Identifier
-
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00278: Binary words —rowmotion⟶ Binary words
St000392: Binary words ⟶ ℤ
Values
[1,0,1,0] => [1,2] => 0 => 0 => 0
[1,1,0,0] => [2,1] => 1 => 1 => 1
[1,0,1,0,1,0] => [1,2,3] => 00 => 00 => 0
[1,0,1,1,0,0] => [1,3,2] => 01 => 10 => 1
[1,1,0,0,1,0] => [2,1,3] => 10 => 01 => 1
[1,1,0,1,0,0] => [2,3,1] => 01 => 10 => 1
[1,1,1,0,0,0] => [3,2,1] => 11 => 11 => 2
[1,0,1,0,1,0,1,0] => [1,2,3,4] => 000 => 000 => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => 001 => 010 => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => 010 => 100 => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => 001 => 010 => 1
[1,0,1,1,1,0,0,0] => [1,4,3,2] => 011 => 101 => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => 100 => 001 => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => 101 => 110 => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => 010 => 100 => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => 001 => 010 => 1
[1,1,0,1,1,0,0,0] => [2,4,3,1] => 011 => 101 => 1
[1,1,1,0,0,0,1,0] => [3,2,1,4] => 110 => 011 => 2
[1,1,1,0,0,1,0,0] => [3,2,4,1] => 101 => 110 => 2
[1,1,1,0,1,0,0,0] => [4,2,3,1] => 101 => 110 => 2
[1,1,1,1,0,0,0,0] => [4,3,2,1] => 111 => 111 => 3
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 0000 => 0000 => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 0001 => 0010 => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 0010 => 0100 => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 0001 => 0010 => 1
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0011 => 0101 => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 0100 => 1000 => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 0101 => 1010 => 1
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 0010 => 0100 => 1
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 0001 => 0010 => 1
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 0011 => 0101 => 1
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 0110 => 1001 => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0101 => 1010 => 1
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0101 => 1010 => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 0111 => 1011 => 2
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 1000 => 0001 => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 1001 => 0110 => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 1010 => 1100 => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 1001 => 0110 => 2
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 1011 => 1101 => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 0100 => 1000 => 1
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 0101 => 1010 => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 0010 => 0100 => 1
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 0001 => 0010 => 1
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => 0011 => 0101 => 1
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0110 => 1001 => 1
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => 0101 => 1010 => 1
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => 0101 => 1010 => 1
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => 0111 => 1011 => 2
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 1100 => 0011 => 2
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 1101 => 1110 => 3
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 1010 => 1100 => 2
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 1001 => 0110 => 2
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => 1011 => 1101 => 2
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 1010 => 1100 => 2
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 1001 => 0110 => 2
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 1001 => 0110 => 2
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1011 => 1101 => 2
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 1110 => 0111 => 3
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1101 => 1110 => 3
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => 1101 => 1110 => 3
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 1011 => 1101 => 2
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 1111 => 1111 => 4
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 00000 => 00000 => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 00001 => 00010 => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 00010 => 00100 => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 00001 => 00010 => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 00011 => 00101 => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 00100 => 01000 => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 00101 => 01010 => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => 00010 => 00100 => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 00001 => 00010 => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => 00011 => 00101 => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 00110 => 01001 => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 00101 => 01010 => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 00101 => 01010 => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 00111 => 01011 => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 01000 => 10000 => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 01001 => 10010 => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 01010 => 10100 => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => 01001 => 10010 => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 01011 => 10101 => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => 00100 => 01000 => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => 00101 => 01010 => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => 00010 => 00100 => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 00001 => 00010 => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => 00011 => 00101 => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => 00110 => 01001 => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => 00101 => 01010 => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => 00101 => 01010 => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 00111 => 01011 => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 01100 => 10001 => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 01101 => 10110 => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => 01010 => 10100 => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 01001 => 10010 => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 01011 => 10101 => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => 01010 => 10100 => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 01001 => 10010 => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => 01001 => 10010 => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => 01011 => 10101 => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 01110 => 10011 => 2
>>> Load all 2174 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 01101 => 10110 => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => 01101 => 10110 => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => 01011 => 10101 => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 01111 => 10111 => 3
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => 10000 => 00001 => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 10001 => 00110 => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => 10010 => 01100 => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => 10001 => 00110 => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 10011 => 01101 => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 10100 => 11000 => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 10101 => 11010 => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => 10010 => 01100 => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => 10001 => 00110 => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => 10011 => 01101 => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 10110 => 11001 => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => 10101 => 11010 => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => 10101 => 11010 => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 10111 => 11011 => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => 01000 => 10000 => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => 01001 => 10010 => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => 01010 => 10100 => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => 01001 => 10010 => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => 01011 => 10101 => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => 00100 => 01000 => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => 00101 => 01010 => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => 00010 => 00100 => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 00001 => 00010 => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => 00011 => 00101 => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => 00110 => 01001 => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => 00101 => 01010 => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => 00101 => 01010 => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => 00111 => 01011 => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => 01100 => 10001 => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => 01101 => 10110 => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => 01010 => 10100 => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => 01001 => 10010 => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => 01011 => 10101 => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => 01010 => 10100 => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => 01001 => 10010 => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => 01001 => 10010 => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => 01011 => 10101 => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 01110 => 10011 => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => 01101 => 10110 => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => 01101 => 10110 => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => 01011 => 10101 => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 01111 => 10111 => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => 11000 => 00011 => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 11001 => 01110 => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 11010 => 11100 => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => 11001 => 01110 => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 11011 => 11101 => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => 10100 => 11000 => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => 10101 => 11010 => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => 10010 => 01100 => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 10001 => 00110 => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => 10011 => 01101 => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 10110 => 11001 => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => 10101 => 11010 => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => 10101 => 11010 => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 10111 => 11011 => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => 10100 => 11000 => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => 10101 => 11010 => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => 10010 => 01100 => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 10001 => 00110 => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => 10011 => 01101 => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => 10010 => 01100 => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => 10001 => 00110 => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => 10001 => 00110 => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => 10011 => 01101 => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => 10110 => 11001 => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => 10101 => 11010 => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => 10101 => 11010 => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => 10011 => 01101 => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => 10111 => 11011 => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 11100 => 00111 => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 11101 => 11110 => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 11010 => 11100 => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 11001 => 01110 => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 11011 => 11101 => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => 11010 => 11100 => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 11001 => 01110 => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => 11001 => 01110 => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => 11011 => 11101 => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => 10110 => 11001 => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => 10101 => 11010 => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => 10101 => 11010 => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => 10011 => 01101 => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => 10111 => 11011 => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 11110 => 01111 => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 11101 => 11110 => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => 11101 => 11110 => 4
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => 11011 => 11101 => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => 11011 => 11101 => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 11111 => 11111 => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 000000 => 000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 000001 => 000010 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => 000010 => 000100 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 000001 => 000010 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 000011 => 000101 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => 000100 => 001000 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => 000101 => 001010 => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => 000010 => 000100 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 000001 => 000010 => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => 000011 => 000101 => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => 000110 => 001001 => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 000101 => 001010 => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => 000101 => 001010 => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => 000111 => 001011 => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => 001000 => 010000 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => 001001 => 010010 => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => 001010 => 010100 => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => 001001 => 010010 => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => 001011 => 010101 => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => 000100 => 001000 => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => 000101 => 001010 => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => 000010 => 000100 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 000001 => 000010 => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => 000011 => 000101 => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => 000110 => 001001 => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => 000101 => 001010 => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => 000101 => 001010 => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => 000111 => 001011 => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => 001100 => 010001 => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => 001101 => 010110 => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => 001010 => 010100 => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 001001 => 010010 => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => 001011 => 010101 => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => 001010 => 010100 => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => 001001 => 010010 => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => 001001 => 010010 => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => 001011 => 010101 => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => 001110 => 010011 => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => 001101 => 010110 => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => 001101 => 010110 => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => 001011 => 010101 => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 001111 => 010111 => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => 010000 => 100000 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => 010001 => 100010 => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => 010010 => 100100 => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => 010001 => 100010 => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => 010011 => 100101 => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => 010100 => 101000 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => 010101 => 101010 => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => 010010 => 100100 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => 010001 => 100010 => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => 010011 => 100101 => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => 010110 => 101001 => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => 010101 => 101010 => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => 010101 => 101010 => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => 010111 => 101011 => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => 001000 => 010000 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => 001001 => 010010 => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => 001010 => 010100 => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => 001001 => 010010 => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => 001011 => 010101 => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => 000100 => 001000 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => 000101 => 001010 => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => 000010 => 000100 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 000001 => 000010 => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => 000011 => 000101 => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => 000110 => 001001 => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => 000101 => 001010 => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => 000101 => 001010 => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => 000111 => 001011 => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => 001100 => 010001 => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => 001101 => 010110 => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => 001010 => 010100 => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => 001001 => 010010 => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => 001011 => 010101 => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => 001010 => 010100 => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => 001001 => 010010 => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => 001001 => 010010 => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => 001011 => 010101 => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => 001110 => 010011 => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => 001101 => 010110 => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => 001101 => 010110 => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => 001011 => 010101 => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 001111 => 010111 => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => 011000 => 100001 => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => 011001 => 100110 => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => 011010 => 101100 => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => 011001 => 100110 => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => 011011 => 101101 => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => 010100 => 101000 => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => 010101 => 101010 => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => 010010 => 100100 => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 010001 => 100010 => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => 010011 => 100101 => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => 010110 => 101001 => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => 010101 => 101010 => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => 010101 => 101010 => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 010111 => 101011 => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => 010100 => 101000 => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => 010101 => 101010 => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => 010010 => 100100 => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => 010001 => 100010 => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => 010011 => 100101 => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => 010010 => 100100 => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => 010001 => 100010 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => 010001 => 100010 => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => 