,3,1,2] => 1011110 => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => [7,6,8,5,4,1,3,2] => 1011101 => 0
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,1,4,8,5,6,7] => [7,6,8,5,1,4,3,2] => 1011011 => 0
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,1,8,4,5,6,7] => [7,6,8,1,5,4,3,2] => 1010111 => 0
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [7,6,1,8,5,4,3,2] => 1101111 => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [7,6,8,5,4,3,2,1] => 1011111 => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,3] => [7,8,5,4,3,2,1,6] => 0111110 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,7,3,8] => [7,8,5,4,3,2,6,1] => 0111101 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,3,8,7] => [7,8,5,4,3,6,1,2] => 0111010 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,4,5,6,8,3,7] => [7,8,5,4,3,1,6,2] => 0111101 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,4,5,6,3,7,8] => [7,8,5,4,3,6,2,1] => 0111011 => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,7,3,8,6] => [7,8,5,4,2,6,1,3] => 0111010 => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4,5,7,8,3,6] => [7,8,5,4,2,1,6,3] => 0111101 => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4,5,8,3,6,7] => [7,8,5,4,1,6,3,2] => 0111011 => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [7,8,5,6,3,2,1,4] => 0101110 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7] => [7,8,5,6,3,4,1,2] => 0101010 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,8,5,7] => [7,8,5,6,3,1,4,2] => 0101101 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,7,8] => [7,8,5,6,3,4,2,1] => 0101011 => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,6,3,7,8,5] => [7,8,5,3,6,2,1,4] => 0110110 => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,6,3,7,5,8] => [7,8,5,3,6,2,4,1] => 0110101 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,6,7,3,8,5] => [7,8,5,3,2,6,1,4] => 0111010 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,6,7,8,3,5] => [7,8,5,3,2,1,6,4] => 0111101 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,6,7,3,5,8] => [7,8,5,3,2,6,4,1] => 0111011 => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,8,7] => [7,8,5,3,6,4,1,2] => 0110110 => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,8,5,7] => [7,8,5,3,6,1,4,2] => 0110101 => 1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,8,3,5,7] => [7,8,5,3,1,6,4,2] => 0111011 => 1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,6,3,5,7,8] => [7,8,5,3,6,4,2,1] => 0110111 => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => [7,8,5,6,4,2,1,3] => 0101110 => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,3,7,5,8,6] => [7,8,5,6,2,4,1,3] => 0101010 => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => [7,8,5,6,2,1,4,3] => 0101101 => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,4,3,7,5,6,8] => [7,8,5,6,2,4,3,1] => 0101011 => 1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,4,7,8,3,5,6] => [7,8,5,2,1,6,4,3] => 0111011 => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,4,7,3,5,6,8] => [7,8,5,2,6,4,3,1] => 0110111 => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,3,5,6,8,7] => [7,8,5,6,4,3,1,2] => 0101110 => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,3,5,8,6,7] => [7,8,5,6,4,1,3,2] => 0101101 => 1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,3,8,5,6,7] => [7,8,5,6,1,4,3,2] => 0101011 => 1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,8,3,5,6,7] => [7,8,5,1,6,4,3,2] => 0110111 => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,5,6,7,8] => [7,8,5,6,4,3,2,1] => 0101111 => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,3] => [7,5,8,4,3,2,1,6] => 1011110 => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,5,6,7,3,8] => [7,5,8,4,3,2,6,1] => 1011101 => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,4,1,5,6,3,8,7] => [7,5,8,4,3,6,1,2] => 1011010 => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,5,6,8,3,7] => [7,5,8,4,3,1,6,2] => 1011101 => 0
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,4,1,5,6,3,7,8] => [7,5,8,4,3,6,2,1] => 1011011 => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,8] => [7,5,8,4,6,2,3,1] => 1010101 => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,4,1,5,7,3,8,6] => [7,5,8,4,2,6,1,3] => 1011010 => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,4,1,5,7,8,3,6] => [7,5,8,4,2,1,6,3] => 1011101 => 0
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,4,1,5,7,3,6,8] => [7,5,8,4,2,6,3,1] => 1011011 => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,3,6,8,7] => [7,5,8,4,6,3,1,2] => 1010110 => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,5,3,8,6,7] => [7,5,8,4,6,1,3,2] => 1010101 => 0
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,4,1,5,8,3,6,7] => [7,5,8,4,1,6,3,2] => 1011011 => 0
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,3,6,7,8] => [7,5,8,4,6,3,2,1] => 1010111 => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,4,5,1,6,7,3,8] => [7,5,4,8,3,2,6,1] => 1101101 => 0
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,4,5,1,6,3,7,8] => [7,5,4,8,3,6,2,1] => 1101011 => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,6,1,7,8,3] => [7,5,4,3,8,2,1,6] => 1110110 => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,6,1,7,3,8] => [7,5,4,3,8,2,6,1] => 1110101 => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,1,8,3] => [7,5,4,3,2,8,1,6] => 1111010 => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,1,3] => [7,5,4,3,2,1,8,6] => 1111101 => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,7,1,3,8] => [7,5,4,3,2,8,6,1] => 1111011 => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,6,1,8,3,7] => [7,5,4,3,8,1,6,2] => 1110101 => 0
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,6,8,1,3,7] => [7,5,4,3,1,8,6,2] => 1111011 => 0
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => [7,5,4,3,8,6,2,1] => 1110111 => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,4,5,1,3,7,8,6] => [7,5,4,8,6,2,1,3] => 1101110 => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,4,5,1,7,3,8,6] => [7,5,4,8,2,6,1,3] => 1101010 => 0
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6,8] => [7,5,4,8,2,6,3,1] => 1101011 => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,7,1,3,8,6] => [7,5,4,2,8,6,1,3] => 1110110 => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,7,1,8,3,6] => [7,5,4,2,8,1,6,3] => 1110101 => 0
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,7,8,1,3,6] => [7,5,4,2,1,8,6,3] => 1111011 => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,4,5,1,3,6,8,7] => [7,5,4,8,6,3,1,2] => 1101110 => 0
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => [7,5,4,8,1,6,3,2] => 1101011 => 0
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,4,5,8,1,3,6,7] => [7,5,4,1,8,6,3,2] => 1110111 => 0
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,1,3,6,7,8] => [7,5,4,8,6,3,2,1] => 1101111 => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,6,7,8,5] => [7,5,8,6,3,2,1,4] => 1011110 => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,6,7,5,8] => [7,5,8,6,3,2,4,1] => 1011101 => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7] => [7,5,8,6,3,4,1,2] => 1011010 => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,8,5,7] => [7,5,8,6,3,1,4,2] => 1011101 => 0
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,6,5,7,8] => [7,5,8,6,3,4,2,1] => 1011011 => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,8,5] => [7,5,8,3,6,2,1,4] => 1010110 => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5,8] => [7,5,8,3,6,2,4,1] => 1010101 => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,6,7,3,8,5] => [7,5,8,3,2,6,1,4] => 1011010 => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,6,7,8,3,5] => [7,5,8,3,2,1,6,4] => 1011101 => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,8,7] => [7,5,8,3,6,4,1,2] => 1010110 => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,7] => [7,5,8,3,6,1,4,2] => 1010101 => 0
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,8,3,5,7] => [7,5,8,3,1,6,4,2] => 1011011 => 0
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,6,3,5,7,8] => [7,5,8,3,6,4,2,1] => 1010111 => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,6,1,3,7,8,5] => [7,5,3,8,6,2,1,4] => 1101110 => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,6,1,3,7,5,8] => [7,5,3,8,6,2,4,1] => 1101101 => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,6,1,7,3,8,5] => [7,5,3,8,2,6,1,4] => 1101010 => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,6,1,7,8,3,5] => [7,5,3,8,2,1,6,4] => 1101101 => 0
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,6,1,7,3,5,8] => [7,5,3,8,2,6,4,1] => 1101011 => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,6,7,1,3,8,5] => [7,5,3,2,8,6,1,4] => 1110110 => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,6,7,1,8,3,5] => [7,5,3,2,8,1,6,4] => 1110101 => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,6,7,8,1,3,5] => [7,5,3,2,1,8,6,4] => 1111011 => 0
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => [7,5,3,2,8,6,4,1] => 1110111 => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,8,7] => [7,5,3,8,6,4,1,2] => 1101110 => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,8,5,7] => [7,5,3,8,6,1,4,2] => 1101101 => 0
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [7,5,3,8,1,6,4,2] => 1101011 => 0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [7,5,3,1,8,6,4,2] => 1110111 => 0
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,6,1,3,5,7,8] => [7,5,3,8,6,4,2,1] => 1101111 => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,3,5,7,8,6] => [7,5,8,6,4,2,1,3] => 1011110 => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,3,7,5,8,6] => [7,5,8,6,2,4,1,3] => 1011010 => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,3,7,8,5,6] => [7,5,8,6,2,1,4,3] => 1011101 => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,7,3,5,8,6] => [7,5,8,2,6,4,1,3] => 1010110 => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,7,3,8,5,6] => [7,5,8,2,6,1,4,3] => 1010101 => 0
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,7,8,3,5,6] => [7,5,8,2,1,6,4,3] => 1011011 => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,4,7,1,3,5,8,6] => [7,5,2,8,6,4,1,3] => 1101110 => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,4,7,1,3,8,5,6] => [7,5,2,8,6,1,4,3] => 1101101 => 0
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,4,7,1,8,3,5,6] => [7,5,2,8,1,6,4,3] => 1101011 => 0
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => [7,5,2,1,8,6,4,3] => 1110111 => 0
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6,8] => [7,5,2,8,6,4,3,1] => 1101111 => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1,3,5,8,6,7] => [7,5,8,6,4,1,3,2] => 1011101 => 0
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1,3,8,5,6,7] => [7,5,8,6,1,4,3,2] => 1011011 => 0
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1,8,3,5,6,7] => [7,5,8,1,6,4,3,2] => 1010111 => 0
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,8,1,3,5,6,7] => [7,5,1,8,6,4,3,2] => 1101111 => 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8] => [7,5,8,6,4,3,2,1] => 1011111 => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,4] => [7,8,6,4,3,2,1,5] => 0111110 => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,1,3,5,6,7,4,8] => [7,8,6,4,3,2,5,1] => 0111101 => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,8,4,7] => [7,8,6,4,3,1,5,2] => 0111101 => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,1,3,5,6,4,7,8] => [7,8,6,4,3,5,2,1] => 0111011 => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,1,3,5,7,4,8,6] => [7,8,6,4,2,5,1,3] => 0111010 => 1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,4,6,8] => [7,8,6,4,2,5,3,1] => 0111011 => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4,6,8,7] => [7,8,6,4,5,3,1,2] => 0110110 => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,3,5,4,6,7,8] => [7,8,6,4,5,3,2,1] => 0110111 => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => [7,8,4,6,3,2,1,5] => 0101110 => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7] => [7,8,4,6,3,5,1,2] => 0101010 => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,1,5,6,3,7,8,4] => [7,8,4,3,6,2,1,5] => 0110110 => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,1,5,6,3,7,4,8] => [7,8,4,3,6,2,5,1] => 0110101 => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,3,4] => [7,8,4,3,2,1,6,5] => 0111101 => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,1,5,6,7,3,4,8] => [7,8,4,3,2,6,5,1] => 0111011 => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,8,7] => [7,8,4,3,6,5,1,2] => 0110110 => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,1,5,6,3,8,4,7] => [7,8,4,3,6,1,5,2] => 0110101 => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,1,5,6,3,4,7,8] => [7,8,4,3,6,5,2,1] => 0110111 => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,1,5,3,7,4,8,6] => [7,8,4,6,2,5,1,3] => 0101010 => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,5,7,3,4,8,6] => [7,8,4,2,6,5,1,3] => 0110110 => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,5,7,3,8,4,6] => [7,8,4,2,6,1,5,3] => 0110101 => 1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,5,7,8,3,4,6] => [7,8,4,2,1,6,5,3] => 0111011 => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6,8] => [7,8,4,2,6,5,3,1] => 0110111 => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,5,3,4,6,8,7] => [7,8,4,6,5,3,1,2] => 0101110 => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,1,5,8,3,4,6,7] => [7,8,4,1,6,5,3,2] => 0110111 => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,5,1,3,6,7,4,8] => [7,4,8,6,3,2,5,1] => 1011101 => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,5,1,3,6,4,8,7] => [7,4,8,6,3,5,1,2] => 1011010 => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,5,1,3,6,8,4,7] => [7,4,8,6,3,1,5,2] => 1011101 => 0
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,1,3,6,4,7,8] => [7,4,8,6,3,5,2,1] => 1011011 => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,5,1,6,3,7,8,4] => [7,4,8,3,6,2,1,5] => 1010110 => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,5,1,6,3,7,4,8] => [7,4,8,3,6,2,5,1] => 1010101 => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,1,6,7,3,8,4] => [7,4,8,3,2,6,1,5] => 1011010 => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,1,6,7,8,3,4] => [7,4,8,3,2,1,6,5] => 1011101 => 0
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,1,6,7,3,4,8] => [7,4,8,3,2,6,5,1] => 1011011 => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,5,1,6,3,4,8,7] => [7,4,8,3,6,5,1,2] => 1010110 => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,1,6,3,8,4,7] => [7,4,8,3,6,1,5,2] => 1010101 => 0
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,1,6,8,3,4,7] => [7,4,8,3,1,6,5,2] => 1011011 => 0
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,1,6,3,4,7,8] => [7,4,8,3,6,5,2,1] => 1010111 => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,5,6,1,3,7,8,4] => [7,4,3,8,6,2,1,5] => 1101110 => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,5,6,1,3,7,4,8] => [7,4,3,8,6,2,5,1] => 1101101 => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,5,6,1,7,3,8,4] => [7,4,3,8,2,6,1,5] => 1101010 => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,5,6,1,7,8,3,4] => [7,4,3,8,2,1,6,5] => 1101101 => 0
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,5,6,1,7,3,4,8] => [7,4,3,8,2,6,5,1] => 1101011 => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,5,6,7,1,3,8,4] => [7,4,3,2,8,6,1,5] => 1110110 => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,5,6,7,1,8,3,4] => [7,4,3,2,8,1,6,5] => 1110101 => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,1,3,4] => [7,4,3,2,1,8,6,5] => 1111011 => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,5,6,1,3,8,4,7] => [7,4,3,8,6,1,5,2] => 1101101 => 0
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,5,6,1,8,3,4,7] => [7,4,3,8,1,6,5,2] => 1101011 => 0
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,5,6,8,1,3,4,7] => [7,4,3,1,8,6,5,2] => 1110111 => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,7,8,6] => [7,4,8,6,5,2,1,3] => 1011110 => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,7,6,8] => [7,4,8,6,5,2,3,1] => 1011101 => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,7,8,4,6] => [7,4,8,6,2,1,5,3] => 1011101 => 0
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6,8] => [7,4,8,6,2,5,3,1] => 1011011 => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,5,1,7,3,4,8,6] => [7,4,8,2,6,5,1,3] => 1010110 => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,5,1,7,3,8,4,6] => [7,4,8,2,6,1,5,3] => 1010101 => 0
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,5,1,7,3,4,6,8] => [7,4,8,2,6,5,3,1] => 1010111 => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,5,7,1,3,4,8,6] => [7,4,2,8,6,5,1,3] => 1101110 => 0
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,5,7,1,8,3,4,6] => [7,4,2,8,1,6,5,3] => 1101011 => 0
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [7,4,2,1,8,6,5,3] => 1110111 => 0
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,5,7,1,3,4,6,8] => [7,4,2,8,6,5,3,1] => 1101111 => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,5,1,3,4,6,8,7] => [7,4,8,6,5,3,1,2] => 1011110 => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,5,1,3,4,8,6,7] => [7,4,8,6,5,1,3,2] => 1011101 => 0
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,5,1,3,8,4,6,7] => [7,4,8,6,1,5,3,2] => 1011011 => 0
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,5,1,8,3,4,6,7] => [7,4,8,1,6,5,3,2] => 1010111 => 0
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,5,8,1,3,4,6,7] => [7,4,1,8,6,5,3,2] => 1101111 => 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,4,6,7,8] => [7,4,8,6,5,3,2,1] => 1011111 => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,5] => [7,8,6,5,3,2,1,4] => 0111110 => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,1,3,4,6,7,5,8] => [7,8,6,5,3,2,4,1] => 0111101 => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,3,4,6,5,8,7] => [7,8,6,5,3,4,1,2] => 0111010 => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,6,5,7,8] => [7,8,6,5,3,4,2,1] => 0111011 => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,6,7,8,4,5] => [7,8,6,3,2,1,5,4] => 0111101 => 1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,1,3,6,7,4,5,8] => [7,8,6,3,2,5,4,1] => 0111011 => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,1,3,6,4,8,5,7] => [7,8,6,3,5,1,4,2] => 0110101 => 1
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,1,3,6,8,4,5,7] => [7,8,6,3,1,5,4,2] => 0111011 => 1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,1,3,6,4,5,7,8] => [7,8,6,3,5,4,2,1] => 0110111 => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [7,8,3,6,5,2,1,4] => 0101110 => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,1,6,3,7,4,8,5] => [7,8,3,6,2,5,1,4] => 0101010 => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,1,6,3,7,8,4,5] => [7,8,3,6,2,1,5,4] => 0101101 => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,1,6,3,7,4,5,8] => [7,8,3,6,2,5,4,1] => 0101011 => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,3,4,5] => [7,8,3,2,1,6,5,4] => 0111011 => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,1,6,7,3,4,5,8] => [7,8,3,2,6,5,4,1] => 0110111 => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,8,7] => [7,8,3,6,5,4,1,2] => 0101110 => 1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,1,6,3,8,4,5,7] => [7,8,3,6,1,5,4,2] => 0101011 => 1
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,1,6,8,3,4,5,7] => [7,8,3,1,6,5,4,2] => 0110111 => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,1,3,4,7,8,5] => [7,3,8,6,5,2,1,4] => 1011110 => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,6,1,3,7,4,8,5] => [7,3,8,6,2,5,1,4] => 1011010 => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,6,1,7,3,4,8,5] => [7,3,8,2,6,5,1,4] => 1010110 => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,6,1,7,3,8,4,5] => [7,3,8,2,6,1,5,4] => 1010101 => 0
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,6,1,7,8,3,4,5] => [7,3,8,2,1,6,5,4] => 1011011 => 0
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,6,1,7,3,4,5,8] => [7,3,8,2,6,5,4,1] => 1010111 => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,6,7,1,3,4,8,5] => [7,3,2,8,6,5,1,4] => 1101110 => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,6,7,1,3,8,4,5] => [7,3,2,8,6,1,5,4] => 1101101 => 0
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,6,7,1,8,3,4,5] => [7,3,2,8,1,6,5,4] => 1101011 => 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,6,7,8,1,3,4,5] => [7,3,2,1,8,6,5,4] => 1110111 => 0
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,6,7,1,3,4,5,8] => [7,3,2,8,6,5,4,1] => 1101111 => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,8,7] => [7,3,8,6,5,4,1,2] => 1011110 => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,8,5,7] => [7,3,8,6,5,1,4,2] => 1011101 => 0
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,6,1,3,8,4,5,7] => [7,3,8,6,1,5,4,2] => 1011011 => 0
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,6,1,8,3,4,5,7] => [7,3,8,1,6,5,4,2] => 1010111 => 0
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => [7,3,1,8,6,5,4,2] => 1101111 => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,6,1,3,4,5,7,8] => [7,3,8,6,5,4,2,1] => 1011111 => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,7,8,6] => [7,8,6,5,4,2,1,3] => 0111110 => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,7,6,8] => [7,8,6,5,4,2,3,1] => 0111101 => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,1,3,4,7,8,5,6] => [7,8,6,5,2,1,4,3] => 0111101 => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,3,4,7,5,6,8] => [7,8,6,5,2,4,3,1] => 0111011 => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,1,3,7,8,4,5,6] => [7,8,6,2,1,5,4,3] => 0111011 => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,7,3,4,5,8,6] => [7,8,2,6,5,4,1,3] => 0101110 => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,1,7,3,4,8,5,6] => [7,8,2,6,5,1,4,3] => 0101101 => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,1,7,3,8,4,5,6] => [7,8,2,6,1,5,4,3] => 0101011 => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,1,7,8,3,4,5,6] => [7,8,2,1,6,5,4,3] => 0110111 => 1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6,8] => [7,8,2,6,5,4,3,1] => 0101111 => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,7,1,3,4,5,8,6] => [7,2,8,6,5,4,1,3] => 1011110 => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,1,3,4,8,5,6] => [7,2,8,6,5,1,4,3] => 1011101 => 0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,7,1,8,3,4,5,6] => [7,2,8,1,6,5,4,3] => 1010111 => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [7,2,1,8,6,5,4,3] => 1101111 => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6,8] => [7,2,8,6,5,4,3,1] => 1011111 => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [7,8,6,5,4,3,1,2] => 0111110 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,3,4,5,8,6,7] => [7,8,6,5,4,1,3,2] => 0111101 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,1,3,4,8,5,6,7] => [7,8,6,5,1,4,3,2] => 0111011 => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => [7,8,6,1,5,4,3,2] => 0110111 => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [7,8,1,6,5,4,3,2] => 0101111 => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [7,1,8,6,5,4,3,2] => 1011111 => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [7,8,6,5,4,3,2,1] => 0111111 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,2] => [8,6,5,4,3,2,1,7] => 1111110 => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,2,8] => [8,6,5,4,3,2,7,1] => 1111101 => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,6,2,8,7] => [8,6,5,4,3,7,1,2] => 1111010 => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,8,2,7] => [8,6,5,4,3,1,7,2] => 1111101 => 0
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,2,7,8] => [8,6,5,4,3,7,2,1] => 1111011 => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,5,2,7,8,6] => [8,6,5,4,7,2,1,3] => 1110110 => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,8] => [8,6,5,4,7,2,3,1] => 1110101 => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,5,7,2,8,6] => [8,6,5,4,2,7,1,3] => 1111010 => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,7,8,2,6] => [8,6,5,4,2,1,7,3] => 1111101 => 0
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6,8] => [8,6,5,4,2,7,3,1] => 1111011 => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,5,2,8,6,7] => [8,6,5,4,7,1,3,2] => 1110101 => 0
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [8,6,5,4,7,3,2,1] => 1110111 => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,4,2,6,7,8,5] => [8,6,5,7,3,2,1,4] => 1101110 => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,6,7,5,8] => [8,6,5,7,3,2,4,1] => 1101101 => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7] => [8,6,5,7,3,4,1,2] => 1101010 => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,6,2,7,8,5] => [8,6,5,3,7,2,1,4] => 1110110 => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,6,2,7,5,8] => [8,6,5,3,7,2,4,1] => 1110101 => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,6,7,2,8,5] => [8,6,5,3,2,7,1,4] => 1111010 => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,6,7,8,2,5] => [8,6,5,3,2,1,7,4] => 1111101 => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,4,2,5,7,8,6] => [8,6,5,7,4,2,1,3] => 1101110 => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,4,2,5,7,6,8] => [8,6,5,7,4,2,3,1] => 1101101 => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,2,7,5,8,6] => [8,6,5,7,2,4,1,3] => 1101010 => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,4,2,7,8,5,6] => [8,6,5,7,2,1,4,3] => 1101101 => 0
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,4,2,7,5,6,8] => [8,6,5,7,2,4,3,1] => 1101011 => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,4,7,2,8,5,6] => [8,6,5,2,7,1,4,3] => 1110101 => 0
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,4,7,8,2,5,6] => [8,6,5,2,1,7,4,3] => 1111011 => 0
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => [8,6,5,2,7,4,3,1] => 1110111 => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,2,5,6,8,7] => [8,6,5,7,4,3,1,2] => 1101110 => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,3,4,2,5,8,6,7] => [8,6,5,7,4,1,3,2] => 1101101 => 0
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [8,6,5,7,1,4,3,2] => 1101011 => 0
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [8,6,5,1,7,4,3,2] => 1110111 => 0
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,2,5,6,7,8] => [8,6,5,7,4,3,2,1] => 1101111 => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,6,7,8,4] => [8,6,7,4,3,2,1,5] => 1011110 => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,5,6,7,4,8] => [8,6,7,4,3,2,5,1] => 1011101 => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,5,6,8,4,7] => [8,6,7,4,3,1,5,2] => 1011101 => 0
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,5,6,4,7,8] => [8,6,7,4,3,5,2,1] => 1011011 => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,8,6] => [8,6,7,4,5,2,1,3] => 1010110 => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8] => [8,6,7,4,5,2,3,1] => 1010101 => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,7,4,8,6] => [8,6,7,4,2,5,1,3] => 1011010 => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,7,8,4,6] => [8,6,7,4,2,1,5,3] => 1011101 => 0
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6,8] => [8,6,7,4,2,5,3,1] => 1011011 => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,5,4,6,8,7] => [8,6,7,4,5,3,1,2] => 1010110 => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => [8,6,7,4,5,1,3,2] => 1010101 => 0
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,5,8,4,6,7] => [8,6,7,4,1,5,3,2] => 1011011 => 0
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8] => [8,6,7,4,5,3,2,1] => 1010111 => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,5,2,6,7,8,4] => [8,6,4,7,3,2,1,5] => 1101110 => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,5,2,6,7,4,8] => [8,6,4,7,3,2,5,1] => 1101101 => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,5,2,6,8,4,7] => [8,6,4,7,3,1,5,2] => 1101101 => 0
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,5,2,6,4,7,8] => [8,6,4,7,3,5,2,1] => 1101011 => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,5,6,2,7,8,4] => [8,6,4,3,7,2,1,5] => 1110110 => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,5,6,2,7,4,8] => [8,6,4,3,7,2,5,1] => 1110101 => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,5,6,7,2,8,4] => [8,6,4,3,2,7,1,5] => 1111010 => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,8,2,4] => [8,6,4,3,2,1,7,5] => 1111101 => 0
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,6,7,2,4,8] => [8,6,4,3,2,7,5,1] => 1111011 => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,5,6,2,4,8,7] => [8,6,4,3,7,5,1,2] => 1110110 => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,5,6,2,8,4,7] => [8,6,4,3,7,1,5,2] => 1110101 => 0
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [8,6,4,3,7,5,2,1] => 1110111 => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,7,8,6] => [8,6,4,7,5,2,1,3] => 1101110 => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6,8] => [8,6,4,7,5,2,3,1] => 1101101 => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,7,4,8,6] => [8,6,4,7,2,5,1,3] => 1101010 => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,7,8,4,6] => [8,6,4,7,2,1,5,3] => 1101101 => 0
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6,8] => [8,6,4,7,2,5,3,1] => 1101011 => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,7,2,4,8,6] => [8,6,4,2,7,5,1,3] => 1110110 => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,7,2,8,4,6] => [8,6,4,2,7,1,5,3] => 1110101 => 0
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,7,8,2,4,6] => [8,6,4,2,1,7,5,3] => 1111011 => 0
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => [8,6,4,2,7,5,3,1] => 1110111 => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,5,2,4,6,8,7] => [8,6,4,7,5,3,1,2] => 1101110 => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,5,2,4,8,6,7] => [8,6,4,7,5,1,3,2] => 1101101 => 0
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => [8,6,4,7,1,5,3,2] => 1101011 => 0
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [8,6,4,1,7,5,3,2] => 1110111 => 0
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,2,4,6,7,8] => [8,6,4,7,5,3,2,1] => 1101111 => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,4,6,7,8,5] => [8,6,7,5,3,2,1,4] => 1011110 => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,2,4,6,7,5,8] => [8,6,7,5,3,2,4,1] => 1011101 => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,4,6,8,5,7] => [8,6,7,5,3,1,4,2] => 1011101 => 0
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,4,6,5,7,8] => [8,6,7,5,3,4,2,1] => 1011011 => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,3,2,6,4,7,8,5] => [8,6,7,3,5,2,1,4] => 1010110 => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,6,4,7,5,8] => [8,6,7,3,5,2,4,1] => 1010101 => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,4,8,5,7] => [8,6,7,3,5,1,4,2] => 1010101 => 0
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,2,6,4,5,7,8] => [8,6,7,3,5,4,2,1] => 1010111 => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,6,2,4,7,8,5] => [8,6,3,7,5,2,1,4] => 1101110 => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,2,4,7,5,8] => [8,6,3,7,5,2,4,1] => 1101101 => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,2,7,4,8,5] => [8,6,3,7,2,5,1,4] => 1101010 => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,2,7,8,4,5] => [8,6,3,7,2,1,5,4] => 1101101 => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,6,7,2,4,8,5] => [8,6,3,2,7,5,1,4] => 1110110 => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,3,6,7,2,8,4,5] => [8,6,3,2,7,1,5,4] => 1110101 => 0
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,6,7,8,2,4,5] => [8,6,3,2,1,7,5,4] => 1111011 => 0
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,6,7,2,4,5,8] => [8,6,3,2,7,5,4,1] => 1110111 => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,6,2,4,8,5,7] => [8,6,3,7,5,1,4,2] => 1101101 => 0
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,6,2,8,4,5,7] => [8,6,3,7,1,5,4,2] => 1101011 => 0
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,3,6,8,2,4,5,7] => [8,6,3,1,7,5,4,2] => 1110111 => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,3,2,4,5,7,8,6] => [8,6,7,5,4,2,1,3] => 1011110 => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,3,2,4,5,7,6,8] => [8,6,7,5,4,2,3,1] => 1011101 => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,4,7,8,5,6] => [8,6,7,5,2,1,4,3] => 1011101 => 0
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,3,2,4,7,5,6,8] => [8,6,7,5,2,4,3,1] => 1011011 => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,7,4,8,5,6] => [8,6,7,2,5,1,4,3] => 1010101 => 0
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,3,2,7,4,5,6,8] => [8,6,7,2,5,4,3,1] => 1010111 => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,3,7,2,4,5,8,6] => [8,6,2,7,5,4,1,3] => 1101110 => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,3,7,2,4,8,5,6] => [8,6,2,7,5,1,4,3] => 1101101 => 0
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [8,6,2,7,1,5,4,3] => 1101011 => 0
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6,8] => [8,6,2,7,5,4,3,1] => 1101111 => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,3,2,4,5,6,8,7] => [8,6,7,5,4,3,1,2] => 1011110 => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [8,6,7,5,4,1,3,2] => 1011101 => 0
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,3,2,4,8,5,6,7] => [8,6,7,5,1,4,3,2] => 1011011 => 0
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,3,2,8,4,5,6,7] => [8,6,7,1,5,4,3,2] => 1010111 => 0
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [8,6,1,7,5,4,3,2] => 1101111 => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8] => [8,6,7,5,4,3,2,1] => 1011111 => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,2] => [6,8,5,4,3,2,1,7] => 0111110 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,2,8] => [6,8,5,4,3,2,7,1] => 0111101 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,5,6,2,8,7] => [6,8,5,4,3,7,1,2] => 0111010 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,4,5,6,8,2,7] => [6,8,5,4,3,1,7,2] => 0111101 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,4,5,6,2,7,8] => [6,8,5,4,3,7,2,1] => 0111011 => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6,8] => [6,8,5,4,7,2,3,1] => 0110101 => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,5,7,2,8,6] => [6,8,5,4,2,7,1,3] => 0111010 => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4,5,7,8,2,6] => [6,8,5,4,2,1,7,3] => 0111101 => 1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6,8] => [6,8,5,4,2,7,3,1] => 0111011 => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,4,5,2,8,6,7] => [6,8,5,4,7,1,3,2] => 0110101 => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,2,6,7,8] => [6,8,5,4,7,3,2,1] => 0110111 => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [6,8,5,7,3,2,1,4] => 0101110 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7] => [6,8,5,7,3,4,1,2] => 0101010 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,8,5,7] => [6,8,5,7,3,1,4,2] => 0101101 => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,6,2,7,8,5] => [6,8,5,3,7,2,1,4] => 0110110 => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,1,4,6,2,7,5,8] => [6,8,5,3,7,2,4,1] => 0110101 => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,6,7,2,8,5] => [6,8,5,3,2,7,1,4] => 0111010 => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,4,6,8,2,5,7] => [6,8,5,3,1,7,4,2] => 0111011 => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,7,8,6] => [6,8,5,7,4,2,1,3] => 0101110 => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,2,5,7,6,8] => [6,8,5,7,4,2,3,1] => 0101101 => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,7,5,8,6] => [6,8,5,7,2,4,1,3] => 0101010 => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,4,2,7,8,5,6] => [6,8,5,7,2,1,4,3] => 0101101 => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,7,2,5,8,6] => [6,8,5,2,7,4,1,3] => 0110110 => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,4,7,2,8,5,6] => [6,8,5,2,7,1,4,3] => 0110101 => 1
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,1,4,7,8,2,5,6] => [6,8,5,2,1,7,4,3] => 0111011 => 1
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,1,4,7,2,5,6,8] => [6,8,5,2,7,4,3,1] => 0110111 => 1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,4,2,8,5,6,7] => [6,8,5,7,1,4,3,2] => 0101011 => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,1,4,8,2,5,6,7] => [6,8,5,1,7,4,3,2] => 0110111 => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,2,5,6,7,8] => [6,8,5,7,4,3,2,1] => 0101111 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,2] => [6,5,8,4,3,2,1,7] => 1011110 => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,5,6,7,2,8] => [6,5,8,4,3,2,7,1] => 1011101 => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,4,1,5,6,2,8,7] => [6,5,8,4,3,7,1,2] => 1011010 => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,5,6,8,2,7] => [6,5,8,4,3,1,7,2] => 1011101 => 0