010011 => 100101 => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => 010110 => 101001 => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => 010101 => 101010 => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => 010101 => 101010 => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => 010011 => 100101 => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => 010111 => 101011 => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => 011100 => 100011 => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => 011101 => 101110 => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => 011010 => 101100 => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => 011001 => 100110 => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => 011011 => 101101 => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => 011010 => 101100 => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => 011001 => 100110 => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => 011001 => 100110 => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => 011011 => 101101 => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => 010110 => 101001 => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => 010101 => 101010 => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => 010101 => 101010 => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => 010011 => 100101 => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => 010111 => 101011 => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => 011110 => 100111 => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => 011101 => 101110 => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => 011101 => 101110 => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => 011011 => 101101 => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => 011011 => 101101 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 011111 => 101111 => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => 100000 => 000001 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => 100001 => 000110 => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => 100010 => 001100 => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => 100001 => 000110 => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => 100011 => 001101 => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => 100100 => 011000 => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => 100101 => 011010 => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => 100010 => 001100 => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => 100001 => 000110 => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => 100011 => 001101 => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => 100110 => 011001 => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => 100101 => 011010 => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => 100101 => 011010 => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => 100111 => 011011 => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => 101000 => 110000 => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => 101001 => 110010 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => 101010 => 110100 => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => 101001 => 110010 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => 101011 => 110101 => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => 100100 => 011000 => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => 100101 => 011010 => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => 100010 => 001100 => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => 100001 => 000110 => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => 100011 => 001101 => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => 100110 => 011001 => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => 100101 => 011010 => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => 100101 => 011010 => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => 100111 => 011011 => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => 101100 => 110001 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => 101101 => 110110 => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => 101010 => 110100 => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => 101001 => 110010 => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => 101011 => 110101 => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => 101010 => 110100 => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => 101001 => 110010 => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => 101001 => 110010 => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => 101011 => 110101 => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => 101110 => 110011 => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => 101101 => 110110 => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => 101101 => 110110 => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => 101011 => 110101 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 101111 => 110111 => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => 010000 => 100000 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => 010001 => 100010 => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => 010010 => 100100 => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => 010001 => 100010 => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => 010011 => 100101 => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => 010100 => 101000 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => 010101 => 101010 => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => 010010 => 100100 => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => 010001 => 100010 => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => 010011 => 100101 => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => 010110 => 101001 => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => 010101 => 101010 => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => 010101 => 101010 => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => 010111 => 101011 => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => 001000 => 010000 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => 001001 => 010010 => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => 001010 => 010100 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => 001001 => 010010 => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => 001011 => 010101 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => 000100 => 001000 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => 000101 => 001010 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => 000010 => 000100 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 000001 => 000010 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => 000011 => 000101 => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => 000110 => 001001 => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => 000101 => 001010 => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => 000101 => 001010 => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => 000111 => 001011 => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => 001100 => 010001 => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => 001101 => 010110 => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => 001010 => 010100 => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => 001001 => 010010 => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => 001011 => 010101 => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => 001010 => 010100 => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => 001001 => 010010 => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => 001001 => 010010 => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => 001011 => 010101 => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => 001110 => 010011 => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => 001101 => 010110 => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => 001101 => 010110 => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => 001011 => 010101 => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => 001111 => 010111 => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => 011000 => 100001 => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => 011001 => 100110 => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => 011010 => 101100 => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => 011001 => 100110 => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => 011011 => 101101 => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => 010100 => 101000 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => 010101 => 101010 => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => 010010 => 100100 => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => 010001 => 100010 => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => 010011 => 100101 => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => 010110 => 101001 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => 010101 => 101010 => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => 010101 => 101010 => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => 010111 => 101011 => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => 010100 => 101000 => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => 010101 => 101010 => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => 010010 => 100100 => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => 010001 => 100010 => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => 010011 => 100101 => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => 010010 => 100100 => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => 010001 => 100010 => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => 010001 => 100010 => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => 010011 => 100101 => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => 010110 => 101001 => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => 010101 => 101010 => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => 010101 => 101010 => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => 010011 => 100101 => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => 010111 => 101011 => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => 011100 => 100011 => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => 011101 => 101110 => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => 011010 => 101100 => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => 011001 => 100110 => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => 011011 => 101101 => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => 011010 => 101100 => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => 011001 => 100110 => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => 011001 => 100110 => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => 011011 => 101101 => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => 010110 => 101001 => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => 010101 => 101010 => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => 010101 => 101010 => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => 010011 => 100101 => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => 010111 => 101011 => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => 011110 => 100111 => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => 011101 => 101110 => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => 011101 => 101110 => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => 011011 => 101101 => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => 011011 => 101101 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => 011111 => 101111 => 4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => 110000 => 000011 => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => 110001 => 001110 => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => 110010 => 011100 => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => 110001 => 001110 => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => 110011 => 011101 => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => 110100 => 111000 => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => 110101 => 111010 => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => 110010 => 011100 => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => 110001 => 001110 => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => 110011 => 011101 => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => 110110 => 111001 => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => 110101 => 111010 => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => 110101 => 111010 => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => 110111 => 111011 => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => 101000 => 110000 => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => 101001 => 110010 => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => 101010 => 110100 => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => 101001 => 110010 => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => 101011 => 110101 => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => 100100 => 011000 => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => 100101 => 011010 => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => 100010 => 001100 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => 100001 => 000110 => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => 100011 => 001101 => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => 100110 => 011001 => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => 100101 => 011010 => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => 100101 => 011010 => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => 100111 => 011011 => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => 101100 => 110001 => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => 101101 => 110110 => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => 101010 => 110100 => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => 101001 => 110010 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => 101011 => 110101 => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => 101010 => 110100 => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => 101001 => 110010 => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => 101001 => 110010 => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => 101011 => 110101 => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => 101110 => 110011 => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => 101101 => 110110 => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => 101101 => 110110 => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => 101011 => 110101 => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => 101111 => 110111 => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => 101000 => 110000 => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => 101001 => 110010 => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => 101010 => 110100 => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => 101001 => 110010 => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => 101011 => 110101 => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => 100100 => 011000 => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => 100101 => 011010 => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => 100010 => 001100 => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => 100001 => 000110 => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => 100011 => 001101 => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => 100110 => 011001 => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => 100101 => 011010 => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => 100101 => 011010 => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => 100111 => 011011 => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => 100100 => 011000 => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => 100101 => 011010 => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => 100010 => 001100 => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => 100001 => 000110 => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => 100011 => 001101 => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => 100010 => 001100 => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => 100001 => 000110 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => 100001 => 000110 => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => 100011 => 001101 => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => 100110 => 011001 => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => 100101 => 011010 => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => 100101 => 011010 => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => 100011 => 001101 => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => 100111 => 011011 => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => 101100 => 110001 => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => 101101 => 110110 => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => 101010 => 110100 => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => 101001 => 110010 => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => 101011 => 110101 => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => 101010 => 110100 => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => 101001 => 110010 => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => 101001 => 110010 => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => 101011 => 110101 => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => 100110 => 011001 => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => 100101 => 011010 => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => 100101 => 011010 => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => 100011 => 001101 => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => 100111 => 011011 => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => 101110 => 110011 => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => 101101 => 110110 => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => 101101 => 110110 => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => 101011 => 110101 => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => 101011 => 110101 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => 101111 => 110111 => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => 111000 => 000111 => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => 111001 => 011110 => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => 111010 => 111100 => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => 111001 => 011110 => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => 111011 => 111101 => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => 110100 => 111000 => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => 110101 => 111010 => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => 110010 => 011100 => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => 110001 => 001110 => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => 110011 => 011101 => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => 110110 => 111001 => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => 110101 => 111010 => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => 110101 => 111010 => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => 110111 => 111011 => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => 110100 => 111000 => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => 110101 => 111010 => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => 110010 => 011100 => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => 110001 => 001110 => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => 110011 => 011101 => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => 110010 => 011100 => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => 110001 => 001110 => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => 110001 => 001110 => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => 110011 => 011101 => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => 110110 => 111001 => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => 110101 => 111010 => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => 110101 => 111010 => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => 110011 => 011101 => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => 110111 => 111011 => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => 101100 => 110001 => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => 101101 => 110110 => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => 101010 => 110100 => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => 101001 => 110010 => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => 101011 => 110101 => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => 101010 => 110100 => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => 101001 => 110010 => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => 101001 => 110010 => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => 101011 => 110101 => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => 100110 => 011001 => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => 100101 => 011010 => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => 100101 => 011010 => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => 100011 => 001101 => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => 100111 => 011011 => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => 101110 => 110011 => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => 101101 => 110110 => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => 101101 => 110110 => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => 101011 => 110101 => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => 101011 => 110101 => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => 101111 => 110111 => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => 111100 => 001111 => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 111101 => 111110 => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => 111010 => 111100 => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => 111001 => 011110 => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => 111011 => 111101 => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => 111010 => 111100 => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => 111001 => 011110 => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => 111001 => 011110 => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => 111011 => 111101 => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => 110110 => 111001 => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => 110101 => 111010 => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => 110101 => 111010 => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => 110011 => 011101 => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => 110111 => 111011 => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => 110110 => 111001 => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => 110101 => 111010 => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => 110101 => 111010 => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => 110011 => 011101 => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => 110011 => 011101 => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => 110111 => 111011 => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => 111110 => 011111 => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => 111101 => 111110 => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => 111101 => 111110 => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => 111011 => 111101 => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => 111011 => 111101 => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => 110111 => 111011 => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => 111111 => 111111 => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => 0000000 => 0000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => 0000001 => 0000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => 0000010 => 0000100 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => 0000001 => 0000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => 0000011 => 0000101 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => 0000100 => 0001000 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => 0000101 => 0001010 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => 0000010 => 0000100 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => 0000001 => 0000010 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => 0000011 => 0000101 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => 0000110 => 0001001 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => 0000101 => 0001010 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => 0000101 => 0001010 => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => 0000111 => 0001011 => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => 0001000 => 0010000 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => 0001001 => 0010010 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => 0001010 => 0010100 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => 0001001 => 0010010 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => 0001011 => 0010101 => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => 0000100 => 0001000 => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => 0000101 => 0001010 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => 0000010 => 0000100 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => 0000001 => 0000010 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => 0000011 => 0000101 => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => 0000110 => 0001001 => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => 0000101 => 0001010 => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => 0000101 => 0001010 => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => 0000111 => 0001011 => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => 0001100 => 0010001 => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => 0001101 => 0010110 => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => 0001010 => 0010100 => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => 0001001 => 0010010 => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => 0001011 => 0010101 => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => 0001010 => 0010100 => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => 0001001 => 0010010 => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => 0001001 => 0010010 => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => 0001011 => 0010101 => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => 0001110 => 0010011 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => 0001101 => 0010110 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => 0001101 => 0010110 => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => 0001011 => 0010101 => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => 0001111 => 0010111 => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => 0010000 => 0100000 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => 0010001 => 0100010 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => 0010010 => 0100100 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => 0010001 => 0100010 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => 0010011 => 0100101 => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => 0010100 => 0101000 => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => 0010101 => 0101010 => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => 0010010 => 0100100 => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => 0010001 => 0100010 => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => 0010011 => 0100101 => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => 0010101 => 0101010 => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => 0010111 => 0101011 => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => 0001010 => 0010100 => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => 0001001 => 0010010 => 1
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => 0001011 => 0010101 => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => 0000100 => 0001000 => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => 0000101 => 0001010 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => 0000010 => 0000100 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => 0000001 => 0000010 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => 0000011 => 0000101 => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => 0000101 => 0001010 => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => 0000111 => 0001011 => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => 0001100 => 0010001 => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,4,6,5,7,8,3] => 0001001 => 0010010 => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,7,5,6,8,3] => 0001001 => 0010010 => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => 0001001 => 0010010 => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => 0001101 => 0010110 => 2
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,8,6,5,7,3] => 0001101 => 0010110 => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => 0001111 => 0010111 => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => 0011000 => 0100001 => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => 0011001 => 0100110 => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => 0011001 => 0100110 => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => 0011011 => 0101101 => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => 0010010 => 0100100 => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => 0010001 => 0100010 => 1
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => 0010011 => 0100101 => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => 0010101 => 0101010 => 1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => 0010101 => 0101010 => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => 0010111 => 0101011 => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => 0010100 => 0101000 => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => 0010001 => 0100010 => 1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,6,4,5,8,7,3] => 0010011 => 0100101 => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => 0010001 => 0100010 => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => 0010001 => 0100010 => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,8,4,6,7,5,3] => 0010011 => 0100101 => 1
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => 0010111 => 0101011 => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => 0011100 => 0100011 => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => 0011001 => 0100110 => 2
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => 0011011 => 0101101 => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,7,5,4,6,3,8] => 0011010 => 0101100 => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,7,5,4,6,8,3] => 0011001 => 0100110 => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => 0011001 => 0100110 => 2
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,8,5,4,7,6,3] => 0011011 => 0101101 => 2
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,8,5,6,4,7,3] => 0010101 => 0101010 => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => 0010011 => 0100101 => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => 0011110 => 0100111 => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => 0011101 => 0101110 => 3
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => 0011101 => 0101110 => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => 0011011 => 0101101 => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => 0011011 => 0101101 => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => 0011111 => 0101111 => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => 0100000 => 1000000 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => 0100001 => 1000010 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => 0100010 => 1000100 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => 0100001 => 1000010 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => 0100011 => 1000101 => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => 0100100 => 1001000 => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => 0100101 => 1001010 => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => 0100001 => 1000010 => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => 0100011 => 1000101 => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => 0100110 => 1001001 => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => 0100101 => 1001010 => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => 0100101 => 1001010 => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => 0100111 => 1001011 => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => 0101000 => 1010000 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 0101010 => 1010100 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => 0101001 => 1010010 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => 0101011 => 1010101 => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => 0100100 => 1001000 => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => 0100101 => 1001010 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => 0100010 => 1000100 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => 0100001 => 1000010 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => 0100011 => 1000101 => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => 0100110 => 1001001 => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => 0100101 => 1001010 => 1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => 0100111 => 1001011 => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => 0101100 => 1010001 => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => 0101101 => 1010110 => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => 0101010 => 1010100 => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => 0101001 => 1010010 => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => 0101011 => 1010101 => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => 0101001 => 1010010 => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => 0101011 => 1010101 => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => 0101110 => 1010011 => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => 0101101 => 1010110 => 2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => 0101101 => 1010110 => 2
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => 0101011 => 1010101 => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => 0101111 => 1010111 => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => 0010000 => 0100000 => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => 0010001 => 0100010 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => 0010010 => 0100100 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => 0010001 => 0100010 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => 0010011 => 0100101 => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => 0010101 => 0101010 => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => 0010010 => 0100100 => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => 0010001 => 0100010 => 1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => 0010011 => 0100101 => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => 0010101 => 0101010 => 1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => 0010101 => 0101010 => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => 0010111 => 0101011 => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => 0001000 => 0010000 => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,5,2,6,8,7] => 0001001 => 0010010 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => 0001010 => 0010100 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => 0001001 => 0010010 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => 0001011 => 0010101 => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => 0000100 => 0001000 => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => 0000101 => 0001010 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => 0000010 => 0000100 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => 0000001 => 0000010 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => 0000011 => 0000101 => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => 0000110 => 0001001 => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => 0000101 => 0001010 => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => 0000101 => 0001010 => 1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => 0000111 => 0001011 => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => 0001010 => 0010100 => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => 0001001 => 0010010 => 1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => 0001001 => 0010010 => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => 0001101 => 0010110 => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,8,6,5,7,2] => 0001101 => 0010110 => 2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,8,6,7,5,2] => 0001011 => 0010101 => 1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => 0001111 => 0010111 => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => 0011000 => 0100001 => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => 0011001 => 0100110 => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => 0011010 => 0101100 => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => 0011001 => 0100110 => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,3,5,4,6,2,7,8] => 0010100 => 0101000 => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,4,6,7,2,8] => 0010010 => 0100100 => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => 0010001 => 0100010 => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => 0010110 => 0101001 => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => 0010101 => 0101010 => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => 0010111 => 0101011 => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,4,5,2,8,7] => 0010101 => 0101010 => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => 0010010 => 0100100 => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => 0010001 => 0100010 => 1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => 0010011 => 0100101 => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,7,4,5,6,2,8] => 0010010 => 0100100 => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => 0010001 => 0100010 => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => 0010001 => 0100010 => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,8,4,6,5,7,2] => 0010101 => 0101010 => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => 0011101 => 0101110 => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => 0011010 => 0101100 => 2
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => 0011011 => 0101101 => 2
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => 0011001 => 0100110 => 2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => 0011011 => 0101101 => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => 0010011 => 0100101 => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => 0010111 => 0101011 => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => 0011110 => 0100111 => 3
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => 0011011 => 0101101 => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => 0011011 => 0101101 => 2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => 0011111 => 0101111 => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => 0110000 => 1000001 => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => 0110001 => 1000110 => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => 0110010 => 1001100 => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => 0110001 => 1000110 => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => 0110011 => 1001101 => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => 0110010 => 1001100 => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => 0110001 => 1000110 => 2
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => 0110011 => 1001101 => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 0110110 => 1011001 => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => 0110101 => 1011010 => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => 0110111 => 1011011 => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => 0101010 => 1010100 => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3,5,2,7,8,6] => 0101001 => 1010010 => 1
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3,5,2,8,7,6] => 0101011 => 1010101 => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => 0100100 => 1001000 => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => 0100001 => 1000010 => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => 0100110 => 1001001 => 1
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => 0100101 => 1001010 => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => 0100111 => 1001011 => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => 0101100 => 1010001 => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => 0101010 => 1010100 => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => 0101001 => 1010010 => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => 0101011 => 1010101 => 1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => 0101001 => 1010010 => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => 0101011 => 1010101 => 1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => 0101101 => 1010110 => 2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => 0101011 => 1010101 => 1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => 0101111 => 1010111 => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => 0101000 => 1010000 => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => 0101001 => 1010010 => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => 0101011 => 1010101 => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,5,3,4,6,2,7,8] => 0100100 => 1001000 => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,3,4,6,2,8,7] => 0100101 => 1001010 => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,5,3,4,6,7,2,8] => 0100010 => 1000100 => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => 0100001 => 1000010 => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,5,3,4,7,6,2,8] => 0100110 => 1001001 => 1