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,4,1,5,6,2,7,8] => [6,5,8,4,3,7,2,1] => 1011011 => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,4,1,5,2,7,8,6] => [6,5,8,4,7,2,1,3] => 1010110 => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6,8] => [6,5,8,4,7,2,3,1] => 1010101 => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,7,8,2,6] => [6,5,8,4,2,1,7,3] => 1011101 => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6,8] => [6,5,8,4,2,7,3,1] => 1011011 => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,2,8,6,7] => [6,5,8,4,7,1,3,2] => 1010101 => 0
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4,1,5,8,2,6,7] => [6,5,8,4,1,7,3,2] => 1011011 => 0
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4,1,5,2,6,7,8] => [6,5,8,4,7,3,2,1] => 1010111 => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,2] => [6,5,4,8,3,2,1,7] => 1101110 => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,5,1,6,7,2,8] => [6,5,4,8,3,2,7,1] => 1101101 => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,1,6,2,8,7] => [6,5,4,8,3,7,1,2] => 1101010 => 0
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,5,1,6,2,7,8] => [6,5,4,8,3,7,2,1] => 1101011 => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,1,7,8,2] => [6,5,4,3,8,2,1,7] => 1110110 => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,6,1,7,2,8] => [6,5,4,3,8,2,7,1] => 1110101 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,1,8,2] => [6,5,4,3,2,8,1,7] => 1111010 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,1,2] => [6,5,4,3,2,1,8,7] => 1111101 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,1,2,8] => [6,5,4,3,2,8,7,1] => 1111011 => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,6,1,2,8,7] => [6,5,4,3,8,7,1,2] => 1110110 => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,6,1,8,2,7] => [6,5,4,3,8,1,7,2] => 1110101 => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,6,8,1,2,7] => [6,5,4,3,1,8,7,2] => 1111011 => 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [6,5,4,3,8,7,2,1] => 1110111 => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,5,1,2,7,8,6] => [6,5,4,8,7,2,1,3] => 1101110 => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6,8] => [6,5,4,8,7,2,3,1] => 1101101 => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,5,1,7,2,8,6] => [6,5,4,8,2,7,1,3] => 1101010 => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,5,1,7,8,2,6] => [6,5,4,8,2,1,7,3] => 1101101 => 0
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6,8] => [6,5,4,8,2,7,3,1] => 1101011 => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,5,7,1,2,8,6] => [6,5,4,2,8,7,1,3] => 1110110 => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,5,1,2,6,8,7] => [6,5,4,8,7,3,1,2] => 1101110 => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,5,1,2,8,6,7] => [6,5,4,8,7,1,3,2] => 1101101 => 0
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [6,5,4,1,8,7,3,2] => 1110111 => 0
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [6,5,4,8,7,3,2,1] => 1101111 => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,6,7,8,5] => [6,5,8,7,3,2,1,4] => 1011110 => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,6,7,5,8] => [6,5,8,7,3,2,4,1] => 1011101 => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => [6,5,8,7,3,4,1,2] => 1011010 => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,8,5,7] => [6,5,8,7,3,1,4,2] => 1011101 => 0
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,6,5,7,8] => [6,5,8,7,3,4,2,1] => 1011011 => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,4,1,6,2,7,8,5] => [6,5,8,3,7,2,1,4] => 1010110 => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,4,1,6,2,7,5,8] => [6,5,8,3,7,2,4,1] => 1010101 => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,4,1,6,7,2,8,5] => [6,5,8,3,2,7,1,4] => 1011010 => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,4,1,6,7,8,2,5] => [6,5,8,3,2,1,7,4] => 1011101 => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,8,7] => [6,5,8,3,7,4,1,2] => 1010110 => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,8,5,7] => [6,5,8,3,7,1,4,2] => 1010101 => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,4,6,1,2,7,8,5] => [6,5,3,8,7,2,1,4] => 1101110 => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,4,6,1,2,7,5,8] => [6,5,3,8,7,2,4,1] => 1101101 => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,4,6,1,7,2,8,5] => [6,5,3,8,2,7,1,4] => 1101010 => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,4,6,1,7,8,2,5] => [6,5,3,8,2,1,7,4] => 1101101 => 0
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,4,6,1,7,2,5,8] => [6,5,3,8,2,7,4,1] => 1101011 => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,4,6,7,1,2,8,5] => [6,5,3,2,8,7,1,4] => 1110110 => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,4,6,7,1,8,2,5] => [6,5,3,2,8,1,7,4] => 1110101 => 0
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,6,7,8,1,2,5] => [6,5,3,2,1,8,7,4] => 1111011 => 0
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,7,1,2,5,8] => [6,5,3,2,8,7,4,1] => 1110111 => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,8,7] => [6,5,3,8,7,4,1,2] => 1101110 => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [3,4,6,1,2,8,5,7] => [6,5,3,8,7,1,4,2] => 1101101 => 0
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [6,5,3,1,8,7,4,2] => 1110111 => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,4,1,2,5,7,8,6] => [6,5,8,7,4,2,1,3] => 1011110 => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,7,6,8] => [6,5,8,7,4,2,3,1] => 1011101 => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,4,1,2,7,5,8,6] => [6,5,8,7,2,4,1,3] => 1011010 => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,2,7,8,5,6] => [6,5,8,7,2,1,4,3] => 1011101 => 0
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,4,1,2,7,5,6,8] => [6,5,8,7,2,4,3,1] => 1011011 => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,4,1,7,2,5,8,6] => [6,5,8,2,7,4,1,3] => 1010110 => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,4,1,7,2,8,5,6] => [6,5,8,2,7,1,4,3] => 1010101 => 0
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,4,1,7,8,2,5,6] => [6,5,8,2,1,7,4,3] => 1011011 => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [3,4,7,1,2,8,5,6] => [6,5,2,8,7,1,4,3] => 1101101 => 0
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => [6,5,2,8,1,7,4,3] => 1101011 => 0
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => [6,5,2,1,8,7,4,3] => 1110111 => 0
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,7,1,2,5,6,8] => [6,5,2,8,7,4,3,1] => 1101111 => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1,2,5,6,8,7] => [6,5,8,7,4,3,1,2] => 1011110 => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1,2,5,8,6,7] => [6,5,8,7,4,1,3,2] => 1011101 => 0
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1,2,8,5,6,7] => [6,5,8,7,1,4,3,2] => 1011011 => 0
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1,8,2,5,6,7] => [6,5,8,1,7,4,3,2] => 1010111 => 0
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,8,1,2,5,6,7] => [6,5,1,8,7,4,3,2] => 1101111 => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [6,5,8,7,4,3,2,1] => 1011111 => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,5,6,7,8,4] => [6,8,7,4,3,2,1,5] => 0111110 => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,5,6,7,4,8] => [6,8,7,4,3,2,5,1] => 0111101 => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,5,6,4,8,7] => [6,8,7,4,3,5,1,2] => 0111010 => 1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,5,6,4,7,8] => [6,8,7,4,3,5,2,1] => 0111011 => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,8] => [6,8,7,4,5,2,3,1] => 0110101 => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,7,4,8,6] => [6,8,7,4,2,5,1,3] => 0111010 => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,7,8,4,6] => [6,8,7,4,2,1,5,3] => 0111101 => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6,8] => [6,8,7,4,2,5,3,1] => 0111011 => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,5,4,6,8,7] => [6,8,7,4,5,3,1,2] => 0110110 => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,2,5,4,8,6,7] => [6,8,7,4,5,1,3,2] => 0110101 => 1
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,5,4,6,7,8] => [6,8,7,4,5,3,2,1] => 0110111 => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,7,8,4] => [6,8,4,7,3,2,1,5] => 0101110 => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,5,2,6,7,4,8] => [6,8,4,7,3,2,5,1] => 0101101 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7] => [6,8,4,7,3,5,1,2] => 0101010 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,5,2,6,8,4,7] => [6,8,4,7,3,1,5,2] => 0101101 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,4,7,8] => [6,8,4,7,3,5,2,1] => 0101011 => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,5,6,2,7,8,4] => [6,8,4,3,7,2,1,5] => 0110110 => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,5,6,7,2,8,4] => [6,8,4,3,2,7,1,5] => 0111010 => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,5,6,7,8,2,4] => [6,8,4,3,2,1,7,5] => 0111101 => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,5,6,7,2,4,8] => [6,8,4,3,2,7,5,1] => 0111011 => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,5,6,2,4,8,7] => [6,8,4,3,7,5,1,2] => 0110110 => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,5,6,2,8,4,7] => [6,8,4,3,7,1,5,2] => 0110101 => 1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,5,6,8,2,4,7] => [6,8,4,3,1,7,5,2] => 0111011 => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,5,6,2,4,7,8] => [6,8,4,3,7,5,2,1] => 0110111 => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,7,8,6] => [6,8,4,7,5,2,1,3] => 0101110 => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6,8] => [6,8,4,7,5,2,3,1] => 0101101 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,8,6] => [6,8,4,7,2,5,1,3] => 0101010 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,7,8,4,6] => [6,8,4,7,2,1,5,3] => 0101101 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6,8] => [6,8,4,7,2,5,3,1] => 0101011 => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,7,2,4,8,6] => [6,8,4,2,7,5,1,3] => 0110110 => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,7,2,8,4,6] => [6,8,4,2,7,1,5,3] => 0110101 => 1
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,7,8,2,4,6] => [6,8,4,2,1,7,5,3] => 0111011 => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6,8] => [6,8,4,2,7,5,3,1] => 0110111 => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,5,2,4,6,8,7] => [6,8,4,7,5,3,1,2] => 0101110 => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,5,2,4,8,6,7] => [6,8,4,7,5,1,3,2] => 0101101 => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,5,2,8,4,6,7] => [6,8,4,7,1,5,3,2] => 0101011 => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,5,8,2,4,6,7] => [6,8,4,1,7,5,3,2] => 0110111 => 1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,5,2,4,6,7,8] => [6,8,4,7,5,3,2,1] => 0101111 => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,5,1,2,6,7,8,4] => [6,4,8,7,3,2,1,5] => 1011110 => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => [6,4,8,7,3,2,5,1] => 1011101 => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,5,1,2,6,4,8,7] => [6,4,8,7,3,5,1,2] => 1011010 => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,5,1,2,6,8,4,7] => [6,4,8,7,3,1,5,2] => 1011101 => 0
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,5,1,2,6,4,7,8] => [6,4,8,7,3,5,2,1] => 1011011 => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,5,1,6,2,7,8,4] => [6,4,8,3,7,2,1,5] => 1010110 => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,5,1,6,2,7,4,8] => [6,4,8,3,7,2,5,1] => 1010101 => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,5,1,6,7,2,8,4] => [6,4,8,3,2,7,1,5] => 1011010 => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,5,1,6,7,8,2,4] => [6,4,8,3,2,1,7,5] => 1011101 => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,5,1,6,2,4,8,7] => [6,4,8,3,7,5,1,2] => 1010110 => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,5,1,6,2,8,4,7] => [6,4,8,3,7,1,5,2] => 1010101 => 0
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,5,1,6,8,2,4,7] => [6,4,8,3,1,7,5,2] => 1011011 => 0
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,5,1,6,2,4,7,8] => [6,4,8,3,7,5,2,1] => 1010111 => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,5,6,1,2,7,8,4] => [6,4,3,8,7,2,1,5] => 1101110 => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,5,6,1,2,7,4,8] => [6,4,3,8,7,2,5,1] => 1101101 => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,5,6,1,7,2,8,4] => [6,4,3,8,2,7,1,5] => 1101010 => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,5,6,1,7,8,2,4] => [6,4,3,8,2,1,7,5] => 1101101 => 0
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,5,6,1,7,2,4,8] => [6,4,3,8,2,7,5,1] => 1101011 => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,5,6,7,1,2,8,4] => [6,4,3,2,8,7,1,5] => 1110110 => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,5,6,7,1,8,2,4] => [6,4,3,2,8,1,7,5] => 1110101 => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,8,1,2,4] => [6,4,3,2,1,8,7,5] => 1111011 => 0
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,5,6,7,1,2,4,8] => [6,4,3,2,8,7,5,1] => 1110111 => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,5,6,1,2,4,8,7] => [6,4,3,8,7,5,1,2] => 1101110 => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,5,6,1,2,8,4,7] => [6,4,3,8,7,1,5,2] => 1101101 => 0
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => [6,4,3,8,1,7,5,2] => 1101011 => 0
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [6,4,3,1,8,7,5,2] => 1110111 => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,7,8,6] => [6,4,8,7,5,2,1,3] => 1011110 => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [6,4,8,7,5,2,3,1] => 1011101 => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,7,4,8,6] => [6,4,8,7,2,5,1,3] => 1011010 => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,7,8,4,6] => [6,4,8,7,2,1,5,3] => 1011101 => 0
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6,8] => [6,4,8,7,2,5,3,1] => 1011011 => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,7,2,4,8,6] => [6,4,8,2,7,5,1,3] => 1010110 => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => [6,4,8,2,7,1,5,3] => 1010101 => 0
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6,8] => [6,4,8,2,7,5,3,1] => 1010111 => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,7,1,2,4,8,6] => [6,4,2,8,7,5,1,3] => 1101110 => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,7,1,2,8,4,6] => [6,4,2,8,7,1,5,3] => 1101101 => 0
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [6,4,2,1,8,7,5,3] => 1110111 => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6,8] => [6,4,2,8,7,5,3,1] => 1101111 => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,5,1,2,4,6,8,7] => [6,4,8,7,5,3,1,2] => 1011110 => 0
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,5,1,8,2,4,6,7] => [6,4,8,1,7,5,3,2] => 1010111 => 0
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,5,8,1,2,4,6,7] => [6,4,1,8,7,5,3,2] => 1101111 => 0
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,5,1,2,4,6,7,8] => [6,4,8,7,5,3,2,1] => 1011111 => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,2,4,6,7,8,5] => [6,8,7,5,3,2,1,4] => 0111110 => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,7,5,8] => [6,8,7,5,3,2,4,1] => 0111101 => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,2,4,6,5,8,7] => [6,8,7,5,3,4,1,2] => 0111010 => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [3,1,2,4,6,8,5,7] => [6,8,7,5,3,1,4,2] => 0111101 => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,1,2,4,6,5,7,8] => [6,8,7,5,3,4,2,1] => 0111011 => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [3,1,2,6,4,7,8,5] => [6,8,7,3,5,2,1,4] => 0110110 => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [3,1,2,6,4,7,5,8] => [6,8,7,3,5,2,4,1] => 0110101 => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,6,7,4,8,5] => [6,8,7,3,2,5,1,4] => 0111010 => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,2,6,7,8,4,5] => [6,8,7,3,2,1,5,4] => 0111101 => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [3,1,2,6,4,8,5,7] => [6,8,7,3,5,1,4,2] => 0110101 => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [3,1,2,6,8,4,5,7] => [6,8,7,3,1,5,4,2] => 0111011 => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,1,2,6,4,5,7,8] => [6,8,7,3,5,4,2,1] => 0110111 => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,7,8,5] => [6,8,3,7,5,2,1,4] => 0101110 => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,1,6,2,4,7,5,8] => [6,8,3,7,5,2,4,1] => 0101101 => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,6,2,7,4,8,5] => [6,8,3,7,2,5,1,4] => 0101010 => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [3,1,6,2,7,8,4,5] => [6,8,3,7,2,1,5,4] => 0101101 => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [3,1,6,2,7,4,5,8] => [6,8,3,7,2,5,4,1] => 0101011 => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [3,1,6,7,2,4,8,5] => [6,8,3,2,7,5,1,4] => 0110110 => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [3,1,6,7,2,8,4,5] => [6,8,3,2,7,1,5,4] => 0110101 => 1
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,1,6,7,2,4,5,8] => [6,8,3,2,7,5,4,1] => 0110111 => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,8,7] => [6,8,3,7,5,4,1,2] => 0101110 => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [3,1,6,2,4,8,5,7] => [6,8,3,7,5,1,4,2] => 0101101 => 1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [3,1,6,2,8,4,5,7] => [6,8,3,7,1,5,4,2] => 0101011 => 1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,1,6,8,2,4,5,7] => [6,8,3,1,7,5,4,2] => 0110111 => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,6,1,2,4,7,8,5] => [6,3,8,7,5,2,1,4] => 1011110 => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => [6,3,8,7,5,2,4,1] => 1011101 => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,6,1,2,7,4,8,5] => [6,3,8,7,2,5,1,4] => 1011010 => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [3,6,1,2,7,8,4,5] => [6,3,8,7,2,1,5,4] => 1011101 => 0
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [3,6,1,2,7,4,5,8] => [6,3,8,7,2,5,4,1] => 1011011 => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,6,1,7,2,4,8,5] => [6,3,8,2,7,5,1,4] => 1010110 => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => [6,3,8,2,7,1,5,4] => 1010101 => 0
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [3,6,1,7,8,2,4,5] => [6,3,8,2,1,7,5,4] => 1011011 => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [3,6,7,1,2,4,8,5] => [6,3,2,8,7,5,1,4] => 1101110 => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [3,6,7,1,2,8,4,5] => [6,3,2,8,7,1,5,4] => 1101101 => 0
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [3,6,7,1,8,2,4,5] => [6,3,2,8,1,7,5,4] => 1101011 => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [6,3,2,1,8,7,5,4] => 1110111 => 0
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,6,7,1,2,4,5,8] => [6,3,2,8,7,5,4,1] => 1101111 => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,8,7] => [6,3,8,7,5,4,1,2] => 1011110 => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,8,5,7] => [6,3,8,7,5,1,4,2] => 1011101 => 0
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [3,6,1,2,8,4,5,7] => [6,3,8,7,1,5,4,2] => 1011011 => 0
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,6,1,8,2,4,5,7] => [6,3,8,1,7,5,4,2] => 1010111 => 0
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,6,8,1,2,4,5,7] => [6,3,1,8,7,5,4,2] => 1101111 => 0
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,6,1,2,4,5,7,8] => [6,3,8,7,5,4,2,1] => 1011111 => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,2,4,5,7,8,6] => [6,8,7,5,4,2,1,3] => 0111110 => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,2,4,5,7,6,8] => [6,8,7,5,4,2,3,1] => 0111101 => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,4,7,5,8,6] => [6,8,7,5,2,4,1,3] => 0111010 => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,2,4,7,8,5,6] => [6,8,7,5,2,1,4,3] => 0111101 => 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [3,1,2,4,7,5,6,8] => [6,8,7,5,2,4,3,1] => 0111011 => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [3,1,2,7,4,5,8,6] => [6,8,7,2,5,4,1,3] => 0110110 => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [3,1,2,7,8,4,5,6] => [6,8,7,2,1,5,4,3] => 0111011 => 1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,1,2,7,4,5,6,8] => [6,8,7,2,5,4,3,1] => 0110111 => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,7,2,4,5,8,6] => [6,8,2,7,5,4,1,3] => 0101110 => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [3,1,7,2,4,8,5,6] => [6,8,2,7,5,1,4,3] => 0101101 => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [3,1,7,2,8,4,5,6] => [6,8,2,7,1,5,4,3] => 0101011 => 1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,7,8,2,4,5,6] => [6,8,2,1,7,5,4,3] => 0110111 => 1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6,8] => [6,8,2,7,5,4,3,1] => 0101111 => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,7,1,2,4,5,8,6] => [6,2,8,7,5,4,1,3] => 1011110 => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [3,7,1,2,4,8,5,6] => [6,2,8,7,5,1,4,3] => 1011101 => 0
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [3,7,1,2,8,4,5,6] => [6,2,8,7,1,5,4,3] => 1011011 => 0
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,7,1,8,2,4,5,6] => [6,2,8,1,7,5,4,3] => 1010111 => 0
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,7,8,1,2,4,5,6] => [6,2,1,8,7,5,4,3] => 1101111 => 0
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6,8] => [6,2,8,7,5,4,3,1] => 1011111 => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [6,8,7,5,4,3,1,2] => 0111110 => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,2,4,5,8,6,7] => [6,8,7,5,4,1,3,2] => 0111101 => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,2,4,8,5,6,7] => [6,8,7,5,1,4,3,2] => 0111011 => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,2,8,4,5,6,7] => [6,8,7,1,5,4,3,2] => 0110111 => 1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [6,8,1,7,5,4,3,2] => 0101111 => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [6,1,8,7,5,4,3,2] => 1011111 => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [6,8,7,5,4,3,2,1] => 0111111 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,3] => [8,7,5,4,3,2,1,6] => 1111110 => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,7,3,8] => [8,7,5,4,3,2,6,1] => 1111101 => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,6,8,3,7] => [8,7,5,4,3,1,6,2] => 1111101 => 0
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,4,5,6,3,7,8] => [8,7,5,4,3,6,2,1] => 1111011 => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6,8] => [8,7,5,4,6,2,3,1] => 1110101 => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,7,3,8,6] => [8,7,5,4,2,6,1,3] => 1111010 => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,7,8,3,6] => [8,7,5,4,2,1,6,3] => 1111101 => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,4,5,3,6,8,7] => [8,7,5,4,6,3,1,2] => 1110110 => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,4,5,3,8,6,7] => [8,7,5,4,6,1,3,2] => 1110101 => 0
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,4,5,8,3,6,7] => [8,7,5,4,1,6,3,2] => 1111011 => 0
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [8,7,5,4,6,3,2,1] => 1110111 => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,5] => [8,7,5,6,3,2,1,4] => 1101110 => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,6,7,5,8] => [8,7,5,6,3,2,4,1] => 1101101 => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7] => [8,7,5,6,3,4,1,2] => 1101010 => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,8,5,7] => [8,7,5,6,3,1,4,2] => 1101101 => 0
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8] => [8,7,5,6,3,4,2,1] => 1101011 => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,6,3,7,5,8] => [8,7,5,3,6,2,4,1] => 1110101 => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,6,7,3,8,5] => [8,7,5,3,2,6,1,4] => 1111010 => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,6,7,8,3,5] => [8,7,5,3,2,1,6,4] => 1111101 => 0
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,6,7,3,5,8] => [8,7,5,3,2,6,4,1] => 1111011 => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,8,7] => [8,7,5,3,6,4,1,2] => 1110110 => 0
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,8,3,5,7] => [8,7,5,3,1,6,4,2] => 1111011 => 0
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => [8,7,5,3,6,4,2,1] => 1110111 => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,4,3,5,7,8,6] => [8,7,5,6,4,2,1,3] => 1101110 => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5,7,6,8] => [8,7,5,6,4,2,3,1] => 1101101 => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,3,7,5,8,6] => [8,7,5,6,2,4,1,3] => 1101010 => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,4,3,7,8,5,6] => [8,7,5,6,2,1,4,3] => 1101101 => 0
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,4,7,8,3,5,6] => [8,7,5,2,1,6,4,3] => 1111011 => 0
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => [8,7,5,2,6,4,3,1] => 1110111 => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,3,5,6,8,7] => [8,7,5,6,4,3,1,2] => 1101110 => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,3,5,8,6,7] => [8,7,5,6,4,1,3,2] => 1101101 => 0
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [8,7,5,6,1,4,3,2] => 1101011 => 0
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [8,7,5,1,6,4,3,2] => 1110111 => 0
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,5,6,7,8] => [8,7,5,6,4,3,2,1] => 1101111 => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,3] => [8,5,7,4,3,2,1,6] => 1011110 => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,4,2,5,6,7,3,8] => [8,5,7,4,3,2,6,1] => 1011101 => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,4,2,5,6,3,8,7] => [8,5,7,4,3,6,1,2] => 1011010 => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,4,2,5,6,8,3,7] => [8,5,7,4,3,1,6,2] => 1011101 => 0
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,4,2,5,6,3,7,8] => [8,5,7,4,3,6,2,1] => 1011011 => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,4,2,5,3,7,8,6] => [8,5,7,4,6,2,1,3] => 1010110 => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,8] => [8,5,7,4,6,2,3,1] => 1010101 => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,4,2,5,7,3,8,6] => [8,5,7,4,2,6,1,3] => 1011010 => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,4,2,5,7,8,3,6] => [8,5,7,4,2,1,6,3] => 1011101 => 0
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6,8] => [8,5,7,4,2,6,3,1] => 1011011 => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3,8,6,7] => [8,5,7,4,6,1,3,2] => 1010101 => 0
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,4,2,5,8,3,6,7] => [8,5,7,4,1,6,3,2] => 1011011 => 0
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,4,2,5,3,6,7,8] => [8,5,7,4,6,3,2,1] => 1010111 => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,5,2,6,7,8,3] => [8,5,4,7,3,2,1,6] => 1101110 => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,5,2,6,3,8,7] => [8,5,4,7,3,6,1,2] => 1101010 => 0
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,5,2,6,3,7,8] => [8,5,4,7,3,6,2,1] => 1101011 => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,4,5,6,2,7,8,3] => [8,5,4,3,7,2,1,6] => 1110110 => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,4,5,6,2,7,3,8] => [8,5,4,3,7,2,6,1] => 1110101 => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,7,2,8,3] => [8,5,4,3,2,7,1,6] => 1111010 => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,2,3] => [8,5,4,3,2,1,7,6] => 1111101 => 0
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,7,2,3,8] => [8,5,4,3,2,7,6,1] => 1111011 => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,4,5,6,2,3,8,7] => [8,5,4,3,7,6,1,2] => 1110110 => 0
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,4,5,6,8,2,3,7] => [8,5,4,3,1,7,6,2] => 1111011 => 0
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3,7,8] => [8,5,4,3,7,6,2,1] => 1110111 => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,4,5,2,3,7,8,6] => [8,5,4,7,6,2,1,3] => 1101110 => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,4,5,2,7,3,8,6] => [8,5,4,7,2,6,1,3] => 1101010 => 0
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6,8] => [8,5,4,7,2,6,3,1] => 1101011 => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,4,5,7,2,3,8,6] => [8,5,4,2,7,6,1,3] => 1110110 => 0
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,4,5,7,8,2,3,6] => [8,5,4,2,1,7,6,3] => 1111011 => 0
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6,8] => [8,5,4,2,7,6,3,1] => 1110111 => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,4,5,2,3,6,8,7] => [8,5,4,7,6,3,1,2] => 1101110 => 0
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,8,3,6,7] => [8,5,4,7,1,6,3,2] => 1101011 => 0
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,4,5,8,2,3,6,7] => [8,5,4,1,7,6,3,2] => 1110111 => 0
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,4,5,2,3,6,7,8] => [8,5,4,7,6,3,2,1] => 1101111 => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,6,7,8,5] => [8,5,7,6,3,2,1,4] => 1011110 => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,6,7,5,8] => [8,5,7,6,3,2,4,1] => 1011101 => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7] => [8,5,7,6,3,4,1,2] => 1011010 => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,8,5,7] => [8,5,7,6,3,1,4,2] => 1011101 => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,6,3,7,5,8] => [8,5,7,3,6,2,4,1] => 1010101 => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,6,7,3,8,5] => [8,5,7,3,2,6,1,4] => 1011010 => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,7,8,3,5] => [8,5,7,3,2,1,6,4] => 1011101 => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,8,7] => [8,5,7,3,6,4,1,2] => 1010110 => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,7] => [8,5,7,3,6,1,4,2] => 1010101 => 0
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,8,3,5,7] => [8,5,7,3,1,6,4,2] => 1011011 => 0
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,6,3,5,7,8] => [8,5,7,3,6,4,2,1] => 1010111 => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,4,6,2,3,7,5,8] => [8,5,3,7,6,2,4,1] => 1101101 => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,4,6,2,7,3,8,5] => [8,5,3,7,2,6,1,4] => 1101010 => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,4,6,2,7,8,3,5] => [8,5,3,7,2,1,6,4] => 1101101 => 0
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,7,3,5,8] => [8,5,3,7,2,6,4,1] => 1101011 => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,4,6,7,2,3,8,5] => [8,5,3,2,7,6,1,4] => 1110110 => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,4,6,7,2,8,3,5] => [8,5,3,2,7,1,6,4] => 1110101 => 0
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => [8,5,3,2,7,6,4,1] => 1110111 => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,8,7] => [8,5,3,7,6,4,1,2] => 1101110 => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,8,5,7] => [8,5,3,7,6,1,4,2] => 1101101 => 0
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,8,3,5,7] => [8,5,3,7,1,6,4,2] => 1101011 => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,4,2,3,5,7,8,6] => [8,5,7,6,4,2,1,3] => 1011110 => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2,3,5,7,6,8] => [8,5,7,6,4,2,3,1] => 1011101 => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,3,7,8,5,6] => [8,5,7,6,2,1,4,3] => 1011101 => 0
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2,3,7,5,6,8] => [8,5,7,6,2,4,3,1] => 1011011 => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,7,3,8,5,6] => [8,5,7,2,6,1,4,3] => 1010101 => 0
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,2,7,8,3,5,6] => [8,5,7,2,1,6,4,3] => 1011011 => 0
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2,7,3,5,6,8] => [8,5,7,2,6,4,3,1] => 1010111 => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,7,2,3,8,5,6] => [8,5,2,7,6,1,4,3] => 1101101 => 0
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,7,2,8,3,5,6] => [8,5,2,7,1,6,4,3] => 1101011 => 0
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,4,7,8,2,3,5,6] => [8,5,2,1,7,6,4,3] => 1110111 => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,4,2,3,5,6,8,7] => [8,5,7,6,4,3,1,2] => 1011110 => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [8,5,7,6,4,1,3,2] => 1011101 => 0
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,2,3,8,5,6,7] => [8,5,7,6,1,4,3,2] => 1011011 => 0
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,2,8,3,5,6,7] => [8,5,7,1,6,4,3,2] => 1010111 => 0
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => [8,5,1,7,6,4,3,2] => 1101111 => 0
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8] => [8,5,7,6,4,3,2,1] => 1011111 => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,3] => [5,8,7,4,3,2,1,6] => 0111110 => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,5,6,3,8,7] => [5,8,7,4,3,6,1,2] => 0111010 => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,5,6,8,3,7] => [5,8,7,4,3,1,6,2] => 0111101 => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3,7,8] => [5,8,7,4,3,6,2,1] => 0111011 => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,5,3,7,8,6] => [5,8,7,4,6,2,1,3] => 0110110 => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6,8] => [5,8,7,4,6,2,3,1] => 0110101 => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,5,7,3,8,6] => [5,8,7,4,2,6,1,3] => 0111010 => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,5,7,8,3,6] => [5,8,7,4,2,1,6,3] => 0111101 => 1
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6,8] => [5,8,7,4,2,6,3,1] => 0111011 => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,5,3,6,8,7] => [5,8,7,4,6,3,1,2] => 0110110 => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,1,2,5,3,8,6,7] => [5,8,7,4,6,1,3,2] => 0110101 => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,1,2,5,8,3,6,7] => [5,8,7,4,1,6,3,2] => 0111011 => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,5,3,6,7,8] => [5,8,7,4,6,3,2,1] => 0110111 => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => [5,8,4,7,3,2,1,6] => 0101110 => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,5,2,6,7,3,8] => [5,8,4,7,3,2,6,1] => 0101101 => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => [5,8,4,7,3,6,1,2] => 0101010 => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,5,2,6,8,3,7] => [5,8,4,7,3,1,6,2] => 0101101 => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,1,5,2,6,3,7,8] => [5,8,4,7,3,6,2,1] => 0101011 => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,5,6,2,7,8,3] => [5,8,4,3,7,2,1,6] => 0110110 => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,1,5,6,2,7,3,8] => [5,8,4,3,7,2,6,1] => 0110101 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,5,6,7,2,8,3] => [5,8,4,3,2,7,1,6] => 0111010 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,5,6,7,8,2,3] => [5,8,4,3,2,1,7,6] => 0111101 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,1,5,6,7,2,3,8] => [5,8,4,3,2,7,6,1] => 0111011 => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,5,6,2,3,8,7] => [5,8,4,3,7,6,1,2] => 0110110 => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [4,1,5,6,2,8,3,7] => [5,8,4,3,7,1,6,2] => 0110101 => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [4,1,5,6,8,2,3,7] => [5,8,4,3,1,7,6,2] => 0111011 => 1
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,1,5,6,2,3,7,8] => [5,8,4,3,7,6,2,1] => 0110111 => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => [5,8,4,7,6,2,1,3] => 0101110 => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6,8] => [5,8,4,7,6,2,3,1] => 0101101 => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,5,2,7,3,8,6] => [5,8,4,7,2,6,1,3] => 0101010 => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => [5,8,4,7,2,1,6,3] => 0101101 => 1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6,8] => [5,8,4,7,2,6,3,1] => 0101011 => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,1,5,7,2,8,3,6] => [5,8,4,2,7,1,6,3] => 0110101 => 1
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,1,5,7,8,2,3,6] => [5,8,4,2,1,7,6,3] => 0111011 => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [4,1,5,2,3,6,8,7] => [5,8,4,7,6,3,1,2] => 0101110 => 1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [4,1,5,2,8,3,6,7] => [5,8,4,7,1,6,3,2] => 0101011 => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,1,5,8,2,3,6,7] => [5,8,4,1,7,6,3,2] => 0110111 => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,1,5,2,3,6,7,8] => [5,8,4,7,6,3,2,1] => 0101111 => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,5,1,2,6,7,8,3] => [5,4,8,7,3,2,1,6] => 1011110 => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => [5,4,8,7,3,2,6,1] => 1011101 => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,5,1,2,6,3,8,7] => [5,4,8,7,3,6,1,2] => 1011010 => 0
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [4,5,1,2,6,3,7,8] => [5,4,8,7,3,6,2,1] => 1011011 => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,5,1,6,2,7,8,3] => [5,4,8,3,7,2,1,6] => 1010110 => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,5,1,6,2,7,3,8] => [5,4,8,3,7,2,6,1] => 1010101 => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,5,1,6,7,2,8,3] => [5,4,8,3,2,7,1,6] => 1011010 => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [4,5,1,6,7,8,2,3] => [5,4,8,3,2,1,7,6] => 1011101 => 0
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [4,5,1,6,7,2,3,8] => [5,4,8,3,2,7,6,1] => 1011011 => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [4,5,1,6,2,3,8,7] => [5,4,8,3,7,6,1,2] => 1010110 => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [4,5,1,6,2,8,3,7] => [5,4,8,3,7,1,6,2] => 1010101 => 0