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,5,3,4,8,6,7,2] => 0100101 => 1001010 => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => 0100100 => 1001000 => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => 0100011 => 1000101 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => 0100010 => 1000100 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => 0100001 => 1000010 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => 0100001 => 1000010 => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => 0100011 => 1000101 => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => 0101100 => 1010001 => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => 0101011 => 1010101 => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => 0101010 => 1010100 => 1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => 0101001 => 1010010 => 1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,8,3,5,4,7,6,2] => 0101011 => 1010101 => 1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => 0100101 => 1001010 => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8,3,5,6,7,4,2] => 0100011 => 1000101 => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => 0100111 => 1001011 => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,7,3,6,5,4,2,8] => 0101110 => 1010011 => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => 0101101 => 1010110 => 2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => 0101101 => 1010110 => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => 0101011 => 1010101 => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => 0101111 => 1010111 => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => 0111000 => 1000011 => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => 0111010 => 1011100 => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => 0111001 => 1001110 => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => 0111011 => 1011101 => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => 0110100 => 1011000 => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => 0110010 => 1001100 => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => 0110001 => 1000110 => 2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => 0110011 => 1001101 => 2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => 0110111 => 1011011 => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => 0110100 => 1011000 => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => 0110011 => 1001101 => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => 0110001 => 1000110 => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => 0110011 => 1001101 => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => 0110101 => 1011010 => 2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => 0110101 => 1011010 => 2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,8,4,3,6,7,5,2] => 0110011 => 1001101 => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => 0101100 => 1010001 => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => 0101101 => 1010110 => 2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => 0101011 => 1010101 => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7,4,5,3,6,8,2] => 0101001 => 1010010 => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => 0101001 => 1010010 => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,7,4,5,6,3,2,8] => 0100110 => 1001001 => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => 0100101 => 1001010 => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,8,4,5,6,3,7,2] => 0100101 => 1001010 => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => 0100011 => 1000101 => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => 0101110 => 1010011 => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => 0101101 => 1010110 => 2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => 0101011 => 1010101 => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => 0101111 => 1010111 => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => 0111100 => 1000111 => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => 0111101 => 1011110 => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => 0111001 => 1001110 => 3
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => 0111011 => 1011101 => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,7,5,4,3,6,2,8] => 0111010 => 1011100 => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7,5,4,3,6,8,2] => 0111001 => 1001110 => 3
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => 0111001 => 1001110 => 3
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8,5,4,3,7,6,2] => 0111011 => 1011101 => 3
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => 0110101 => 1011010 => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => 0110011 => 1001101 => 2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => 0110111 => 1011011 => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => 0110110 => 1011001 => 2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => 0110101 => 1011010 => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => 0110011 => 1001101 => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => 0110011 => 1001101 => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => 0110111 => 1011011 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => 0111110 => 1001111 => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => 0111101 => 1011110 => 4
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => 0111101 => 1011110 => 4
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => 0111011 => 1011101 => 3
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => 0111011 => 1011101 => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => 0110111 => 1011011 => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 0111111 => 1011111 => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => 1000000 => 0000001 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => 1000001 => 0000110 => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => 1000010 => 0001100 => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => 1000001 => 0000110 => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => 1000011 => 0001101 => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => 1000100 => 0011000 => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => 1000101 => 0011010 => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,4,6,7,5,8] => 1000010 => 0001100 => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => 1000001 => 0000110 => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => 1000101 => 0011010 => 2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => 1000101 => 0011010 => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => 1000111 => 0011011 => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => 1001001 => 0110010 => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => 1001001 => 0110010 => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => 1001011 => 0110101 => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => 1000101 => 0011010 => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => 1000001 => 0000110 => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,6,8,4] => 1000101 => 0011010 => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => 1000101 => 0011010 => 2
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => 1001011 => 0110101 => 2
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => 1001001 => 0110010 => 2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => 1001011 => 0110101 => 2
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,8,6,5,7,4] => 1001101 => 0110110 => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => 1001011 => 0110101 => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => 1001111 => 0110111 => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => 1010000 => 1100000 => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => 1010001 => 1100010 => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => 1010001 => 1100010 => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => 1010011 => 1100101 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => 1010100 => 1101000 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 1010101 => 1101010 => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => 1010001 => 1100010 => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => 1010011 => 1100101 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => 1010101 => 1101010 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => 1010101 => 1101010 => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 1010111 => 1101011 => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => 1001000 => 0110000 => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => 1001001 => 0110010 => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => 1001011 => 0110101 => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => 1000101 => 0011010 => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => 1000010 => 0001100 => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => 1000001 => 0000110 => 2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => 1000011 => 0001101 => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => 1000101 => 0011010 => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => 1000111 => 0011011 => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => 1001100 => 0110001 => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => 1001101 => 0110110 => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => 1001011 => 0110101 => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => 1001001 => 0110010 => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => 1001011 => 0110101 => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => 1001101 => 0110110 => 2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => 1001101 => 0110110 => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => 1001011 => 0110101 => 2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => 1001111 => 0110111 => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => 1011000 => 1100001 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => 1011010 => 1101100 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => 1011011 => 1101101 => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => 1010101 => 1101010 => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => 1010001 => 1100010 => 2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => 1010011 => 1100101 => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => 1010101 => 1101010 => 2
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => 1010101 => 1101010 => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => 1010111 => 1101011 => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => 1010101 => 1101010 => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => 1010001 => 1100010 => 2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => 1010011 => 1100101 => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => 1010001 => 1100010 => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => 1010011 => 1100101 => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => 1010101 => 1101010 => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => 1010101 => 1101010 => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => 1010011 => 1100101 => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => 1010111 => 1101011 => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 1011101 => 1101110 => 3
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => 1011011 => 1101101 => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,7,5,4,6,8,3] => 1011001 => 1100110 => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => 1011001 => 1100110 => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => 1011011 => 1101101 => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => 1010101 => 1101010 => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => 1010101 => 1101010 => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => 1010011 => 1100101 => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => 1010111 => 1101011 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => 1011110 => 1100111 => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => 1011101 => 1101110 => 3
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => 1011101 => 1101110 => 3
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => 1011011 => 1101101 => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => 1011011 => 1101101 => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 1011111 => 1101111 => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => 0100000 => 1000000 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => 0100001 => 1000010 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => 0100010 => 1000100 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => 0100001 => 1000010 => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => 0100101 => 1001010 => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => 0100010 => 1000100 => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => 0100001 => 1000010 => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => 0100101 => 1001010 => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => 0100111 => 1001011 => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => 0101000 => 1010000 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => 0101010 => 1010100 => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => 0100100 => 1001000 => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => 0100010 => 1000100 => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => 0100001 => 1000010 => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => 0100101 => 1001010 => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => 0101100 => 1010001 => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => 0101101 => 1010110 => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => 0101010 => 1010100 => 1
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => 0101011 => 1010101 => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,7,5,6,4,8] => 0101010 => 1010100 => 1
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => 0101001 => 1010010 => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => 0101101 => 1010110 => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => 0101011 => 1010101 => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => 0101111 => 1010111 => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => 0010000 => 0100000 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => 0010001 => 0100010 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => 0010010 => 0100100 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => 0010001 => 0100010 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => 0010011 => 0100101 => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => 0010100 => 0101000 => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => 0010101 => 0101010 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => 0010010 => 0100100 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => 0010001 => 0100010 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => 0010011 => 0100101 => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => 0010110 => 0101001 => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => 0010101 => 0101010 => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => 0010101 => 0101010 => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => 0010111 => 0101011 => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => 0001000 => 0010000 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => 0001001 => 0010010 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => 0001010 => 0010100 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => 0001001 => 0010010 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => 0001011 => 0010101 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => 0000100 => 0001000 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => 0000101 => 0001010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => 0000010 => 0000100 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 0000001 => 0000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => 0000011 => 0000101 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => 0000110 => 0001001 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => 0000101 => 0001010 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => 0000101 => 0001010 => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => 0000111 => 0001011 => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => 0001100 => 0010001 => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => 0001010 => 0010100 => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => 0001001 => 0010010 => 1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => 0001011 => 0010101 => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => 0001010 => 0010100 => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,7,5,6,8,1] => 0001001 => 0010010 => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => 0001001 => 0010010 => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => 0001011 => 0010101 => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => 0001110 => 0010011 => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => 0001101 => 0010110 => 2
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => 0001101 => 0010110 => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => 0001011 => 0010101 => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => 0001111 => 0010111 => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => 0011000 => 0100001 => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => 0011001 => 0100110 => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => 0011010 => 0101100 => 2
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => 0011011 => 0101101 => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => 0010100 => 0101000 => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => 0010010 => 0100100 => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => 0010001 => 0100010 => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => 0010101 => 0101010 => 1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => 0010101 => 0101010 => 1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => 0010111 => 0101011 => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => 0010100 => 0101000 => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => 0010101 => 0101010 => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,4,5,7,8,1] => 0010001 => 0100010 => 1
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,4,5,8,7,1] => 0010011 => 0100101 => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => 0010001 => 0100010 => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => 0010001 => 0100010 => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => 0010101 => 0101010 => 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => 0010011 => 0100101 => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => 0011100 => 0100011 => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => 0011101 => 0101110 => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => 0011001 => 0100110 => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,7,5,4,6,1,8] => 0011010 => 0101100 => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,7,5,4,6,8,1] => 0011001 => 0100110 => 2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => 0011001 => 0100110 => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => 0010110 => 0101001 => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => 0010101 => 0101010 => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,8,5,6,4,7,1] => 0010101 => 0101010 => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => 0010011 => 0100101 => 1
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,8,5,7,6,4,1] => 0010111 => 0101011 => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => 0011110 => 0100111 => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => 0011101 => 0101110 => 3
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => 0011101 => 0101110 => 3
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => 0011111 => 0101111 => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => 0110000 => 1000001 => 1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => 0110011 => 1001101 => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => 0110100 => 1011000 => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => 0110101 => 1011010 => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => 0110001 => 1000110 => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => 0110011 => 1001101 => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => 0110101 => 1011010 => 2
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,8,6,7,5] => 0110101 => 1011010 => 2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => 0110111 => 1011011 => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => 0101000 => 1010000 => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => 0101001 => 1010010 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => 0101010 => 1010100 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => 0101001 => 1010010 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => 0101011 => 1010101 => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => 0100101 => 1001010 => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => 0100001 => 1000010 => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => 0100011 => 1000101 => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => 0100101 => 1001010 => 1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => 0100101 => 1001010 => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,4,3,5,8,7,6,1] => 0100111 => 1001011 => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => 0101100 => 1010001 => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => 0101101 => 1010110 => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => 0101010 => 1010100 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => 0101001 => 1010010 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => 0101011 => 1010101 => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => 0101001 => 1010010 => 1
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => 0101001 => 1010010 => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,8,5,7,6,1] => 0101011 => 1010101 => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => 0101101 => 1010110 => 2