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [4,5,1,6,8,2,3,7] => [5,4,8,3,1,7,6,2] => 1011011 => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,1,7,2,8,3] => [5,4,3,8,2,7,1,6] => 1101010 => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,6,1,7,8,2,3] => [5,4,3,8,2,1,7,6] => 1101101 => 0
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,6,1,7,2,3,8] => [5,4,3,8,2,7,6,1] => 1101011 => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,1,2,8,3] => [5,4,3,2,8,7,1,6] => 1110110 => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,1,8,2,3] => [5,4,3,2,8,1,7,6] => 1110101 => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,1,2,3] => [5,4,3,2,1,8,7,6] => 1111011 => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => [5,4,3,2,8,7,6,1] => 1110111 => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => [5,4,3,8,7,6,1,2] => 1101110 => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,6,1,2,8,3,7] => [5,4,3,8,7,1,6,2] => 1101101 => 0
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => [5,4,3,8,1,7,6,2] => 1101011 => 0
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [5,4,3,1,8,7,6,2] => 1110111 => 0
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [5,4,3,8,7,6,2,1] => 1101111 => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,7,8,6] => [5,4,8,7,6,2,1,3] => 1011110 => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6,8] => [5,4,8,7,6,2,3,1] => 1011101 => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [4,5,1,2,7,3,8,6] => [5,4,8,7,2,6,1,3] => 1011010 => 0
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6,8] => [5,4,8,7,2,6,3,1] => 1011011 => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [4,5,1,7,2,3,8,6] => [5,4,8,2,7,6,1,3] => 1010110 => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [4,5,1,7,2,8,3,6] => [5,4,8,2,7,1,6,3] => 1010101 => 0
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [4,5,1,7,8,2,3,6] => [5,4,8,2,1,7,6,3] => 1011011 => 0
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6,8] => [5,4,8,2,7,6,3,1] => 1010111 => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [4,5,7,1,2,3,8,6] => [5,4,2,8,7,6,1,3] => 1101110 => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [4,5,7,1,2,8,3,6] => [5,4,2,8,7,1,6,3] => 1101101 => 0
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [4,5,7,1,8,2,3,6] => [5,4,2,8,1,7,6,3] => 1101011 => 0
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [5,4,2,1,8,7,6,3] => 1110111 => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,5,1,2,3,6,8,7] => [5,4,8,7,6,3,1,2] => 1011110 => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [4,5,1,2,3,8,6,7] => [5,4,8,7,6,1,3,2] => 1011101 => 0
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,5,1,2,8,3,6,7] => [5,4,8,7,1,6,3,2] => 1011011 => 0
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,5,1,8,2,3,6,7] => [5,4,8,1,7,6,3,2] => 1010111 => 0
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => [5,4,1,8,7,6,3,2] => 1101111 => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,6,7,8,5] => [5,8,7,6,3,2,1,4] => 0111110 => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,6,7,5,8] => [5,8,7,6,3,2,4,1] => 0111101 => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => [5,8,7,6,3,4,1,2] => 0111010 => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,8,5,7] => [5,8,7,6,3,1,4,2] => 0111101 => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,6,5,7,8] => [5,8,7,6,3,4,2,1] => 0111011 => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5,8] => [5,8,7,3,6,2,4,1] => 0110101 => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,6,7,3,8,5] => [5,8,7,3,2,6,1,4] => 0111010 => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,2,6,7,8,3,5] => [5,8,7,3,2,1,6,4] => 0111101 => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,6,7,3,5,8] => [5,8,7,3,2,6,4,1] => 0111011 => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,8,5,7] => [5,8,7,3,6,1,4,2] => 0110101 => 1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,8,3,5,7] => [5,8,7,3,1,6,4,2] => 0111011 => 1
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,6,3,5,7,8] => [5,8,7,3,6,4,2,1] => 0110111 => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [5,8,3,7,6,2,1,4] => 0101110 => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,6,2,3,7,5,8] => [5,8,3,7,6,2,4,1] => 0101101 => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => [5,8,3,7,2,6,1,4] => 0101010 => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,6,2,7,8,3,5] => [5,8,3,7,2,1,6,4] => 0101101 => 1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,6,2,7,3,5,8] => [5,8,3,7,2,6,4,1] => 0101011 => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,6,7,2,3,8,5] => [5,8,3,2,7,6,1,4] => 0110110 => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,6,7,2,8,3,5] => [5,8,3,2,7,1,6,4] => 0110101 => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,6,7,8,2,3,5] => [5,8,3,2,1,7,6,4] => 0111011 => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,6,7,2,3,5,8] => [5,8,3,2,7,6,4,1] => 0110111 => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,8,7] => [5,8,3,7,6,4,1,2] => 0101110 => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,8,5,7] => [5,8,3,7,6,1,4,2] => 0101101 => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,8,3,5,7] => [5,8,3,7,1,6,4,2] => 0101011 => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,8,2,3,5,7] => [5,8,3,1,7,6,4,2] => 0110111 => 1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,6,2,3,5,7,8] => [5,8,3,7,6,4,2,1] => 0101111 => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [4,6,1,2,3,7,8,5] => [5,3,8,7,6,2,1,4] => 1011110 => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => [5,3,8,7,6,2,4,1] => 1011101 => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [4,6,1,2,7,8,3,5] => [5,3,8,7,2,1,6,4] => 1011101 => 0
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [4,6,1,2,7,3,5,8] => [5,3,8,7,2,6,4,1] => 1011011 => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [4,6,1,7,2,3,8,5] => [5,3,8,2,7,6,1,4] => 1010110 => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [4,6,1,7,2,8,3,5] => [5,3,8,2,7,1,6,4] => 1010101 => 0
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [4,6,1,7,8,2,3,5] => [5,3,8,2,1,7,6,4] => 1011011 => 0
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,6,1,7,2,3,5,8] => [5,3,8,2,7,6,4,1] => 1010111 => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [4,6,7,1,2,8,3,5] => [5,3,2,8,7,1,6,4] => 1101101 => 0
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [5,3,2,8,1,7,6,4] => 1101011 => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => [5,3,2,1,8,7,6,4] => 1110111 => 0
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,6,7,1,2,3,5,8] => [5,3,2,8,7,6,4,1] => 1101111 => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,8,7] => [5,3,8,7,6,4,1,2] => 1011110 => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,8,5,7] => [5,3,8,7,6,1,4,2] => 1011101 => 0
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,8,3,5,7] => [5,3,8,7,1,6,4,2] => 1011011 => 0
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,8,2,3,5,7] => [5,3,8,1,7,6,4,2] => 1010111 => 0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,8,1,2,3,5,7] => [5,3,1,8,7,6,4,2] => 1101111 => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [4,6,1,2,3,5,7,8] => [5,3,8,7,6,4,2,1] => 1011111 => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,2,3,5,7,8,6] => [5,8,7,6,4,2,1,3] => 0111110 => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,7,6,8] => [5,8,7,6,4,2,3,1] => 0111101 => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,3,7,5,8,6] => [5,8,7,6,2,4,1,3] => 0111010 => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,3,7,8,5,6] => [5,8,7,6,2,1,4,3] => 0111101 => 1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,3,7,5,6,8] => [5,8,7,6,2,4,3,1] => 0111011 => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,7,3,5,8,6] => [5,8,7,2,6,4,1,3] => 0110110 => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [4,1,2,7,3,8,5,6] => [5,8,7,2,6,1,4,3] => 0110101 => 1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [4,1,2,7,8,3,5,6] => [5,8,7,2,1,6,4,3] => 0111011 => 1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,1,2,7,3,5,6,8] => [5,8,7,2,6,4,3,1] => 0110111 => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,7,2,3,5,8,6] => [5,8,2,7,6,4,1,3] => 0101110 => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [4,1,7,2,3,8,5,6] => [5,8,2,7,6,1,4,3] => 0101101 => 1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [4,1,7,2,8,3,5,6] => [5,8,2,7,1,6,4,3] => 0101011 => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,1,7,8,2,3,5,6] => [5,8,2,1,7,6,4,3] => 0110111 => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6,8] => [5,8,2,7,6,4,3,1] => 0101111 => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [4,7,1,2,3,5,8,6] => [5,2,8,7,6,4,1,3] => 1011110 => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [4,7,1,2,3,8,5,6] => [5,2,8,7,6,1,4,3] => 1011101 => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [4,7,1,2,8,3,5,6] => [5,2,8,7,1,6,4,3] => 1011011 => 0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,7,1,8,2,3,5,6] => [5,2,8,1,7,6,4,3] => 1010111 => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,7,8,1,2,3,5,6] => [5,2,1,8,7,6,4,3] => 1101111 => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6,8] => [5,2,8,7,6,4,3,1] => 1011111 => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [5,8,7,6,4,3,1,2] => 0111110 => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [4,1,2,3,5,8,6,7] => [5,8,7,6,4,1,3,2] => 0111101 => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,1,2,3,8,5,6,7] => [5,8,7,6,1,4,3,2] => 0111011 => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,8,3,5,6,7] => [5,8,7,1,6,4,3,2] => 0110111 => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [5,8,1,7,6,4,3,2] => 0101111 => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [5,1,8,7,6,4,3,2] => 1011111 => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [5,8,7,6,4,3,2,1] => 0111111 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,4] => [8,7,6,4,3,2,1,5] => 1111110 => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,5,6,7,4,8] => [8,7,6,4,3,2,5,1] => 1111101 => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,8,4,7] => [8,7,6,4,3,1,5,2] => 1111101 => 0
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,5,6,4,7,8] => [8,7,6,4,3,5,2,1] => 1111011 => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,7,8,6] => [8,7,6,4,5,2,1,3] => 1110110 => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,8] => [8,7,6,4,5,2,3,1] => 1110101 => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,2,3,5,7,4,8,6] => [8,7,6,4,2,5,1,3] => 1111010 => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,2,3,5,7,8,4,6] => [8,7,6,4,2,1,5,3] => 1111101 => 0
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6,8] => [8,7,6,4,2,5,3,1] => 1111011 => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,5,4,6,8,7] => [8,7,6,4,5,3,1,2] => 1110110 => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => [8,7,6,4,5,1,3,2] => 1110101 => 0
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,5,8,4,6,7] => [8,7,6,4,1,5,3,2] => 1111011 => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [8,7,6,4,5,3,2,1] => 1110111 => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,4] => [8,7,4,6,3,2,1,5] => 1101110 => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,2,5,3,6,7,4,8] => [8,7,4,6,3,2,5,1] => 1101101 => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,2,5,3,6,4,8,7] => [8,7,4,6,3,5,1,2] => 1101010 => 0
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,2,5,3,6,4,7,8] => [8,7,4,6,3,5,2,1] => 1101011 => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,2,5,6,3,7,8,4] => [8,7,4,3,6,2,1,5] => 1110110 => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,2,5,6,3,7,4,8] => [8,7,4,3,6,2,5,1] => 1110101 => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,2,5,6,7,3,8,4] => [8,7,4,3,2,6,1,5] => 1111010 => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,6,7,8,3,4] => [8,7,4,3,2,1,6,5] => 1111101 => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,2,5,6,3,4,8,7] => [8,7,4,3,6,5,1,2] => 1110110 => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,2,5,6,3,8,4,7] => [8,7,4,3,6,1,5,2] => 1110101 => 0
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [8,7,4,3,6,5,2,1] => 1110111 => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,7,8,6] => [8,7,4,6,5,2,1,3] => 1101110 => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6,8] => [8,7,4,6,5,2,3,1] => 1101101 => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,2,5,3,7,4,8,6] => [8,7,4,6,2,5,1,3] => 1101010 => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,2,5,3,7,8,4,6] => [8,7,4,6,2,1,5,3] => 1101101 => 0
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6,8] => [8,7,4,6,2,5,3,1] => 1101011 => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,2,5,7,3,4,8,6] => [8,7,4,2,6,5,1,3] => 1110110 => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,2,5,7,3,8,4,6] => [8,7,4,2,6,1,5,3] => 1110101 => 0
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,2,5,7,8,3,4,6] => [8,7,4,2,1,6,5,3] => 1111011 => 0
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [8,7,4,2,6,5,3,1] => 1110111 => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,2,5,3,4,6,8,7] => [8,7,4,6,5,3,1,2] => 1101110 => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4,8,6,7] => [8,7,4,6,5,1,3,2] => 1101101 => 0
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [8,7,4,6,1,5,3,2] => 1101011 => 0
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => [8,7,4,1,6,5,3,2] => 1110111 => 0
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,2,5,3,4,6,7,8] => [8,7,4,6,5,3,2,1] => 1101111 => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,5,2,3,6,7,8,4] => [8,4,7,6,3,2,1,5] => 1011110 => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,5,2,3,6,4,8,7] => [8,4,7,6,3,5,1,2] => 1011010 => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,5,2,3,6,8,4,7] => [8,4,7,6,3,1,5,2] => 1011101 => 0
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,2,3,6,4,7,8] => [8,4,7,6,3,5,2,1] => 1011011 => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,5,2,6,3,7,8,4] => [8,4,7,3,6,2,1,5] => 1010110 => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2,6,3,7,4,8] => [8,4,7,3,6,2,5,1] => 1010101 => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,5,2,6,7,3,8,4] => [8,4,7,3,2,6,1,5] => 1011010 => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,5,2,6,3,4,8,7] => [8,4,7,3,6,5,1,2] => 1010110 => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,3,8,4,7] => [8,4,7,3,6,1,5,2] => 1010101 => 0
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,2,6,8,3,4,7] => [8,4,7,3,1,6,5,2] => 1011011 => 0
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,2,6,3,4,7,8] => [8,4,7,3,6,5,2,1] => 1010111 => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,5,6,2,3,7,8,4] => [8,4,3,7,6,2,1,5] => 1101110 => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,5,6,2,7,3,8,4] => [8,4,3,7,2,6,1,5] => 1101010 => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,5,6,2,7,8,3,4] => [8,4,3,7,2,1,6,5] => 1101101 => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,5,6,7,2,3,8,4] => [8,4,3,2,7,6,1,5] => 1110110 => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,5,6,7,2,8,3,4] => [8,4,3,2,7,1,6,5] => 1110101 => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,2,3,4] => [8,4,3,2,1,7,6,5] => 1111011 => 0
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,5,6,7,2,3,4,8] => [8,4,3,2,7,6,5,1] => 1110111 => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,5,6,2,3,4,8,7] => [8,4,3,7,6,5,1,2] => 1101110 => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,6,2,3,8,4,7] => [8,4,3,7,6,1,5,2] => 1101101 => 0
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,5,6,2,8,3,4,7] => [8,4,3,7,1,6,5,2] => 1101011 => 0
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,5,6,8,2,3,4,7] => [8,4,3,1,7,6,5,2] => 1110111 => 0
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,5,6,2,3,4,7,8] => [8,4,3,7,6,5,2,1] => 1101111 => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,7,8,6] => [8,4,7,6,5,2,1,3] => 1011110 => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6,8] => [8,4,7,6,5,2,3,1] => 1011101 => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,7,4,8,6] => [8,4,7,6,2,5,1,3] => 1011010 => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,7,8,4,6] => [8,4,7,6,2,1,5,3] => 1011101 => 0
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6,8] => [8,4,7,6,2,5,3,1] => 1011011 => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,5,2,7,3,4,8,6] => [8,4,7,2,6,5,1,3] => 1010110 => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,7,3,8,4,6] => [8,4,7,2,6,1,5,3] => 1010101 => 0
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,5,2,7,8,3,4,6] => [8,4,7,2,1,6,5,3] => 1011011 => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6,8] => [8,4,7,2,6,5,3,1] => 1010111 => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,5,7,2,3,4,8,6] => [8,4,2,7,6,5,1,3] => 1101110 => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,7,2,3,8,4,6] => [8,4,2,7,6,1,5,3] => 1101101 => 0
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [8,4,2,7,1,6,5,3] => 1101011 => 0
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,5,7,8,2,3,4,6] => [8,4,2,1,7,6,5,3] => 1110111 => 0
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6,8] => [8,4,2,7,6,5,3,1] => 1101111 => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,5,2,3,4,6,8,7] => [8,4,7,6,5,3,1,2] => 1011110 => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [8,4,7,6,5,1,3,2] => 1011101 => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,5,2,8,3,4,6,7] => [8,4,7,1,6,5,3,2] => 1010111 => 0
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [8,4,1,7,6,5,3,2] => 1101111 => 0
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8] => [8,4,7,6,5,3,2,1] => 1011111 => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,4] => [4,8,7,6,3,2,1,5] => 0111110 => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,6,7,4,8] => [4,8,7,6,3,2,5,1] => 0111101 => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,1,2,3,6,8,4,7] => [4,8,7,6,3,1,5,2] => 0111101 => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,6,4,7,8] => [4,8,7,6,3,5,2,1] => 0111011 => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,2,6,3,7,8,4] => [4,8,7,3,6,2,1,5] => 0110110 => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,1,2,6,3,7,4,8] => [4,8,7,3,6,2,5,1] => 0110101 => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,7,3,8,4] => [4,8,7,3,2,6,1,5] => 0111010 => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,1,2,6,7,8,3,4] => [4,8,7,3,2,1,6,5] => 0111101 => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,1,2,6,7,3,4,8] => [4,8,7,3,2,6,5,1] => 0111011 => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,3,4,8,7] => [4,8,7,3,6,5,1,2] => 0110110 => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,1,2,6,3,8,4,7] => [4,8,7,3,6,1,5,2] => 0110101 => 1
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,1,2,6,8,3,4,7] => [4,8,7,3,1,6,5,2] => 0111011 => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,1,2,6,3,4,7,8] => [4,8,7,3,6,5,2,1] => 0110111 => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,1,6,2,3,7,4,8] => [4,8,3,7,6,2,5,1] => 0101101 => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => [4,8,3,7,2,6,1,5] => 0101010 => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [5,1,6,2,7,8,3,4] => [4,8,3,7,2,1,6,5] => 0101101 => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,6,7,2,3,8,4] => [4,8,3,2,7,6,1,5] => 0110110 => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,1,6,7,8,2,3,4] => [4,8,3,2,1,7,6,5] => 0111011 => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,1,6,7,2,3,4,8] => [4,8,3,2,7,6,5,1] => 0110111 => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [5,1,6,2,3,4,8,7] => [4,8,3,7,6,5,1,2] => 0101110 => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [5,1,6,2,3,8,4,7] => [4,8,3,7,6,1,5,2] => 0101101 => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,1,6,2,8,3,4,7] => [4,8,3,7,1,6,5,2] => 0101011 => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,1,6,8,2,3,4,7] => [4,8,3,1,7,6,5,2] => 0110111 => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [5,1,6,2,3,4,7,8] => [4,8,3,7,6,5,2,1] => 0101111 => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,6,1,2,3,7,8,4] => [4,3,8,7,6,2,1,5] => 1011110 => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,7,4,8] => [4,3,8,7,6,2,5,1] => 1011101 => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1,2,7,3,8,4] => [4,3,8,7,2,6,1,5] => 1011010 => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [5,6,1,2,7,8,3,4] => [4,3,8,7,2,1,6,5] => 1011101 => 0
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,6,1,2,7,3,4,8] => [4,3,8,7,2,6,5,1] => 1011011 => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,6,1,7,2,3,8,4] => [4,3,8,2,7,6,1,5] => 1010110 => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [5,6,1,7,2,8,3,4] => [4,3,8,2,7,1,6,5] => 1010101 => 0
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,1,7,2,3,4,8] => [4,3,8,2,7,6,5,1] => 1010111 => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,6,7,1,2,3,8,4] => [4,3,2,8,7,6,1,5] => 1101110 => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [5,6,7,1,2,8,3,4] => [4,3,2,8,7,1,6,5] => 1101101 => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [4,3,2,8,1,7,6,5] => 1101011 => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => 1110111 => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,1,2,3,4,8] => [4,3,2,8,7,6,5,1] => 1101111 => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,8,7] => [4,3,8,7,6,5,1,2] => 1011110 => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [5,6,1,2,3,8,4,7] => [4,3,8,7,6,1,5,2] => 1011101 => 0
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,6,1,2,8,3,4,7] => [4,3,8,7,1,6,5,2] => 1011011 => 0
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,6,1,8,2,3,4,7] => [4,3,8,1,7,6,5,2] => 1010111 => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => [4,3,1,8,7,6,5,2] => 1101111 => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,6,1,2,3,4,7,8] => [4,3,8,7,6,5,2,1] => 1011111 => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,7,8,6] => [4,8,7,6,5,2,1,3] => 0111110 => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6,8] => [4,8,7,6,5,2,3,1] => 0111101 => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,7,8,4,6] => [4,8,7,6,2,1,5,3] => 0111101 => 1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6,8] => [4,8,7,6,2,5,3,1] => 0111011 => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,7,3,4,8,6] => [4,8,7,2,6,5,1,3] => 0110110 => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,7,3,8,4,6] => [4,8,7,2,6,1,5,3] => 0110101 => 1
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,7,8,3,4,6] => [4,8,7,2,1,6,5,3] => 0111011 => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6,8] => [4,8,7,2,6,5,3,1] => 0110111 => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [5,1,7,2,3,4,8,6] => [4,8,2,7,6,5,1,3] => 0101110 => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [5,1,7,2,3,8,4,6] => [4,8,2,7,6,1,5,3] => 0101101 => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,1,7,2,8,3,4,6] => [4,8,2,7,1,6,5,3] => 0101011 => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,1,7,8,2,3,4,6] => [4,8,2,1,7,6,5,3] => 0110111 => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6,8] => [4,8,2,7,6,5,3,1] => 0101111 => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,7,1,2,3,4,8,6] => [4,2,8,7,6,5,1,3] => 1011110 => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [5,7,1,2,3,8,4,6] => [4,2,8,7,6,1,5,3] => 1011101 => 0
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,7,1,2,8,3,4,6] => [4,2,8,7,1,6,5,3] => 1011011 => 0
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,7,1,8,2,3,4,6] => [4,2,8,1,7,6,5,3] => 1010111 => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => [4,2,1,8,7,6,5,3] => 1101111 => 0
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6,8] => [4,2,8,7,6,5,3,1] => 1011111 => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [4,8,7,6,5,3,1,2] => 0111110 => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [5,1,2,3,4,8,6,7] => [4,8,7,6,5,1,3,2] => 0111101 => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,8,4,6,7] => [4,8,7,6,1,5,3,2] => 0111011 => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,1,2,8,3,4,6,7] => [4,8,7,1,6,5,3,2] => 0110111 => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [5,1,8,2,3,4,6,7] => [4,8,1,7,6,5,3,2] => 0101111 => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [4,1,8,7,6,5,3,2] => 1011111 => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8] => [4,8,7,6,5,3,2,1] => 0111111 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,5] => [8,7,6,5,3,2,1,4] => 1111110 => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,6,7,5,8] => [8,7,6,5,3,2,4,1] => 1111101 => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7] => [8,7,6,5,3,4,1,2] => 1111010 => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,6,8,5,7] => [8,7,6,5,3,1,4,2] => 1111101 => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,7,8] => [8,7,6,5,3,4,2,1] => 1111011 => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,6,4,7,8,5] => [8,7,6,3,5,2,1,4] => 1110110 => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,6,4,7,5,8] => [8,7,6,3,5,2,4,1] => 1110101 => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,2,3,6,7,4,8,5] => [8,7,6,3,2,5,1,4] => 1111010 => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,2,3,6,7,8,4,5] => [8,7,6,3,2,1,5,4] => 1111101 => 0
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,2,3,6,7,4,5,8] => [8,7,6,3,2,5,4,1] => 1111011 => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,6,4,5,8,7] => [8,7,6,3,5,4,1,2] => 1110110 => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,2,3,6,4,8,5,7] => [8,7,6,3,5,1,4,2] => 1110101 => 0
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,2,3,6,8,4,5,7] => [8,7,6,3,1,5,4,2] => 1111011 => 0
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [8,7,6,3,5,4,2,1] => 1110111 => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,2,6,3,4,7,8,5] => [8,7,3,6,5,2,1,4] => 1101110 => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,2,6,3,4,7,5,8] => [8,7,3,6,5,2,4,1] => 1101101 => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,2,6,3,7,4,8,5] => [8,7,3,6,2,5,1,4] => 1101010 => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,2,6,3,7,8,4,5] => [8,7,3,6,2,1,5,4] => 1101101 => 0
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,2,6,3,7,4,5,8] => [8,7,3,6,2,5,4,1] => 1101011 => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,2,6,7,3,4,8,5] => [8,7,3,2,6,5,1,4] => 1110110 => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,2,6,7,3,8,4,5] => [8,7,3,2,6,1,5,4] => 1110101 => 0
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,7,8,3,4,5] => [8,7,3,2,1,6,5,4] => 1111011 => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,2,6,3,4,8,5,7] => [8,7,3,6,5,1,4,2] => 1101101 => 0
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => [8,7,3,6,1,5,4,2] => 1101011 => 0
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,8,3,4,5,7] => [8,7,3,1,6,5,4,2] => 1110111 => 0
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,3,4,5,7,8] => [8,7,3,6,5,4,2,1] => 1101111 => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,6,2,3,4,7,5,8] => [8,3,7,6,5,2,4,1] => 1011101 => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,6,2,3,7,4,8,5] => [8,3,7,6,2,5,1,4] => 1011010 => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,6,2,3,7,8,4,5] => [8,3,7,6,2,1,5,4] => 1011101 => 0
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,2,3,7,4,5,8] => [8,3,7,6,2,5,4,1] => 1011011 => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,6,2,7,3,4,8,5] => [8,3,7,2,6,5,1,4] => 1010110 => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,5] => [8,3,7,2,6,1,5,4] => 1010101 => 0
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,6,2,7,8,3,4,5] => [8,3,7,2,1,6,5,4] => 1011011 => 0
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,6,2,7,3,4,5,8] => [8,3,7,2,6,5,4,1] => 1010111 => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,6,7,2,3,4,8,5] => [8,3,2,7,6,5,1,4] => 1101110 => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,7,2,3,8,4,5] => [8,3,2,7,6,1,5,4] => 1101101 => 0
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,6,7,2,8,3,4,5] => [8,3,2,7,1,6,5,4] => 1101011 => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [8,3,2,1,7,6,5,4] => 1110111 => 0
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,6,7,2,3,4,5,8] => [8,3,2,7,6,5,4,1] => 1101111 => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [8,3,7,6,5,1,4,2] => 1011101 => 0
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,6,2,3,8,4,5,7] => [8,3,7,6,1,5,4,2] => 1011011 => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,6,2,8,3,4,5,7] => [8,3,7,1,6,5,4,2] => 1010111 => 0
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [8,3,1,7,6,5,4,2] => 1101111 => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,6,2,3,4,5,7,8] => [8,3,7,6,5,4,2,1] => 1011111 => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,7,8,5] => [3,8,7,6,5,2,1,4] => 0111110 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,7,5,8] => [3,8,7,6,5,2,4,1] => 0111101 => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,3,7,4,8,5] => [3,8,7,6,2,5,1,4] => 0111010 => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,1,2,3,7,8,4,5] => [3,8,7,6,2,1,5,4] => 0111101 => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [6,1,2,3,7,4,5,8] => [3,8,7,6,2,5,4,1] => 0111011 => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,7,3,4,8,5] => [3,8,7,2,6,5,1,4] => 0110110 => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,1,2,7,3,8,4,5] => [3,8,7,2,6,1,5,4] => 0110101 => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,1,2,7,8,3,4,5] => [3,8,7,2,1,6,5,4] => 0111011 => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [6,1,2,7,3,4,5,8] => [3,8,7,2,6,5,4,1] => 0110111 => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,7,2,3,4,8,5] => [3,8,2,7,6,5,1,4] => 0101110 => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,1,7,2,3,8,4,5] => [3,8,2,7,6,1,5,4] => 0101101 => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,1,7,2,8,3,4,5] => [3,8,2,7,1,6,5,4] => 0101011 => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [6,1,7,8,2,3,4,5] => [3,8,2,1,7,6,5,4] => 0110111 => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [6,1,7,2,3,4,5,8] => [3,8,2,7,6,5,4,1] => 0101111 => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => [3,2,8,7,6,5,1,4] => 1011110 => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,7,1,2,3,8,4,5] => [3,2,8,7,6,1,5,4] => 1011101 => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,7,1,2,8,3,4,5] => [3,2,8,7,1,6,5,4] => 1011011 => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [6,7,1,8,2,3,4,5] => [3,2,8,1,7,6,5,4] => 1010111 => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => [3,2,1,8,7,6,5,4] => 1101111 => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5,8] => [3,2,8,7,6,5,4,1] => 1011111 => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [3,8,7,6,5,4,1,2] => 0111110 => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,8,5,7] => [3,8,7,6,5,1,4,2] => 0111101 => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,8,4,5,7] => [3,8,7,6,1,5,4,2] => 0111011 => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [6,1,2,8,3,4,5,7] => [3,8,7,1,6,5,4,2] => 0110111 => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [3,8,1,7,6,5,4,2] => 0101111 => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => [3,1,8,7,6,5,4,2] => 1011111 => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8] => [3,8,7,6,5,4,2,1] => 0111111 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => [8,7,6,5,4,2,1,3] => 1111110 => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,7,6,8] => [8,7,6,5,4,2,3,1] => 1111101 => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6] => [8,7,6,5,2,4,1,3] => 1111010 => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,7,8,5,6] => [8,7,6,5,2,1,4,3] => 1111101 => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,7,5,6,8] => [8,7,6,5,2,4,3,1] => 1111011 => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,2,3,7,4,5,8,6] => [8,7,6,2,5,4,1,3] => 1110110 => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,2,3,7,4,8,5,6] => [8,7,6,2,5,1,4,3] => 1110101 => 0
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [8,7,6,2,5,4,3,1] => 1110111 => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => [8,7,2,6,5,4,1,3] => 1101110 => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,2,7,3,4,8,5,6] => [8,7,2,6,5,1,4,3] => 1101101 => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [8,7,2,6,1,5,4,3] => 1101011 => 0
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [8,7,2,1,6,5,4,3] => 1110111 => 0
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6,8] => [8,7,2,6,5,4,3,1] => 1101111 => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => [8,2,7,6,5,4,1,3] => 1011110 => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [8,2,7,6,5,1,4,3] => 1011101 => 0
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,7,2,3,8,4,5,6] => [8,2,7,6,1,5,4,3] => 1011011 => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,7,2,8,3,4,5,6] => [8,2,7,1,6,5,4,3] => 1010111 => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [8,2,1,7,6,5,4,3] => 1101111 => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8] => [8,2,7,6,5,4,3,1] => 1011111 => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [2,8,7,6,5,4,1,3] => 0111110 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => [2,8,7,6,5,1,4,3] => 0111101 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [7,1,2,3,8,4,5,6] => [2,8,7,6,1,5,4,3] => 0111011 => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [7,1,2,8,3,4,5,6] => [2,8,7,1,6,5,4,3] => 0110111 => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [2,8,1,7,6,5,4,3] => 0101111 => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [2,1,8,7,6,5,4,3] => 1011111 => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8] => [2,8,7,6,5,4,3,1] => 0111111 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => [8,7,6,5,4,3,1,2] => 1111110 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,8,6,7] => [8,7,6,5,4,1,3,2] => 1111101 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,3,4,8,5,6,7] => [8,7,6,5,1,4,3,2] => 1111011 => 0
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [8,7,6,1,5,4,3,2] => 1110111 => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [8,7,1,6,5,4,3,2] => 1101111 => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [8,1,7,6,5,4,3,2] => 1011111 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => 1111111 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => [9,8,7,6,5,4,3,1,2] => 11111110 => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [8,9,7,6,5,4,3,2,1] => 01111111 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => [10,9,8,7,6,5,4,3,1,2] => 111111110 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => [2,9,8,7,6,5,4,1,3] => 01111110 => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => [8,1,9,7,6,5,4,3,2] => 10111111 => 0
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [9,10,8,7,6,5,4,3,2,1] => 011111111 => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => [11,10,9,8,7,6,5,4,3,1,2] => 1111111110 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => [2,10,9,8,7,6,5,4,1,3] => 011111110 => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => [9,2,8,7,6,5,4,1,3] => 10111110 => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => [3,9,8,7,6,5,4,1,2] => 01111110 => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => [8,9,1,7,6,5,4,3,2] => 01011111 => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7,9] => [8,2,9,7,6,5,4,3,1] => 10111111 => 0
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => [9,1,10,8,7,6,5,4,3,2] => 101111111 => 0
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [10,11,9,8,7,6,5,4,3,2,1] => 0111111111 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => [9,10,1,8,7,6,5,4,3,2] => 010111111 => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [8,9,1,2,3,4,5,6,10,7] => [3,2,10,9,8,7,6,5,1,4] => 101111110 => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,9,8] => [5,9,8,7,6,4,3,1,2] => 01111110 => 1
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,9,10,1,3,4,5,6,7,8] => [9,2,1,10,8,7,6,5,4,3] => 110111111 => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [6,7,1,2,3,4,5,9,8] => [4,3,9,8,7,6,5,1,2] => 10111110 => 0
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [2,1,8,9,3,4,5,6,7] => [8,9,2,1,7,6,5,4,3] => 01101111 => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8,10,9] => [6,10,9,8,7,5,4,3,1,2] => 011111110 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,8,6,9,7] => [9,8,7,6,5,2,4,1,3] => 11111010 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,9] => [9,8,7,6,5,4,2,3,1] => 11111101 => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,9,7,8] => [8,9,7,6,5,4,1,3,2] => 01111101 => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9] => [9,7,8,6,5,4,3,2,1] => 10111111 => 0