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,8,6,5,7,1] => 0101101 => 1010110 => 2
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,3,8,6,7,5,1] => 0101011 => 1010101 => 1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => 0101111 => 1010111 => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => 0101000 => 1010000 => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => 0101011 => 1010101 => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => 0100010 => 1000100 => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => 0100001 => 1000010 => 1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => 0100011 => 1000101 => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,3,4,7,6,8,1] => 0100101 => 1001010 => 1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => 0100101 => 1001010 => 1
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,3,4,8,7,6,1] => 0100111 => 1001011 => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => 0100100 => 1001000 => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => 0100001 => 1000010 => 1
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => 0100011 => 1000101 => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,7,3,4,5,6,1,8] => 0100010 => 1000100 => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => 0100001 => 1000010 => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,8,3,4,5,7,6,1] => 0100011 => 1000101 => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,6,3,5,4,1,7,8] => 0101100 => 1010001 => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => 0101101 => 1010110 => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,6,3,5,4,7,8,1] => 0101001 => 1010010 => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,6,3,5,4,8,7,1] => 0101011 => 1010101 => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7,3,5,4,6,8,1] => 0101001 => 1010010 => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => 0101011 => 1010101 => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,7,3,5,6,4,8,1] => 0100101 => 1001010 => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8,3,5,6,7,4,1] => 0100011 => 1000101 => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => 0100111 => 1001011 => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => 0101110 => 1010011 => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,8,3,7,5,6,4,1] => 0101011 => 1010101 => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => 0101111 => 1010111 => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => 0111000 => 1000011 => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => 0111001 => 1001110 => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => 0111010 => 1011100 => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => 0111001 => 1001110 => 3
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => 0111011 => 1011101 => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => 0110101 => 1011010 => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => 0110010 => 1001100 => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => 0110001 => 1000110 => 2
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => 0110011 => 1001101 => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => 0110101 => 1011010 => 2
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => 0110101 => 1011010 => 2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => 0110111 => 1011011 => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => 0110101 => 1011010 => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,6,4,3,5,7,8,1] => 0110001 => 1000110 => 2
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,6,4,3,5,8,7,1] => 0110011 => 1001101 => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => 0110001 => 1000110 => 2
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => 0110001 => 1000110 => 2
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => 0110011 => 1001101 => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => 0110101 => 1011010 => 2
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => 0110101 => 1011010 => 2
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => 0110011 => 1001101 => 2
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => 0110111 => 1011011 => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,4,5,3,1,7,8] => 0101100 => 1010001 => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,4,5,3,1,8,7] => 0101101 => 1010110 => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,4,5,3,7,8,1] => 0101001 => 1010010 => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,6,4,5,3,8,7,1] => 0101011 => 1010101 => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,8,4,5,3,6,7,1] => 0101001 => 1010010 => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,7,4,5,6,3,1,8] => 0100110 => 1001001 => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => 0100101 => 1001010 => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => 0100101 => 1001010 => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => 0100011 => 1000101 => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,7,4,6,5,3,1,8] => 0101110 => 1010011 => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,7,4,6,5,3,8,1] => 0101101 => 1010110 => 2
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => 0101101 => 1010110 => 2
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => 0101111 => 1010111 => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => 0111101 => 1011110 => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => 0111001 => 1001110 => 3
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => 0111011 => 1011101 => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => 0111001 => 1001110 => 3
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => 0111001 => 1001110 => 3
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,8,5,4,3,7,6,1] => 0111011 => 1011101 => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => 0110101 => 1011010 => 2
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,5,4,6,7,3,1] => 0110011 => 1001101 => 2
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => 0110111 => 1011011 => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,6,4,5,3,8,1] => 0110101 => 1011010 => 2
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,8,7,4,5,6,3,1] => 0110011 => 1001101 => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => 0110111 => 1011011 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => 0111110 => 1001111 => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => 0111101 => 1011110 => 4
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => 0111011 => 1011101 => 3
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => 0110111 => 1011011 => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => 0111111 => 1011111 => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => 1100000 => 0000011 => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => 1100001 => 0001110 => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => 1100001 => 0001110 => 3
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => 1100011 => 0011101 => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => 1100001 => 0001110 => 3
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => 1100011 => 0011101 => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => 1100110 => 0111001 => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => 1100101 => 0111010 => 3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => 1100101 => 0111010 => 3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => 1100111 => 0111011 => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => 1101000 => 1110000 => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => 1101010 => 1110100 => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => 1100100 => 0111000 => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,5,6,7,4,8] => 1100010 => 0011100 => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => 1100001 => 0001110 => 3
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => 1100011 => 0011101 => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => 1100110 => 0111001 => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => 1100101 => 0111010 => 3
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => 1100101 => 0111010 => 3
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => 1100111 => 0111011 => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => 1101100 => 1110001 => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => 1101101 => 1110110 => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => 1101001 => 1110010 => 3
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => 1101011 => 1110101 => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => 1101001 => 1110010 => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => 1101001 => 1110010 => 3
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => 1101011 => 1110101 => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => 1101110 => 1110011 => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => 1101101 => 1110110 => 3
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => 1101101 => 1110110 => 3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => 1101011 => 1110101 => 3
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 1101111 => 1110111 => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => 1010000 => 1100000 => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => 1010001 => 1100010 => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => 1010010 => 1100100 => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => 1010001 => 1100010 => 2
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => 1010011 => 1100101 => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => 1010100 => 1101000 => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => 1010101 => 1101010 => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => 1010010 => 1100100 => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => 1010001 => 1100010 => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => 1010011 => 1100101 => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => 1010110 => 1101001 => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => 1010101 => 1101010 => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => 1010101 => 1101010 => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => 1010111 => 1101011 => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => 1001000 => 0110000 => 2
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => 1001011 => 0110101 => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => 1000100 => 0011000 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => 1000010 => 0001100 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => 1000001 => 0000110 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => 1000011 => 0001101 => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => 1000101 => 0011010 => 2
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => 1000101 => 0011010 => 2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => 1001011 => 0110101 => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,7,5,6,8,1] => 1001001 => 0110010 => 2
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => 1001001 => 0110010 => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => 1001101 => 0110110 => 2
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,8,6,7,5,1] => 1001011 => 0110101 => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => 1001111 => 0110111 => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => 1011000 => 1100001 => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => 1011001 => 1100110 => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => 1011010 => 1101100 => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => 1011001 => 1100110 => 2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => 1011011 => 1101101 => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => 1010101 => 1101010 => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => 1010001 => 1100010 => 2
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => 1010011 => 1100101 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => 1010110 => 1101001 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => 1010101 => 1101010 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => 1010101 => 1101010 => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => 1010101 => 1101010 => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,2,6,4,5,7,1,8] => 1010010 => 1100100 => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => 1010010 => 1100100 => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => 1010001 => 1100010 => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => 1010110 => 1101001 => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => 1010101 => 1101010 => 2
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => 1010101 => 1101010 => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => 1011101 => 1101110 => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => 1011010 => 1101100 => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => 1011011 => 1101101 => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => 1011010 => 1101100 => 2
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => 1011001 => 1100110 => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => 1011011 => 1101101 => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => 1010110 => 1101001 => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => 1010101 => 1101010 => 2
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => 1010101 => 1101010 => 2
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => 1010111 => 1101011 => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => 1011110 => 1100111 => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => 1011101 => 1101110 => 3
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,8,6,5,7,4,1] => 1011011 => 1101101 => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,8,7,5,6,4,1] => 1011011 => 1101101 => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => 1011111 => 1101111 => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => 1010000 => 1100000 => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,2,3,1,5,7,6,8] => 1010010 => 1100100 => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,2,3,1,5,7,8,6] => 1010001 => 1100010 => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => 1010101 => 1101010 => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => 1010001 => 1100010 => 2
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => 1010011 => 1100101 => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => 1010101 => 1101010 => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => 1010101 => 1101010 => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => 1010111 => 1101011 => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => 1001000 => 0110000 => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,2,3,5,1,6,8,7] => 1001001 => 0110010 => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => 1001001 => 0110010 => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => 1001011 => 0110101 => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => 1000100 => 0011000 => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => 1000101 => 0011010 => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => 1000010 => 0001100 => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => 1000001 => 0000110 => 2
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => 1000011 => 0001101 => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,2,3,5,7,6,1,8] => 1000110 => 0011001 => 2
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,2,3,5,8,7,6,1] => 1000111 => 0011011 => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,2,3,6,5,1,7,8] => 1001100 => 0110001 => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,2,3,6,5,1,8,7] => 1001101 => 0110110 => 2
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => 1001011 => 0110101 => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,2,3,7,5,6,1,8] => 1001010 => 0110100 => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => 1001001 => 0110010 => 2
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => 1001001 => 0110010 => 2
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,2,3,8,5,7,6,1] => 1001011 => 0110101 => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,2,3,7,6,5,8,1] => 1001101 => 0110110 => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,2,3,8,6,7,5,1] => 1001011 => 0110101 => 2
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,2,3,8,7,6,5,1] => 1001111 => 0110111 => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => 1001000 => 0110000 => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => 1001001 => 0110010 => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => 1001001 => 0110010 => 2
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => 1001011 => 0110101 => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => 1000100 => 0011000 => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2,3,4,6,1,8,7] => 1000101 => 0011010 => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => 1000010 => 0001100 => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => 1000001 => 0000110 => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => 1000110 => 0011001 => 2
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => 1000101 => 0011010 => 2
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => 1000111 => 0011011 => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => 1000100 => 0011000 => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => 1000101 => 0011010 => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => 1000010 => 0001100 => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => 1000001 => 0000110 => 2
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => 1000011 => 0001101 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => 1000010 => 0001100 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => 1000001 => 0000110 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => 1000001 => 0000110 => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => 1000011 => 0001101 => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,2,3,4,6,5,1,8] => 1000110 => 0011001 => 2
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8,2,3,4,7,6,5,1] => 1000111 => 0011011 => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => 1001100 => 0110001 => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => 1001101 => 0110110 => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [6,2,3,5,4,7,1,8] => 1001010 => 0110100 => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,2,3,5,4,7,8,1] => 1001001 => 0110010 => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => 1001010 => 0110100 => 2
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => 1001001 => 0110010 => 2
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8,2,3,5,4,7,6,1] => 1001011 => 0110101 => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => 1000110 => 0011001 => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8,2,3,5,6,7,4,1] => 1000011 => 0001101 => 2
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8,2,3,5,7,6,4,1] => 1000111 => 0011011 => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => 1001110 => 0110011 => 2
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8,2,3,6,5,4,7,1] => 1001101 => 0110110 => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => 1001011 => 0110101 => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8,2,3,7,6,5,4,1] => 1001111 => 0110111 => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => 1011000 => 1100001 => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => 1011001 => 1100110 => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => 1011010 => 1101100 => 2
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => 1011011 => 1101101 => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [5,2,4,3,6,1,7,8] => 1010100 => 1101000 => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => 1010101 => 1101010 => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [5,2,4,3,6,7,1,8] => 1010010 => 1100100 => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [5,2,4,3,7,6,1,8] => 1010110 => 1101001 => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => 1010101 => 1101010 => 2
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,2,4,3,8,7,6,1] => 1010111 => 1101011 => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => 1010101 => 1101010 => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => 1010110 => 1101001 => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => 1010101 => 1101010 => 2
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => 1010101 => 1101010 => 2
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => 1010011 => 1100101 => 2
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8,2,4,3,7,6,5,1] => 1010111 => 1101011 => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,2,4,5,3,1,7,8] => 1001100 => 0110001 => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2,4,5,3,1,8,7] => 1001101 => 0110110 => 2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,2,4,5,3,8,7,1] => 1001011 => 0110101 => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => 1001010 => 0110100 => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => 1001001 => 0110010 => 2
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => 1001011 => 0110101 => 2
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8,2,4,5,6,3,7,1] => 1000101 => 0011010 => 2
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8,2,4,5,6,7,3,1] => 1000011 => 0001101 => 2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8,2,4,5,7,6,3,1] => 1000111 => 0011011 => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => 1001110 => 0110011 => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,2,4,6,5,3,8,1] => 1001101 => 0110110 => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8,2,4,7,5,6,3,1] => 1001011 => 0110101 => 2