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8,9] => [8,6,9,7,5,4,3,2,1] => 10111111 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,8,9,7] => [9,8,7,6,5,4,2,1,3] => 11111110 => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => [8,9,7,6,5,4,3,1,2] => 01111110 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,8,6,9] => [3,9,8,7,6,5,2,4,1] => 01111101 => 1
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,9,2,4,5,6,7,8] => [9,7,1,8,6,5,4,3,2] => 11011111 => 0
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [8,7,9,6,5,4,3,2,1] => 10111111 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,6,9,7,10,8] => [10,9,8,7,6,5,2,4,1,3] => 111111010 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8,10] => [10,9,8,7,6,5,4,2,3,1] => 111111101 => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,8,9,6] => [3,9,8,7,6,5,2,1,4] => 01111110 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,7,10,8,9] => [9,10,8,7,6,5,4,1,3,2] => 011111101 => 1
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,9,1,4,5,6,7,8] => [8,7,1,9,6,5,4,3,2] => 11011111 => 0
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9,10] => [10,8,9,7,6,5,4,3,2,1] => 101111111 => 0
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8,9,10] => [9,7,10,8,6,5,4,3,2,1] => 101111111 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,9,10,8] => [10,9,8,7,6,5,4,2,1,3] => 111111110 => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => [9,10,8,7,6,5,4,3,1,2] => 011111110 => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,8,9,7] => [4,9,8,7,6,5,2,1,3] => 01111110 => 1
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,3,1,9,4,5,6,7,8] => [8,7,9,1,6,5,4,3,2] => 10101111 => 0
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [9,8,10,7,6,5,4,3,2,1] => 101111111 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,1,2] => [7,6,5,4,3,2,1,9,8] => 11111101 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,1,2,9] => [7,6,5,4,3,2,9,8,1] => 11111011 => 0
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => [7,6,9,8,5,4,3,2,1] => 10111111 => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,9,6,8] => [7,9,5,8,3,6,1,4,2] => 01010101 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,7,4,6,8,9] => [7,9,5,8,3,6,4,2,1] => 01010111 => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,5,2,8,4,9,6,7] => [7,9,5,8,2,6,1,4,3] => 01010101 => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,9,1,2,4,6,8] => [7,5,3,1,9,8,6,4,2] => 11101111 => 0
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [3,1,2,8,9,4,5,6,7] => [7,9,8,2,1,6,5,4,3] => 01110111 => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,9,1,2,4,5,6,7,8] => [7,1,9,8,6,5,4,3,2] => 10111111 => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [7,9,8,6,5,4,3,2,1] => 01111111 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,9,2,3] => [9,6,5,4,3,2,1,8,7] => 11111101 => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,9,1,2,3] => [6,5,4,3,2,1,9,8,7] => 11111011 => 0
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => [6,5,4,9,8,7,3,2,1] => 11011111 => 0
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,5,1,2,3,9,6,7,8] => [6,5,9,8,7,1,4,3,2] => 10111011 => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [4,1,2,3,8,9,5,6,7] => [6,9,8,7,2,1,5,4,3] => 01111011 => 1
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,9,1,2,3,5,6,7,8] => [6,1,9,8,7,5,4,3,2] => 10111111 => 0
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [6,9,8,7,5,4,3,2,1] => 01111111 => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,9,6,8] => [9,8,5,7,3,6,1,4,2] => 11010101 => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [5,4,3,2,1,9,8,7,6] => 11110111 => 0
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [5,4,3,2,9,8,7,6,1] => 11101111 => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [5,6,1,2,3,4,9,7,8] => [5,4,9,8,7,6,1,3,2] => 10111101 => 0
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [5,9,1,2,3,4,6,7,8] => [5,1,9,8,7,6,4,3,2] => 10111111 => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [5,9,8,7,6,4,3,2,1] => 01111111 => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,2,3,6,4,5,7,8,9] => [9,8,7,4,6,5,3,2,1] => 11101111 => 0
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,6,3,4,5,7,8,9] => [9,8,4,7,6,5,3,2,1] => 11011111 => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,9,2,3,4,5] => [9,4,3,2,1,8,7,6,5] => 11110111 => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [4,3,2,1,9,8,7,6,5] => 11101111 => 0
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7,9] => [4,2,9,8,7,6,5,3,1] => 10111111 => 0
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [6,9,1,2,3,4,5,7,8] => [4,1,9,8,7,6,5,3,2] => 10111111 => 0
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [4,9,8,7,6,5,3,2,1] => 01111111 => 1
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [1,2,7,3,4,5,6,8,9] => [9,8,3,7,6,5,4,2,1] => 11011111 => 0
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [1,7,9,2,3,4,5,6,8] => [9,3,1,8,7,6,5,4,2] => 11011111 => 0
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8,9] => [9,3,8,7,6,5,4,2,1] => 10111111 => 0
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [7,1,8,2,3,4,5,6,9] => [3,9,2,8,7,6,5,4,1] => 01011111 => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => [3,2,1,9,8,7,6,5,4] => 11011111 => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6,9] => [3,2,9,8,7,6,5,4,1] => 10111111 => 0
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [7,9,1,2,3,4,5,6,8] => [3,1,9,8,7,6,5,4,2] => 10111111 => 0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9] => [3,9,8,7,6,5,4,2,1] => 01111111 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,5,8,9,6,7] => [9,8,7,6,5,2,1,4,3] => 11111101 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,5,8,6,7,9] => [9,8,7,6,5,2,4,3,1] => 11111011 => 0
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,8,2,9,3,4,5,6,7] => [9,2,8,1,7,6,5,4,3] => 10101111 => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7] => [9,2,1,8,7,6,5,4,3] => 11011111 => 0
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7,9] => [9,2,8,7,6,5,4,3,1] => 10111111 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,9,6,7] => [2,9,8,7,6,5,1,4,3] => 01111101 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,9,5,6,7] => [2,9,8,7,6,1,5,4,3] => 01111011 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [8,1,2,3,9,4,5,6,7] => [2,9,8,7,1,6,5,4,3] => 01110111 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [8,1,2,9,3,4,5,6,7] => [2,9,8,1,7,6,5,4,3] => 01101111 => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [8,1,9,2,3,4,5,6,7] => [2,9,1,8,7,6,5,4,3] => 01011111 => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => [2,1,9,8,7,6,5,4,3] => 10111111 => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9] => [2,9,8,7,6,5,4,3,1] => 01111111 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,9,7,8] => [9,8,7,6,5,4,1,3,2] => 11111101 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,9,6,7,8] => [9,8,7,6,5,1,4,3,2] => 11111011 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [9,8,7,6,1,5,4,3,2] => 11110111 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [9,8,7,1,6,5,4,3,2] => 11101111 => 0
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => [9,8,1,7,6,5,4,3,2] => 11011111 => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => [9,1,8,7,6,5,4,3,2] => 10111111 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1] => 11111111 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,1] => [8,7,6,5,4,3,2,1,9] => 11111110 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,1,9] => [8,7,6,5,4,3,2,9,1] => 11111101 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,9,1,8] => [8,7,6,5,4,3,1,9,2] => 11111101 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,8,9,1,7] => [8,7,6,5,4,2,1,9,3] => 11111101 => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,7,8,9,1,6] => [8,7,6,5,3,2,1,9,4] => 11111101 => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,9,1,5] => [8,7,6,4,3,2,1,9,5] => 11111101 => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,9,1,4] => [8,7,5,4,3,2,1,9,6] => 11111101 => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,9,1,3] => [8,6,5,4,3,2,1,9,7] => 11111101 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,1] => [9,8,7,6,5,4,3,2,1,10] => 111111110 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,10] => [9,8,7,6,5,4,3,2,10,1] => 111111101 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,1,8,9] => [8,7,6,5,4,3,9,2,1] => 11111011 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,10,1,9] => [9,8,7,6,5,4,3,1,10,2] => 111111101 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,6,1,9,7,8] => [8,7,6,5,4,9,1,3,2] => 11110101 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,7,9,10,1,8] => [9,8,7,6,5,4,2,1,10,3] => 111111101 => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,5,1,8,9,6,7] => [8,7,6,5,9,2,1,4,3] => 11101101 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,8,9,10,1,7] => [9,8,7,6,5,3,2,1,10,4] => 111111101 => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,1,7,8,9,5,6] => [8,7,6,9,3,2,1,5,4] => 11011101 => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,7,8,9,10,1,6] => [9,8,7,6,4,3,2,1,10,5] => 111111101 => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,9,4,5] => [8,7,9,4,3,2,1,6,5] => 10111101 => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,9,10,1,5] => [9,8,7,5,4,3,2,1,10,6] => 111111101 => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,9,3,4] => [8,9,5,4,3,2,1,7,6] => 01111101 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,9,10,1,4] => [9,8,6,5,4,3,2,1,10,7] => 111111101 => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,9,10,1,3] => [9,7,6,5,4,3,2,1,10,8] => 111111101 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,10,1,2] => [8,7,6,5,4,3,2,1,10,9] => 111111101 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,11,1] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => [10,9,8,7,6,5,4,3,2,11,1] => 1111111101 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => [9,8,7,6,5,4,3,10,2,1] => 111111011 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,9,11,1,10] => [10,9,8,7,6,5,4,3,1,11,2] => 1111111101 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,9,1,7,8] => [8,7,6,5,4,1,9,3,2] => 11111011 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [8,7,6,5,4,9,3,2,1] => 11110111 => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,6,1,7,8,9,4,5] => [8,7,4,9,3,2,1,6,5] => 11011101 => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,9,10,2,3] => [10,7,6,5,4,3,2,1,9,8] => 111111101 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => [9,8,7,6,5,4,3,2,1,11,10] => 1111111101 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,7,10,1,8,9] => [9,8,7,6,5,4,1,10,3,2] => 111111011 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => [9,8,7,6,5,4,10,3,2,1] => 111110111 => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,9,1,6,7,8] => [8,7,6,5,1,9,4,3,2] => 11110111 => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,5,6,7,8,9,10,2,3] => [7,10,6,5,4,3,2,1,9,8] => 011111101 => 1
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [8,7,6,5,9,4,3,2,1] => 11101111 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [9,8,7,6,5,10,4,3,2,1] => 111101111 => 0
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,9,1,5,6,7,8] => [8,7,6,1,9,5,4,3,2] => 11101111 => 0
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [8,7,6,9,5,4,3,2,1] => 11011111 => 0
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => [9,8,7,6,10,5,4,3,2,1] => 111011111 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8] => [8,7,6,5,4,3,9,1,2] => 11111010 => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,4,1,5,7,6,8,9] => [8,7,6,9,5,3,4,2,1] => 11011011 => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8] => [8,7,9,5,6,3,4,1,2] => 10101010 => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,1,4,5,6,8,9,7] => [8,7,9,6,5,4,2,1,3] => 10111110 => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,1,4,5,6,8,7,9] => [8,7,9,6,5,4,2,3,1] => 10111101 => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,1,4,5,6,7,9,8] => [8,7,9,6,5,4,3,1,2] => 10111110 => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,9,3] => [8,9,6,5,4,3,2,1,7] => 01111110 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,8,9,7] => [8,9,6,7,4,5,2,1,3] => 01010110 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,9] => [8,9,6,7,4,5,2,3,1] => 01010101 => 1
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9] => [8,9,6,7,5,4,3,2,1] => 01011111 => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,9,5] => [8,9,7,6,4,3,2,1,5] => 01111110 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,6,8,9,7] => [8,9,7,6,5,4,2,1,3] => 01111110 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,6,8,7,9] => [8,9,7,6,5,4,2,3,1] => 01111101 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,2] => [9,7,6,5,4,3,2,1,8] => 11111110 => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,8,2,9] => [9,7,6,5,4,3,2,8,1] => 11111101 => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,7,2,8,9] => [9,7,6,5,4,3,8,2,1] => 11111011 => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,5,6,7,8,9,4] => [9,7,8,5,4,3,2,1,6] => 10111110 => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8] => [9,7,8,5,6,3,4,1,2] => 10101010 => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,3,2,4,5,6,7,9,8] => [9,7,8,6,5,4,3,1,2] => 10111110 => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,3] => [9,8,6,5,4,3,2,1,7] => 11111110 => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,4,5,6,7,3,8,9] => [9,8,6,5,4,3,7,2,1] => 11111011 => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,4] => [9,8,7,5,4,3,2,1,6] => 11111110 => 0
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,5,6,4,7,8,9] => [9,8,7,5,4,6,3,2,1] => 11110111 => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8] => [9,8,7,5,6,3,4,1,2] => 11101010 => 0
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => [9,8,7,5,6,4,3,2,1] => 11101111 => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,5] => [9,8,7,6,4,3,2,1,5] => 11111110 => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,7,8,5,9] => [9,8,7,6,4,3,2,5,1] => 11111101 => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,7,5,9,8] => [9,8,7,6,4,3,5,1,2] => 11111010 => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,4,6,7,5,8,9] => [9,8,7,6,4,3,5,2,1] => 11111011 => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => [9,8,7,6,4,5,3,2,1] => 11110111 => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,6] => [9,8,7,6,5,3,2,1,4] => 11111110 => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,5,7,8,6,9] => [9,8,7,6,5,3,2,4,1] => 11111101 => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,9,8] => [9,8,7,6,5,3,4,1,2] => 11111010 => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,7,6,8,9] => [9,8,7,6,5,3,4,2,1] => 11111011 => 0
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => [9,8,7,10,6,5,4,3,2,1] => 110111111 => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => [9,8,10,6,7,4,5,2,3,1] => 101010101 => 0
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,1,4,5,6,7,8,10,9] => [9,8,10,7,6,5,4,3,1,2] => 101111110 => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,9,10,3] => [9,10,7,6,5,4,3,2,1,8] => 011111110 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [9,10,7,8,5,6,3,4,1,2] => 010101010 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,2] => [10,8,7,6,5,4,3,2,1,9] => 111111110 => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,8,9,2,10] => [10,8,7,6,5,4,3,2,9,1] => 111111101 => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,7,8,2,9,10] => [10,8,7,6,5,4,3,9,2,1] => 111111011 => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,5,6,7,8,9,10,4] => [10,8,9,6,5,4,3,2,1,7] => 101111110 => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,6,9,10,8] => [10,8,9,6,7,4,5,2,1,3] => 101010110 => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [10,8,9,6,7,4,5,2,3,1] => 101010101 => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,10,3] => [10,9,7,6,5,4,3,2,1,8] => 111111110 => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,10,9] => [10,9,7,8,5,6,3,4,1,2] => 110101010 => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,10,4] => [10,9,8,6,5,4,3,2,1,7] => 111111110 => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,5,6,7,4,8,9,10] => [10,9,8,6,5,4,7,3,2,1] => 111110111 => 0
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [10,9,8,6,7,5,4,3,2,1] => 111011111 => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,10,5] => [10,9,8,7,5,4,3,2,1,6] => 111111110 => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,10,9] => [10,9,8,7,5,6,3,4,1,2] => 111101010 => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => [10,9,8,7,5,6,4,3,2,1] => 111101111 => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,10,6] => [10,9,8,7,6,4,3,2,1,5] => 111111110 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,6,8,9,10,7] => [10,9,8,7,6,5,3,2,1,4] => 111111110 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,10,9] => [10,9,8,7,6,5,3,4,1,2] => 111111010 => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,2,1] => 111111111 => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,2] => [7,9,6,5,4,3,2,1,8] => 01111110 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,9,2] => [7,6,9,5,4,3,2,1,8] => 10111110 => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,9,2] => [7,6,5,9,4,3,2,1,8] => 11011110 => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,6,1,7,8,9,2] => [7,6,5,4,9,3,2,1,8] => 11101110 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,1,8,9,2] => [7,6,5,4,3,9,2,1,8] => 11110110 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,1,9,2] => [7,6,5,4,3,2,9,1,8] => 11111010 => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,2] => [8,10,7,6,5,4,3,2,1,9] => 011111110 => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,5,6,7,8,9,4] => [7,9,8,5,4,3,2,1,6] => 01111110 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,9,10,2] => [8,7,10,6,5,4,3,2,1,9] => 101111110 => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,1,2,6,7,8,9,5] => [7,6,9,8,4,3,2,1,5] => 10111110 => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,9,10,2] => [8,7,6,10,5,4,3,2,1,9] => 110111110 => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,4,5,1,2,7,8,9,6] => [7,6,5,9,8,3,2,1,4] => 11011110 => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,5,6,1,7,8,9,10,2] => [8,7,6,5,10,4,3,2,1,9] => 111011110 => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,5,6,1,2,8,9,7] => [7,6,5,4,9,8,2,1,3] => 11101110 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,6,7,1,8,9,10,2] => [8,7,6,5,4,10,3,2,1,9] => 111101110 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,6,7,1,2,9,8] => [7,6,5,4,3,9,8,1,2] => 11110110 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,8,1,9,10,2] => [8,7,6,5,4,3,10,2,1,9] => 111110110 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,1,10,2] => [8,7,6,5,4,3,2,10,1,9] => 111111010 => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,11,2] => [11,9,8,7,6,5,4,3,2,1,10] => 1111111110 => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,7,9,2,8] => [9,7,6,5,4,3,1,8,2] => 11111101 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => [8,7,6,5,4,3,2,10,9,1] => 111111011 => 0