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => 1001111 => 0110111 => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,2,5,4,3,1,7,8] => 1011100 => 1100011 => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => 1011101 => 1101110 => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => 1011010 => 1101100 => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,2,5,4,3,7,8,1] => 1011001 => 1100110 => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => 1011010 => 1101100 => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8,2,5,4,3,6,7,1] => 1011001 => 1100110 => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => 1011011 => 1101101 => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,2,5,4,6,3,8,1] => 1010101 => 1101010 => 2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8,2,5,4,7,6,3,1] => 1010111 => 1101011 => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,6,4,5,3,1,8] => 1010110 => 1101001 => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => 1010101 => 1101010 => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => 1010101 => 1101010 => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => 1010011 => 1100101 => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => 1010011 => 1100101 => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => 1010111 => 1101011 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,2,6,5,4,3,1,8] => 1011110 => 1100111 => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,6,5,4,3,8,1] => 1011101 => 1101110 => 3
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => 1011101 => 1101110 => 3
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => 1011011 => 1101101 => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => 1011011 => 1101101 => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => 1010111 => 1101011 => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => 1011111 => 1101111 => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => 1110000 => 0000111 => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => 1110001 => 0011110 => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => 1110010 => 0111100 => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => 1110001 => 0011110 => 4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => 1110011 => 0111101 => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => 1110100 => 1111000 => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 1110101 => 1111010 => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => 1110010 => 0111100 => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => 1110001 => 0011110 => 4
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => 1110011 => 0111101 => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => 1110110 => 1111001 => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => 1110101 => 1111010 => 4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => 1110101 => 1111010 => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 1110111 => 1111011 => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => 1101000 => 1110000 => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => 1101001 => 1110010 => 3
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => 1101011 => 1110101 => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => 1100100 => 0111000 => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => 1100101 => 0111010 => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => 1100010 => 0011100 => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => 1100001 => 0001110 => 3
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => 1100011 => 0011101 => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => 1100110 => 0111001 => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => 1100101 => 0111010 => 3
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => 1100111 => 0111011 => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => 1101100 => 1110001 => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => 1101101 => 1110110 => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => 1101010 => 1110100 => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => 1101001 => 1110010 => 3
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => 1101011 => 1110101 => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => 1101001 => 1110010 => 3
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => 1101001 => 1110010 => 3
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => 1101011 => 1110101 => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => 1101101 => 1110110 => 3
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => 1101011 => 1110101 => 3
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => 1101111 => 1110111 => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => 1101000 => 1110000 => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => 1101001 => 1110010 => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => 1101010 => 1110100 => 3
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => 1101011 => 1110101 => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => 1100100 => 0111000 => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => 1100101 => 0111010 => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => 1100001 => 0001110 => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => 1100110 => 0111001 => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [6,3,2,4,5,7,1,8] => 1100010 => 0011100 => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => 1100001 => 0001110 => 3
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => 1100001 => 0001110 => 3
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8,3,2,4,6,5,7,1] => 1100101 => 0111010 => 3
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => 1100011 => 0011101 => 3
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8,3,2,4,7,6,5,1] => 1100111 => 0111011 => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,3,2,5,4,1,7,8] => 1101100 => 1110001 => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => 1101101 => 1110110 => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => 1101010 => 1110100 => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => 1101001 => 1110010 => 3
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,3,2,5,4,8,7,1] => 1101011 => 1110101 => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => 1101010 => 1110100 => 3
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => 1101011 => 1110101 => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,3,2,5,6,4,8,1] => 1100101 => 0111010 => 3
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8,3,2,5,6,4,7,1] => 1100101 => 0111010 => 3
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8,3,2,5,6,7,4,1] => 1100011 => 0011101 => 3
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => 1100111 => 0111011 => 3
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => 1101011 => 1110101 => 3
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => 1101011 => 1110101 => 3
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => 1101111 => 1110111 => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => 1011000 => 1100001 => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => 1011001 => 1100110 => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => 1011001 => 1100110 => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => 1011011 => 1101101 => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => 1010101 => 1101010 => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => 1010001 => 1100010 => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => 1010110 => 1101001 => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,3,4,2,7,6,8,1] => 1010101 => 1101010 => 2
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => 1010101 => 1101010 => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => 1010101 => 1101010 => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => 1010001 => 1100010 => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,2,6,5,1,8] => 1010110 => 1101001 => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => 1010101 => 1101010 => 2
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8,3,4,2,6,5,7,1] => 1010101 => 1101010 => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => 1001101 => 0110110 => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => 1001010 => 0110100 => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => 1001001 => 0110010 => 2
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => 1001011 => 0110101 => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => 1001001 => 0110010 => 2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => 1001011 => 0110101 => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => 1000110 => 0011001 => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => 1000101 => 0011010 => 2
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => 1000101 => 0011010 => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => 1000011 => 0001101 => 2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => 1000111 => 0011011 => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,3,4,6,5,2,1,8] => 1001110 => 0110011 => 2
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => 1001111 => 0110111 => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => 1011101 => 1101110 => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => 1011010 => 1101100 => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,3,5,4,2,7,8,1] => 1011001 => 1100110 => 2
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,3,5,4,2,8,7,1] => 1011011 => 1101101 => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => 1011010 => 1101100 => 2
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8,3,5,4,2,6,7,1] => 1011001 => 1100110 => 2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8,3,5,4,2,7,6,1] => 1011011 => 1101101 => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,5,4,6,2,1,8] => 1010110 => 1101001 => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => 1010101 => 1101010 => 2
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,5,4,6,7,2,1] => 1010011 => 1100101 => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => 1010111 => 1101011 => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => 1010110 => 1101001 => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => 1010101 => 1101010 => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => 1010101 => 1101010 => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [8,3,6,4,5,7,2,1] => 1010011 => 1100101 => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8,3,7,4,5,6,2,1] => 1010011 => 1100101 => 2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => 1010111 => 1101011 => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => 1011110 => 1100111 => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => 1011101 => 1101110 => 3
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => 1011101 => 1101110 => 3
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => 1011011 => 1101101 => 2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8,3,7,5,4,6,2,1] => 1011011 => 1101101 => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => 1010111 => 1101011 => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => 1011111 => 1101111 => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => 1111000 => 0001111 => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => 1111001 => 0111110 => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => 1111010 => 1111100 => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => 1111001 => 0111110 => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 1111011 => 1111101 => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => 1110100 => 1111000 => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => 1110101 => 1111010 => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => 1110010 => 0111100 => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => 1110001 => 0011110 => 4
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => 1110011 => 0111101 => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => 1110110 => 1111001 => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => 1110101 => 1111010 => 4
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,8,6,7,1] => 1110101 => 1111010 => 4
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => 1110111 => 1111011 => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => 1110100 => 1111000 => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => 1110101 => 1111010 => 4
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [6,4,3,2,5,8,7,1] => 1110011 => 0111101 => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => 1110001 => 0011110 => 4
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => 1110001 => 0011110 => 4
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8,4,3,2,5,7,6,1] => 1110011 => 0111101 => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,4,3,2,6,5,1,8] => 1110110 => 1111001 => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => 1110101 => 1111010 => 4
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8,4,3,2,6,5,7,1] => 1110101 => 1111010 => 4
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8,4,3,2,6,7,5,1] => 1110011 => 0111101 => 4
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => 1110111 => 1111011 => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => 1101101 => 1110110 => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => 1101010 => 1110100 => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => 1101001 => 1110010 => 3
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8,4,3,5,2,7,6,1] => 1101011 => 1110101 => 3
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => 1100101 => 0111010 => 3
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => 1100011 => 0011101 => 3
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => 1100111 => 0111011 => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => 1101110 => 1110011 => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => 1101101 => 1110110 => 3
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => 1101011 => 1110101 => 3
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8,4,3,7,6,5,2,1] => 1101111 => 1110111 => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => 1101100 => 1110001 => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => 1101101 => 1110110 => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,3,4,2,7,8,1] => 1101001 => 1110010 => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => 1101010 => 1110100 => 3
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => 1101001 => 1110010 => 3
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => 1101011 => 1110101 => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => 1100101 => 0111010 => 3
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => 1100011 => 0011101 => 3
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => 1100111 => 0111011 => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => 1100110 => 0111001 => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => 1100101 => 0111010 => 3
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8,6,3,4,5,2,7,1] => 1100101 => 0111010 => 3
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => 1100011 => 0011101 => 3
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => 1100111 => 0111011 => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => 1101110 => 1110011 => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => 1101101 => 1110110 => 3
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8,6,3,5,4,2,7,1] => 1101101 => 1110110 => 3
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8,6,3,5,4,7,2,1] => 1101011 => 1110101 => 3
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => 1101011 => 1110101 => 3
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => 1100111 => 0111011 => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => 1101111 => 1110111 => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => 1111100 => 0011111 => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => 1111101 => 1111110 => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => 1111010 => 1111100 => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => 1111001 => 0111110 => 5
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => 1111011 => 1111101 => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => 1111010 => 1111100 => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => 1111001 => 0111110 => 5
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => 1111001 => 0111110 => 5
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => 1111011 => 1111101 => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => 1110110 => 1111001 => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => 1110101 => 1111010 => 4
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => 1110101 => 1111010 => 4
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => 1110011 => 0111101 => 4
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => 1110111 => 1111011 => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => 1110110 => 1111001 => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => 1110101 => 1111010 => 4
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => 1110101 => 1111010 => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => 1110011 => 0111101 => 4
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => 1110011 => 0111101 => 4
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => 1110111 => 1111011 => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => 1101110 => 1110011 => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => 1101101 => 1110110 => 3
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => 1101101 => 1110110 => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8,6,4,5,3,7,2,1] => 1101011 => 1110101 => 3
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => 1101011 => 1110101 => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => 1100111 => 0111011 => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => 1101111 => 1110111 => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => 1111110 => 0111111 => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => 1111101 => 1111110 => 6
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => 1111101 => 1111110 => 6
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => 1111011 => 1111101 => 5
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => 1111011 => 1111101 => 5
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => 1110111 => 1111011 => 4
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => 1110111 => 1111011 => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => 1111111 => 1111111 => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => 11111110 => 01111111 => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => 01111111 => 10111111 => 6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => 111111110 => 011111111 => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,7,6,4,5,3,2,1,9] => 11101110 => 11110011 => 4
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,9,8,7,5,6,4,3,2] => 01110111 => 10111011 => 3
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 101111111 => 7
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110 => 0111111111 => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,8,7,5,6,4,3,2,1,10] => 111011110 => 111100111 => 4
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,7,5,4,6,3,2,1,9] => 11101110 => 11110011 => 4
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,7,4,6,5,3,2,1,9] => 11011110 => 11100111 => 3
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,9,8,6,5,7,4,3,2] => 01110111 => 10111011 => 3
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,9,8,5,7,6,4,3,2] => 01101111 => 10110111 => 3
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,10,9,8,6,7,5,4,3,2] => 011101111 => 101110111 => 3
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1,12] => 11111111110 => 01111111111 => 10
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,9,8,5,6,7,4,3,2] => 01100111 => 10011011 => 2
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,10,9,8,6,5,7,4,3,2] => 011110111 => 101111011 => 4
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,10,9,8,5,6,7,4,3,2] => 011100111 => 100111011 => 3
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,9,8,5,4,6,7,3,2] => 01110011 => 10011101 => 3
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,10,9,6,5,8,7,4,3,2] => 011101111 => 101110111 => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,6,5,4,3,2,8,1,9] => 11111010 => 11111100 => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => 01111110 => 10011111 => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => 11111101 => 11111110 => 7
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,9,8,4,5,6,7,3,2] => 01100011 => 10001101 => 2
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => 10111111 => 11011111 => 5
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => 00111111 => 01011111 => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => 11111100 => 00111111 => 6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => 01111110 => 10011111 => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,6,4,5,3,2,1,9,8] => 11011101 => 11101110 => 3
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,10,9,5,6,7,8,4,3,2] => 011000111 => 100011011 => 2
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,9,8,6,7,5,4,3] => 10110111 => 11011011 => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => 00111111 => 01011111 => 5
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,7,6,5,4,3,2,9,1,10] => 111111010 => 111111100 => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => 111111101 => 111111110 => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,6,4,3,5,2,1,9,8] => 11101101 => 11110110 => 4
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [7,6,3,5,4,2,1,9,8] => 11011101 => 11101110 => 3
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,9,8,6,5,7,4,3] => 10111011 => 11011101 => 3
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 110111111 => 6
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,10,9,8,7,6,5,4,2] => 001111111 => 010111111 => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => 111111100 => 001111111 => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => 011111110 => 100111111 => 6
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,4,5,3,2,1,10,9] => 111011101 => 111101110 => 4
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,9,5,4,6,7,8,3,2] => 01100011 => 10001101 => 2
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,10,9,8,6,7,5,4,3] => 101110111 => 110111011 => 3
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => 001111111 => 010111111 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => 00000001 => 00000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => 00000011 => 00000101 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => 00000101 => 00001010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,9,7,8,1] => 00000101 => 00001010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => 00000111 => 00001011 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,1] => 00001001 => 00010010 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,5,8,6,7,9,1] => 00001001 => 00010010 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,9,6,7,8,1] => 00001001 => 00010010 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,5,9,6,8,7,1] => 00001011 => 00010101 => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,5,8,7,6,9,1] => 00001101 => 00010110 => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,5,9,7,6,8,1] => 00001101 => 00010110 => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,9,7,8,6,1] => 00001011 => 00010101 => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,1] => 00010001 => 00100010 => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,4,7,5,6,8,9,1] => 00010001 => 00100010 => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,9,5,6,7,8,1] => 00010001 => 00100010 => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,4,9,6,5,7,8,1] => 00011001 => 00100110 => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,9,6,7,8,5,1] => 00010011 => 00100101 => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,6,4,5,7,8,9,1] => 00100001 => 01000010 => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,9,4,5,6,7,8,1] => 00100001 => 01000010 => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,9,5,4,6,7,8,1] => 00110001 => 01000110 => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,9,5,6,7,8,4,1] => 00100011 => 01000101 => 1
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => 00111111 => 01011111 => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => 01000001 => 10000010 => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,9,3,4,5,6,7,8,1] => 01000001 => 10000010 => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,9,4,3,5,6,7,8,1] => 01100001 => 10000110 => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,9,4,5,6,7,8,3,1] => 01000011 => 10000101 => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => 01111101 => 10111110 => 5
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,9,8,6,5,7,4,3,1] => 01110111 => 10111011 => 3
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,8,7,5,6,4,3,1] => 01110111 => 10111011 => 3
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => 01111111 => 10111111 => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => 10000001 => 00000110 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,9,8,1] => 10101011 => 11010101 => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,9,4,5,6,7,8,1] => 10100001 => 11000010 => 2
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,9,8,7,6,5,4,1] => 10111111 => 11011111 => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,1] => 10000001 => 00000110 => 2
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,2,3,4,9,6,7,8,1] => 10001001 => 00110010 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [7,2,3,4,5,6,9,8,1] => 10000011 => 00001101 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => 10000001 => 00000110 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => 10000001 => 00000110 => 2
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9,2,4,5,6,8,7,3,1] => 10000111 => 00011011 => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [9,2,7,4,5,6,3,8,1] => 10100101 => 11001010 => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9,2,7,6,5,4,3,8,1] => 10111101 => 11011110 => 4
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9,2,8,7,6,5,4,3,1] => 10111111 => 11011111 => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => 11000001 => 00001110 => 3
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,3,2,4,5,6,7,8,1] => 11000001 => 00001110 => 3
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [9,3,2,5,6,7,8,4,1] => 11000011 => 00011101 => 3
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9,3,4,2,5,6,7,8,1] => 10100001 => 11000010 => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [9,3,4,5,2,6,7,8,1] => 10010001 => 01100010 => 2
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [9,3,4,5,6,2,8,7,1] => 10001011 => 00110101 => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,3,4,5,6,7,8,2,1] => 10000011 => 00001101 => 2
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9,3,4,5,6,8,7,2,1] => 10000111 => 00011011 => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9,3,7,6,5,4,8,2,1] => 10111011 => 11011101 => 3
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9,3,8,7,6,5,4,2,1] => 10111111 => 11011111 => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => 11100001 => 00011110 => 4
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,4,3,2,9,8,7,6,1] => 11101111 => 11110111 => 4
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [9,4,3,2,5,6,7,8,1] => 11100001 => 00011110 => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [9,4,3,5,6,7,2,8,1] => 11000101 => 00111010 => 3
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [9,4,3,5,6,7,8,2,1] => 11000011 => 00011101 => 3
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [9,8,3,4,5,7,6,2,1] => 11000111 => 00111011 => 3
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [9,8,3,5,7,6,4,2,1] => 11001111 => 01110111 => 3
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [9,8,3,6,5,4,7,2,1] => 11011011 => 11101101 => 3
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [9,8,3,7,6,5,4,2,1] => 11011111 => 11101111 => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,1] => 11110001 => 00111110 => 5
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [9,8,4,3,5,6,7,2,1] => 11100011 => 00111101 => 4
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [9,8,4,3,6,7,5,2,1] => 11100111 => 01111011 => 4
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [9,8,4,5,3,7,6,2,1] => 11010111 => 11101011 => 3
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [9,8,4,5,7,6,3,2,1] => 11001111 => 01110111 => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [8,7,4,6,5,3,2,9,1] => 11011101 => 11101110 => 3
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [9,8,4,6,5,7,3,2,1] => 11010111 => 11101011 => 3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [9,8,4,7,6,5,3,2,1] => 11011111 => 11101111 => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,1] => 11111001 => 01111110 => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,6,5,4,3,2,9,8,1] => 11111011 => 11111101 => 6
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => 11111001 => 01111110 => 6
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [8,7,5,4,6,3,2,9,1] => 11101101 => 11110110 => 4
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [9,8,5,4,6,3,7,2,1] => 11101011 => 11110101 => 4
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [9,8,5,4,6,7,3,2,1] => 11100111 => 01111011 => 4
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,7,6,4,5,3,2,9,1] => 11101101 => 11110110 => 4
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [9,8,7,4,5,6,3,2,1] => 11100111 => 01111011 => 4
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9,8,7,4,6,5,3,2,1] => 11101111 => 11110111 => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => 11111101 => 11111110 => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9,7,6,5,4,3,2,8,1] => 11111101 => 11111110 => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [9,7,6,5,4,3,8,2,1] => 11111011 => 11111101 => 6
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [9,8,6,5,4,3,7,2,1] => 11111011 => 11111101 => 6
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [9,8,6,5,4,7,3,2,1] => 11110111 => 11111011 => 5
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [9,8,7,5,4,6,3,2,1] => 11110111 => 11111011 => 5
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,8,7,5,6,4,3,2,1] => 11101111 => 11110111 => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => 11111111 => 11111111 => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => 00000000 => 00000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => 00000001 => 00000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => 00000001 => 00000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => 00000001 => 00000010 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => 00000001 => 00000010 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => 00000001 => 00000010 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => 00000001 => 00000010 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => 00000001 => 00000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 000000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => 000000001 => 000000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => 00000011 => 00000101 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => 000000001 => 000000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => 00000101 => 00001010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => 000000001 => 000000010 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,6,8,9,5] => 00001001 => 00010010 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => 000000001 => 000000010 => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,5,7,8,9,4] => 00010001 => 00100010 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => 000000001 => 000000010 => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => 00100001 => 01000010 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => 000000001 => 000000010 => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => 01000001 => 10000010 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => 000000001 => 000000010 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => 000000001 => 000000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => 000000001 => 000000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000 => 0000000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => 0000000001 => 0000000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => 000000011 => 000000101 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => 0000000001 => 0000000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,9,7,8,6] => 00000101 => 00001010 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => 00000111 => 00001011 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => 100000001 => 000000110 => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => 0000000001 => 0000000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000001 => 0000000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,6,10,8,9,7] => 000000101 => 000001010 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,9,6,7,8,5] => 00001001 => 00010010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => 000000111 => 000001011 => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,2,7,4,5,6,8,9,3] => 00100001 => 01000010 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,10,1] => 100000001 => 000000110 => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,10,1] => 110000001 => 000001110 => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,11,1] => 1000000001 => 0000000110 => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,12,2] => 00000000001 => 00000000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,5,10,7,8,9,6] => 000001001 => 000010010 => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,9,5,6,7,8,4] => 00010001 => 00100010 => 1
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => 00001111 => 00010111 => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,4,10,6,7,8,9,5] => 000010001 => 000100010 => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,9,4,5,6,7,8,3] => 00100001 => 01000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => 000001111 => 000010111 => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,8,3,4,5,6,7,9,2] => 01000001 => 10000010 => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,2,3,4,5,7,8,9,10,1] => 100000001 => 000000110 => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,10,1] => 111000001 => 000011110 => 4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,3,10,5,6,7,8,9,4] => 000100001 => 001000010 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9,3,4,5,6,7,8,2] => 01000001 => 10000010 => 1
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => 00011111 => 00101111 => 4
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,9,4,5,6,7,8,3,2] => 01000011 => 10000101 => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,10,4,5,6,7,8,9,3] => 001000001 => 010000010 => 1
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => 000011111 => 000101111 => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,10,1] => 111100001 => 000111110 => 5
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,10,3,4,5,6,7,8,9,2] => 010000001 => 100000010 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => 100000001 => 000000110 => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,10,4,5,6,7,8,9,3,2] => 010000011 => 100000101 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => 00000010 => 00000100 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => 00000100 => 00001000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => 00000101 => 00001010 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => 00001000 => 00010000 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => 00001010 => 00010100 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,9,8,7] => 00001011 => 00010101 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => 00010000 => 00100000 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => 00010101 => 00101010 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,9,8,7,6] => 00010111 => 00101011 => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,3,6,5,4,9,8,7] => 00011011 => 00101101 => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => 00100000 => 01000000 => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => 00101010 => 01010100 => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,9,8,7] => 00101011 => 01010101 => 1
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,9,8,7,6,5] => 00101111 => 01010111 => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => 01000000 => 10000000 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => 01000001 => 10000010 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,8,7] => 01000011 => 10000101 => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => 01010000 => 10100000 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => 01010101 => 10101010 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,9,8,7,6] => 01010111 => 10101011 => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4,9,8,7] => 01011011 => 10101101 => 2
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,9,8,7,6,5,4] => 01011111 => 10101111 => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => 01100000 => 10000001 => 1
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,4,3,2,9,8,7,6,5] => 01101111 => 10110111 => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2,9,8,7,6] => 01110111 => 10111011 => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,6,5,4,3,2,9,8] => 01111101 => 10111110 => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => 10000000 => 00000001 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => 10000001 => 00000110 => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => 10000010 => 00001100 => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => 10100000 => 11000000 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9] => 10101000 => 11010000 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => 10101010 => 11010100 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,9,8,7] => 10101011 => 11010101 => 2
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,9,8,7,6,5] => 10101111 => 11010111 => 3
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,5,4,3,9,8,7,6] => 10110111 => 11011011 => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => 10111110 => 11001111 => 4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => 11000000 => 00000011 => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9] => 11010000 => 11100000 => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6,9,8] => 11010101 => 11101010 => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,6,5,4,7,8,9] => 11011000 => 11100001 => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4,9,8,7] => 11011011 => 11101101 => 3
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => 11011111 => 11101111 => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => 11100000 => 00000111 => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,3,2,1,6,5,7,8,9] => 11101000 => 11110000 => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,8,7,9] => 11101010 => 11110100 => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,3,2,1,7,6,5,8,9] => 11101100 => 11110001 => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2,1,7,6,5,9,8] => 11101101 => 11110110 => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,8,7,6,5,9] => 11101110 => 11110011 => 4
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => 11101111 => 11110111 => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => 11110000 => 00001111 => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,4,3,2,1,7,6,8,9] => 11110100 => 11111000 => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,4,3,2,1,8,7,6,9] => 11110110 => 11111001 => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => 11110111 => 11111011 => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => 11111000 => 00011111 => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,5,4,3,2,1,8,7,9] => 11111010 => 11111100 => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => 11111011 => 11111101 => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => 000000010 => 000000100 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => 000000100 => 000001000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => 000000101 => 000001010 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => 000001000 => 000010000 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => 000010000 => 000100000 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7,10,9] => 000010101 => 000101010 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => 000100000 => 001000000 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => 000101010 => 001010100 => 1
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => 000111111 => 001011111 => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => 001000000 => 010000000 => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => 001010101 => 010101010 => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3,10,9,8,7] => 001110111 => 010111011 => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => 010000000 => 100000000 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => 010101010 => 101010100 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,9,8] => 010101011 => 101010101 => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,2,6,5,4,10,9,8,7] => 010110111 => 101011011 => 2
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,10,9,8,7,6,5,4] => 010111111 => 101011111 => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5,10,9,8] => 011011011 => 101101101 => 2
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,4,3,2,10,9,8,7,6,5] => 011011111 => 101101111 => 4
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,5,4,3,2,10,9,8,7,6] => 011101111 => 101110111 => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => 100000000 => 000000001 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => 100000001 => 000000110 => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => 101000000 => 110000000 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9,10] => 101010000 => 110100000 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9,10] => 101010100 => 110101000 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 101010101 => 110101010 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => 101010111 => 110101011 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5,10,9,8] => 101011011 => 110101101 => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 101110111 => 110111011 => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => 101111101 => 110111110 => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => 110000000 => 000000011 => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9,10] => 110100000 => 111000000 => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,9,8,10] => 110101010 => 111010100 => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7,10,9] => 110110101 => 111011010 => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,6,5,4,10,9,8,7] => 110110111 => 111011011 => 3