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8,10] => [2,10,9,8,7,6,5,4,3,1] => 011111111 => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => [10,1,9,8,7,6,5,4,3,2] => 101111111 => 0
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [2,11,10,9,8,7,6,5,4,3,1] => 0111111111 => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [3,2,10,9,8,7,6,5,4,1] => 101111111 => 0
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => [10,2,1,9,8,7,6,5,4,3] => 110111111 => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,8,2,9] => [7,9,6,5,4,3,2,8,1] => 01111101 => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,9,3] => [6,9,8,5,4,3,2,1,7] => 01111110 => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [8,10,9,7,6,5,4,3,2,1] => 011111111 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,10,8,9] => [10,9,8,7,6,5,4,1,3,2] => 111111101 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,10,7,8] => [2,10,9,8,7,6,5,1,4,3] => 011111101 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,4,7,5,8,9,6] => [9,8,7,6,3,5,2,1,4] => 11110110 => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,3,6,4,7,8,9,5] => [9,8,7,4,6,3,2,1,5] => 11101110 => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,9,4] => [9,8,5,7,4,3,2,1,6] => 11011110 => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,9,3] => [9,6,8,5,4,3,2,1,7] => 10111110 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [3,10,9,8,7,6,5,4,2,1] => 011111111 => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [4,10,9,8,7,6,5,3,2,1] => 011111111 => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [5,10,9,8,7,6,4,3,2,1] => 011111111 => 1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [6,10,9,8,7,5,4,3,2,1] => 011111111 => 1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [7,10,9,8,6,5,4,3,2,1] => 011111111 => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 1
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,2,5,6,7,8,9] => [7,9,6,8,5,4,3,2,1] => 01011111 => 1
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,3,6,7,8,9] => [6,9,8,5,7,4,3,2,1] => 01101111 => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,4,7,8,9] => [5,9,8,7,4,6,3,2,1] => 01110111 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,7,5,8,9] => [4,9,8,7,6,3,5,2,1] => 01111011 => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,7,8,9,10,1,3,4,5,6] => [9,4,3,2,1,10,8,7,6,5] => 111101111 => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,7,8,2,9,3] => [9,6,5,4,3,2,8,1,7] => 11111010 => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,7,8,1,3,9] => [8,6,5,4,3,2,9,7,1] => 11111011 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,6,7,1,8,2,9] => [7,6,5,4,3,9,2,8,1] => 11110101 => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,8,9,2,4] => [9,7,5,4,3,2,1,8,6] => 11111101 => 0
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,1,4,8,9,2,5,6,7] => [7,9,6,2,1,8,5,4,3] => 01110111 => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [6,5,4,3,2,1,10,9,8,7] => 111110111 => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => [9,8,7,5,1,6,4,3,2] => 11110111 => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,5,7,9,6,8] => [9,8,7,6,5,3,1,4,2] => 11111101 => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [10,9,8,7,6,5,1,4,3,2] => 111111011 => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,4,6,9,5,7,8] => [9,8,7,6,4,1,5,3,2] => 11111011 => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [10,9,8,7,6,1,5,4,3,2] => 111110111 => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [10,9,8,7,1,6,5,4,3,2] => 111101111 => 0
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,4,9,3,5,6,7,8] => [9,8,6,1,7,5,4,3,2] => 11101111 => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [10,9,8,1,7,6,5,4,3,2] => 111011111 => 0
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [10,9,1,8,7,6,5,4,3,2] => 110111111 => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => [7,9,8,5,6,3,4,1,2] => 01101010 => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,2,4,7,6,9,8] => [7,9,5,8,6,3,4,1,2] => 01011010 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,7,4,6,9,8] => [7,9,5,8,3,6,4,1,2] => 01010110 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6,9] => [7,9,5,8,3,6,2,4,1] => 01010101 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7,9] => [7,9,5,8,4,6,2,3,1] => 01010101 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7,9] => [7,9,6,8,4,5,2,3,1] => 01010101 => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8,10] => [8,10,9,6,7,4,5,2,3,1] => 011010101 => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,4,7,6,9,8,10] => [8,10,6,9,7,4,5,2,3,1] => 010110101 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,7,4,6,9,8,10] => [8,10,6,9,4,7,5,2,3,1] => 010101101 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,9,6,8,10] => [8,10,6,9,4,7,2,5,3,1] => 010101011 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,9,6,10,8] => [8,10,6,9,4,7,2,5,1,3] => 010101010 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,8,6,10,9] => [8,10,6,9,4,7,3,5,1,2] => 010101010 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7,10,9] => [8,10,6,9,5,7,3,4,1,2] => 010101010 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => [8,10,7,9,5,6,3,4,1,2] => 010101010 => 1
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => [8,7,10,9,6,5,4,3,2,1] => 101111111 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,6,7,8,10,1,2,9] => [8,7,6,5,4,3,1,10,9,2] => 111111011 => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [7,6,5,4,3,2,1,10,9,8] => 111111011 => 0
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8,10] => [10,2,9,8,7,6,5,4,3,1] => 101111111 => 0
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7,9,10] => [10,9,3,8,7,6,5,4,2,1] => 110111111 => 0
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,3,7,4,5,6,8,9,10] => [10,9,8,4,7,6,5,3,2,1] => 111011111 => 0
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => [9,7,5,3,1,10,8,6,4,2] => 111101111 => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => [5,10,4,9,3,8,2,7,1,6] => 010101010 => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1,8,2,9,3,10,4,11,5,12,6] => [6,12,5,11,4,10,3,9,2,8,1,7] => 01010101010 => 1
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [8,10,1,2,3,4,5,6,7,9] => [3,1,10,9,8,7,6,5,4,2] => 101111111 => 0
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,10,1,2,4,5,6,7,8,9] => [8,1,10,9,7,6,5,4,3,2] => 101111111 => 0
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [9,11,10,8,7,6,5,4,3,2,1] => 0111111111 => 1
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,4,6,7,8,9] => [8,7,5,9,6,4,3,2,1] => 11011111 => 0
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,6,1,5,7,8,9] => [8,7,6,4,9,5,3,2,1] => 11101111 => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,4,5,7,1,6,8,9] => [8,7,6,5,3,9,4,2,1] => 11110111 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,5,6,8,1,7,9] => [8,7,6,5,4,2,9,3,1] => 11111011 => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,6,1,2,3,7,9,4,8] => [5,4,9,8,7,3,1,6,2] => 10111101 => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [5,4,3,2,1,10,9,8,7,6] => 111101111 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [9,1,10,2,3,4,5,6,7,8] => [2,10,1,9,8,7,6,5,4,3] => 010111111 => 1
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [3,7,8,9,10,1,2,4,5,6] => [8,4,3,2,1,10,9,7,6,5] => 111101111 => 0
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,10,1,4,5,6,7,8,9] => [9,8,1,10,7,6,5,4,3,2] => 110111111 => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,2,3,4,7,8,9,5] => [4,9,8,7,6,3,2,1,5] => 01111110 => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,9,4] => [5,9,8,7,4,3,2,1,6] => 01111110 => 1
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [5,10,1,2,3,4,6,7,8,9] => [6,1,10,9,8,7,5,4,3,2] => 101111111 => 0
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [9,10,1,2,3,4,5,6,7,8] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,6,7,1,8,3,9] => [8,6,5,4,3,9,2,7,1] => 11110101 => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [4,3,2,1,10,9,8,7,6,5] => 111011111 => 0
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [3,2,1,10,9,8,7,6,5,4] => 110111111 => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,8,1,9,3] => [8,6,5,4,3,2,9,1,7] => 11111010 => 0
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => [6,5,4,3,10,9,8,7,2,1] => 111011111 => 0
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => [7,6,5,10,9,8,4,3,2,1] => 110111111 => 0
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,6,4,5,7,8,9,10] => [10,9,8,5,7,6,4,3,2,1] => 111011111 => 0
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,7,8,9,10,1,2,3,4,6] => [6,4,3,2,1,10,9,8,7,5] => 111101111 => 0
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,7,8,9,10,1,2,3,5,6] => [7,4,3,2,1,10,9,8,6,5] => 111101111 => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,6,7,8,9,1,3,5] => [8,6,4,3,2,1,9,7,5] => 11111011 => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,9,10,3] => [7,10,9,6,5,4,3,2,1,8] => 011111110 => 1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,7,8,10,1,2,3,4,9] => [6,5,4,3,1,10,9,8,7,2] => 111101111 => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,9,6,8] => [9,7,8,5,6,3,1,4,2] => 10101101 => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,4,7,9,6,10,8] => [10,8,9,6,7,4,2,5,1,3] => 101011010 => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7,9] => [6,9,5,8,4,7,2,3,1] => 01010101 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,8,9,1,10,3] => [9,7,6,5,4,3,2,10,1,8] => 111111010 => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,6,7,8,9,2,3,4,5,10] => [10,5,4,3,2,9,8,7,6,1] => 111101111 => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,9,8] => [9,6,8,5,7,3,4,1,2] => 10101010 => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,8,5,9,7] => [9,6,8,4,7,2,5,1,3] => 10101010 => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,10,7,9] => [10,7,9,5,8,3,6,1,4,2] => 101010101 => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7,9] => [8,6,9,7,4,5,2,3,1] => 10110101 => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,4,5,7,1,2,8,9,6] => [7,6,5,3,9,8,2,1,4] => 11101110 => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,7,1,8,2,9,3] => [6,5,4,3,9,2,8,1,7] => 11101010 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,2,3,4,5,6,9,10,7] => [3,10,9,8,7,6,5,2,1,4] => 011111110 => 1
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7,9,10] => [10,3,9,8,7,6,5,4,2,1] => 101111111 => 0
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0] => [1,2,7,3,4,5,6,8,9,10] => [10,9,4,8,7,6,5,3,2,1] => 110111111 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [9,1,2,3,4,5,10,6,7,8] => [2,10,9,8,7,6,1,5,4,3] => 011111011 => 1
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [4,10,1,2,3,5,6,7,8,9] => [7,1,10,9,8,6,5,4,3,2] => 101111111 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,5,6,9,10,7,8] => [10,9,8,7,6,5,2,1,4,3] => 111111101 => 0
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,7,8] => [8,9,6,7,4,5,1,3,2] => 01010101 => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,7,5,9,6,8] => [8,9,6,7,3,5,1,4,2] => 01010101 => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,9,6,8] => [8,9,5,7,3,6,1,4,2] => 01010101 => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,9,6,8] => [9,7,5,8,3,6,1,4,2] => 11010101 => 0
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,9,6,8] => [9,7,8,5,3,6,1,4,2] => 10110101 => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,7,6,10,8,9] => [10,8,9,6,7,4,5,1,3,2] => 101010101 => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,10,7,9] => [10,8,9,6,7,3,5,1,4,2] => 101010101 => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,4,8,5,10,7,9] => [10,8,9,5,7,3,6,1,4,2] => 101010101 => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => [9,7,10,5,8,3,6,1,4,2] => 101010101 => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,6,3,8,5,10,7,9] => [9,10,7,5,8,3,6,1,4,2] => 011010101 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,3,6,8,5,10,7,9] => [9,10,7,8,5,3,6,1,4,2] => 010110101 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,5,8,10,7,9] => [9,10,7,8,5,6,3,1,4,2] => 010101101 => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,7,8,9,10,3,4,5,6] => [10,9,4,3,2,1,8,7,6,5] => 111110111 => 0
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,1,3,5,7,9] => [8,6,4,2,9,7,5,3,1] => 11101111 => 0
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,5,7,9,2,4,6,8,10] => [10,8,6,4,2,9,7,5,3,1] => 111101111 => 0
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,4,6,8,10,1,2,5,7,9] => [8,7,5,3,1,10,9,6,4,2] => 111101111 => 0
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,6,8,10,1,2,3,5,7,9] => [7,5,3,1,10,9,8,6,4,2] => 111011111 => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,7,5,8,6,9] => [8,9,6,7,3,5,2,4,1] => 01010101 => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,6,2,7,3,8,4,9,5,10] => [10,5,9,4,8,3,7,2,6,1] => 101010101 => 0
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [1,12,11,10,9,8,7,6,5,4,3,2] => 01111111111 => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => [9,7,10,6,8,4,5,2,3,1] => 101010101 => 0
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [2,1,7,3,8,4,9,5,10,6] => [9,10,4,8,3,7,2,6,1,5] => 010101010 => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [2,1,8,3,9,4,10,5,11,6,12,7] => [11,12,5,10,4,9,3,8,2,7,1,6] => 01010101010 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,7,8,9,2,3,10] => [10,7,6,5,4,3,2,9,8,1] => 111111011 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,10,7,9] => [10,9,8,7,6,5,3,1,4,2] => 111111101 => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,9,8] => [9,7,5,8,6,3,4,1,2] => 11011010 => 0
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,2,5,7,4,9,6,10,8] => [10,8,9,6,4,7,2,5,1,3] => 101101010 => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,5,7,9] => [8,9,6,7,4,2,5,3,1] => 01011011 => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,7,9] => [8,6,9,4,7,2,5,3,1] => 10101011 => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,5,4,8,6,9,7] => [9,7,8,5,6,2,4,1,3] => 10101010 => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7,10,9] => [9,10,6,8,5,7,3,4,1,2] => 010101010 => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [3,1,4,2,9,5,10,6,11,7,12,8] => [10,12,9,11,4,8,3,7,2,6,1,5] => 01010101010 => 1
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,5,6,9,10,1,2,3,7,8] => [7,6,5,2,1,10,9,8,4,3] => 111101111 => 0
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,5,8,9,10,1,2,3,6,7] => [7,6,3,2,1,10,9,8,5,4] => 111101111 => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7,9] => [8,6,9,4,7,5,2,3,1] => 10101101 => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,9,8] => [8,6,9,5,7,3,4,1,2] => 10101010 => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7,10,9] => [9,7,10,8,5,6,3,4,1,2] => 101101010 => 0
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,8,3,9,5,10,7] => [7,10,5,9,3,8,2,6,1,4] => 010101010 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [11,12,9,10,7,8,5,6,3,4,1,2] => 01010101010 => 1
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,6,8,9,10,1,3,4,5,7] => [9,5,3,2,1,10,8,7,6,4] => 111101111 => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,6,2,7,3,8,4,9,5] => [9,4,8,3,7,2,6,1,5] => 10101010 => 0
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,9,8] => [7,9,8,5,3,6,4,1,2] => 01110110 => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5,8,9,10] => [10,9,8,5,4,7,6,3,2,1] => 111101111 => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,11,12,2] => [12,10,9,8,7,6,5,4,3,2,1,11] => 11111111110 => 0
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7,10] => [10,3,2,9,8,7,6,5,4,1] => 110111111 => 0
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,7,2,8,3,9,4,10,6] => [6,10,4,9,3,8,2,7,1,5] => 010101010 => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,6,7,8,9,10,1,3,5] => [9,7,5,4,3,2,1,10,8,6] => 111111011 => 0
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,6,1,3,5,7,8,9] => [8,6,4,9,7,5,3,2,1] => 11011111 => 0
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,6,1,3,5,7,8,9,10] => [9,7,5,10,8,6,4,3,2,1] => 110111111 => 0
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,4,6,8,1,3,5,7,9,10] => [9,7,5,3,10,8,6,4,2,1] => 111011111 => 0
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,8,9,1,3,5,7] => [8,6,4,2,1,9,7,5,3] => 11110111 => 0
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 3,2 9,5 28,14 90,42 297,132
F2=1+q
F3=3+2 q
F4=9+5 q
F5=28+14 q
F6=90+42 q
F7=297+132 q
Description
The depth of the binary word interpreted as a path.
This is the maximal value of the number of zeros minus the number of ones occurring in a prefix of the binary word, see [1, sec.9.1.2].
The number of binary words of length n with depth k is \binom{n}{\lfloor\frac{(n+1) - (-1)^{n-k}(k+1)}{2}\rfloor}, see [2].
This is the maximal value of the number of zeros minus the number of ones occurring in a prefix of the binary word, see [1, sec.9.1.2].
The number of binary words of length n with depth k is \binom{n}{\lfloor\frac{(n+1) - (-1)^{n-k}(k+1)}{2}\rfloor}, see [2].
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation \sigma of length n is the permutation \tau with \tau(i) = n+1-\sigma(i)
The complement of a permutation \sigma of length n is the permutation \tau with \tau(i) = n+1-\sigma(i)
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation \pi of n letters and each 1\leq i\leq n-1 such that \pi(i) > \pi(i+1) we set w_i=1, otherwise w_i=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 \pi of n letters and each 1\leq i\leq n-1 such that \pi(i) > \pi(i+1) we set w_i=1, otherwise w_i=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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