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => 110111111 => 111011111 => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => 111000000 => 000000111 => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => 111010101 => 111101010 => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => 111010111 => 111101011 => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5,10,9,8] => 111011011 => 111101101 => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,8,7,6,5,9,10] => 111011100 => 111100011 => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 111011101 => 111101110 => 4
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 111011111 => 111101111 => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => 111100000 => 000001111 => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,9,8,10] => 111101010 => 111110100 => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,3,2,1,9,8,7,6,10] => 111101110 => 111110011 => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => 111101111 => 111110111 => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => 111110000 => 000011111 => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,5,4,3,2,1,9,8,7,10] => 111110110 => 111111001 => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 111110111 => 111111011 => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => 111111000 => 000111111 => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,6,5,4,3,2,1,9,8,10] => 111111010 => 111111100 => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => 111111011 => 111111101 => 7
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => 111111111 => 111111111 => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => 01000000 => 10000000 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => 00100000 => 01000000 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => 00010000 => 00100000 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => 00001000 => 00010000 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => 00000100 => 00001000 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => 00000010 => 00000100 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => 010000000 => 100000000 => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => 01100000 => 10000001 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => 001000000 => 010000000 => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8,9] => 00110000 => 01000001 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => 000100000 => 001000000 => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,4,6,5,1,7,8,9] => 00011000 => 00100001 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => 000010000 => 000100000 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,5,7,6,1,8,9] => 00001100 => 00010001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => 000001000 => 000010000 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => 00000110 => 00001001 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => 000000100 => 000001000 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => 000000010 => 000000100 => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [10,9,3,4,5,6,8,7,2,1] => 110000111 => 000111011 => 3
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [10,9,4,3,5,6,7,8,2,1] => 111000011 => 000111101 => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [10,3,4,5,6,7,9,8,2,1] => 100000111 => 000011011 => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10,4,3,5,6,7,8,9,2,1] => 110000011 => 000011101 => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000 => 0000000001 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => 10000001 => 00000110 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => 000000011 => 000000101 => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [10,9,8,5,7,6,4,3,2,1] => 111011111 => 111101111 => 4
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [10,9,8,6,5,7,4,3,2,1] => 111101111 => 111110111 => 5
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [10,9,8,4,5,7,6,3,2,1] => 111001111 => 011110111 => 4
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [10,9,8,5,4,6,7,3,2,1] => 111100111 => 011111011 => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,7,9,10,8] => 100000001 => 000000110 => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,6,8,9,7] => 01000001 => 10000010 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,6,8,9,7] => 01000001 => 10000010 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => 01000001 => 10000010 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,2,3,4,5,6,7,1,9] => 10000010 => 00001100 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,2,3,4,5,6,1,8,9] => 10000100 => 00011000 => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,2,3,4,5,1,7,8,9] => 10001000 => 00110000 => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8,9] => 10010000 => 01100000 => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8,9] => 10100000 => 11000000 => 2
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => 011111111 => 101111111 => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => 111111101 => 111111110 => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => 1111111101 => 1111111110 => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,8,7,5,6,4,3,2,10,1] => 111011101 => 111101110 => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,5,4,3,2,7,1,8,9] => 11110100 => 11111000 => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,4,3,2,6,1,7,8,9] => 11101000 => 11110000 => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8,9] => 11010000 => 11100000 => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => 10100000 => 11000000 => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,9,8,7,5,6,4,3,2,1] => 111101111 => 111110111 => 5
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [10,9,8,4,7,6,5,3,2,1] => 111011111 => 111101111 => 4
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,9,4,8,7,6,5,3,2,1] => 110111111 => 111011111 => 5
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,9,3,8,7,6,5,4,2,1] => 110111111 => 111011111 => 5
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,3,9,8,7,6,5,4,2,1] => 101111111 => 110111111 => 6
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,2,9,8,7,6,5,4,3,1] => 101111111 => 110111111 => 6
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,2,3,4,5,6,1,9,8] => 10000101 => 00011010 => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,9,4,5,6,7,8,3] => 10100001 => 11000010 => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,8,3,4,5,6,7,1,9] => 01000010 => 10000100 => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,10,3,4,5,6,7,8,9,1] => 010000001 => 100000010 => 1
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => 01011111 => 10101111 => 4
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,2,3,1,9,8,7,6,5] => 10101111 => 11010111 => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,3,4,2,1,9,8,7,6] => 10110111 => 11011011 => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,5,3,4,2,1,9,8,7] => 11011011 => 11101101 => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => 00010000 => 00100000 => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8,9] => 00010000 => 00100000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6,9,10] => 000000100 => 000001000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,9,6,10] => 000000010 => 000000100 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6,7,9,8] => 00010001 => 00100010 => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8,9] => 10010000 => 01100000 => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,6,3,4,5,7,8,9,10,1] => 010000001 => 100000010 => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,6,4,5,7,8,9,10,1] => 001000001 => 010000010 => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,10,1] => 000100001 => 001000010 => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,10,9,4,5,6,7,8,3,2] => 011000011 => 100001101 => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,9,4,3,5,6,7,8,2] => 01100001 => 10000110 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => 10000010 => 00001100 => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => 00000011 => 00000101 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => 00000101 => 00001010 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => 10000001 => 00000110 => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => 00001011 => 00010101 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => 000000111 => 000001011 => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,9,8,7,6] => 00010111 => 00101011 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,6,10,8,9,7,1] => 000001011 => 000010101 => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,1,9,7,8,6,5] => 00101011 => 01010101 => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,10,7,8,9,6,1] => 000010011 => 000100101 => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,1,9,6,7,8,5,4] => 01010011 => 10100101 => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,10,6,7,8,9,5,1] => 000100011 => 001000101 => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,1,9,5,6,7,8,4,3] => 10100011 => 11000101 => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,10,5,6,7,8,9,4,1] => 001000011 => 010000101 => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,10,4,5,6,7,8,9,3,1] => 010000011 => 100000101 => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10,3,4,5,6,7,8,9,2,1] => 100000011 => 000001101 => 2
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,4,9,8,7,6,5,3] => 10011111 => 01101111 => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2,6,5,4,3,1,9,8] => 10111101 => 11011110 => 4
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,2,1,9,5,8,7,6,4] => 11010111 => 11101011 => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3,5,4,2,1,9,8,7] => 10111011 => 11011101 => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,2,1,9,7,8,6,5] => 11101011 => 11110101 => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,5,4,3,2,1,8,9,7] => 11111001 => 01111110 => 6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [10,8,7,6,5,4,3,2,9,1] => 111111101 => 111111110 => 8
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,3,2,1,9,7,8,6] => 11110101 => 11111010 => 5
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [10,8,7,6,5,4,3,9,2,1] => 111111011 => 111111101 => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [10,9,7,6,5,4,3,8,2,1] => 111111011 => 111111101 => 7
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,1,9,8,6,7,5,4] => 11011011 => 11101101 => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [10,9,7,6,5,4,8,3,2,1] => 111110111 => 111111011 => 6
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [10,9,8,6,5,4,7,3,2,1] => 111110111 => 111111011 => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,3,5,7,8,9,6] => 00100001 => 01000010 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,5,10,6,7,8,9,1] => 000010001 => 000100010 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,10,1] => 000010001 => 000100010 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,9] => 00001010 => 00010100 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,6,8,9] => 00010100 => 00101000 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,8,7,1,9] => 01010110 => 10101001 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => 01010101 => 10101010 => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9] => 011010101 => 101101010 => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,1] => 010101011 => 101010101 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => 010101010 => 101010100 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,7,10,8,9,1] => 000000101 => 000001010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,10,7,8,9,1] => 000001001 => 000010010 => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,10,5,6,7,8,9,1] => 000100001 => 001000010 => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,10,4,5,6,7,8,9,1] => 001000001 => 010000010 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,2,3,4,5,6,7,8,9,1] => 100000001 => 000000110 => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,3,2,4,5,6,7,8,9,1] => 110000001 => 000001110 => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [11,2,3,4,5,6,7,8,9,10,1] => 1000000001 => 0000000110 => 2
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [10,9,8,5,4,7,6,3,2,1] => 111101111 => 111110111 => 5
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [10,5,4,3,2,9,8,7,6,1] => 111101111 => 111110111 => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1,10] => 100000010 => 000001100 => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10,11] => 0100000000 => 1000000000 => 1
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => 00011111 => 00101111 => 4
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => 00001111 => 00010111 => 3
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => 00000111 => 00001011 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => 00000011 => 00000101 => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,9,4] => 11000001 => 00001110 => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,9,5] => 11100001 => 00011110 => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,8,7,6,5,4,3,2,1,11,10] => 1111111101 => 1111111110 => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [10,7,6,5,4,3,2,9,8,1] => 111111011 => 111111101 => 7
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => 00100000 => 01000000 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => 100000001 => 000000110 => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => 01000001 => 10000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => 0000000010 => 0000000100 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,1,8,9,10,7] => 000010001 => 000100010 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => 00000010 => 00000100 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,7,9,8,4] => 00000011 => 00000101 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,6,8,9,7,10] => 000000010 => 000000100 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => 0000000010 => 0000000100 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => 00000010 => 00000100 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,7,6,5,4,3,2,10,9,1] => 111111011 => 111111101 => 7
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,2,10,9,8,7,6,5,4,1] => 101111111 => 110111111 => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,5,7,6,8,1,9] => 00001010 => 00010100 => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,5,8,7,6,1,9] => 00001110 => 00010011 => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,9,4] => 10000001 => 00000110 => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,9,4,5,6,7,8,2] => 00100001 => 01000010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => 000000101 => 000001010 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => 00001001 => 00010010 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => 0101010101 => 1010101010 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,2,3,4,5,6,7,8,9,11,1] => 1000000001 => 0000000110 => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => 001000000 => 010000000 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => 000000010 => 000000100 => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,3,7,8,9,10] => 000010000 => 000100000 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,9,5] => 00100001 => 01000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,6,8,10,9,7] => 000000011 => 000000101 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,7,8,4,9,10] => 000000100 => 000001000 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,7,6,5,4,3,9,8,2] => 01111011 => 10111101 => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,7,10,9,8,5] => 000000111 => 000001011 => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,8,7,9] => 10101010 => 11010100 => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,5,4,6,1,8,7,9] => 10101010 => 11010100 => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7,10,9] => 101010101 => 110101010 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,10,1] => 101010101 => 110101010 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,9,8,1,10] => 101010110 => 110101001 => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,4,8,5,6,7,1,9] => 00010010 => 00100100 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,8,1,9] => 10000010 => 00001100 => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,9,5,4,6,7,8,3] => 00110001 => 01000110 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,2,1,7,8,9,6] => 11110001 => 00111110 => 5
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,6,8,7,9,2] => 00000101 => 00001010 => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,2,8,7,6,5,4,1,9] => 10111110 => 11001111 => 4
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10,3,2,9,8,7,6,5,4,1] => 110111111 => 111011111 => 5
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,2,1,10,7,6,9,8,5] => 111011011 => 111101101 => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => 000000011 => 000000101 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,8,3,9] => 10000010 => 00001100 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,10,1] => 111111001 => 011111110 => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,10,1] => 111110001 => 001111110 => 6
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,8,7,9,2] => 01010101 => 10101010 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => 010101001 => 101010010 => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,4,9,7,6,8,5] => 00001101 => 00010110 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,3,9,6,5,7,8,4] => 00011001 => 00100110 => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9,10] => 011000000 => 100000001 => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,5] => 10100001 => 11000010 => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9,10] => 101000000 => 110000000 => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => 00000100 => 00001000 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,6,5,7,10,8,9,1] => 010100101 => 101001010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,7,9,8,1,10] => 000000110 => 000001001 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,9,8,5] => 00000011 => 00000101 => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,9,8,3] => 00101011 => 01010101 => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,10,9,2] => 010101011 => 101010101 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,4,5,7,8,9,10,6] => 100000001 => 000000110 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [8,2,3,4,5,6,7,10,9,1] => 100000011 => 000001101 => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,10,4,5,6,7,8,9,1] => 101000001 => 110000010 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8,10] => 000001010 => 000010100 => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10,3,2,5,4,7,6,9,8,1] => 110101011 => 111010101 => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => 11111111101 => 11111111110 => 10
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,10,9] => 001010101 => 010101010 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,11,10] => 0000000101 => 0000001010 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,1,7,8,9,6] => 00010001 => 00100010 => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,4,6,10,7,8,9,1] => 001001001 => 010010010 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,7,8,10,9,1] => 100000011 => 000001101 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,5,4,3,2,1,9,10,8] => 111111001 => 011111110 => 7
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,6,9,8,7,2] => 00000111 => 00001011 => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9] => 100110101 => 011011010 => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9] => 101001101 => 110010110 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => 101010011 => 110100101 => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3,8,10,9,7] => 100110011 => 011001101 => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,5,8,10,9,7] => 011010011 => 101100101 => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,8,7,5,10,9] => 011001101 => 100110110 => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,12,11,1] => 01010101011 => 10101010101 => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7,9] => 00101010 => 01010100 => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,10,9,8,1] => 110110111 => 111011011 => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,7,1,9,10,8] => 000001001 => 000010010 => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,5,8,9,10,7] => 001010001 => 010100010 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,8,10,9,5] => 000000011 => 000000101 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,5,7,8,10,9,6] => 000000011 => 000000101 => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,10,5] => 101000001 => 110000010 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,5,8,9,10,7] => 101010001 => 110100010 => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7,9] => 00101010 => 01010100 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,9,8,10] => 000101010 => 001010100 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,9,8] => 00010101 => 00101010 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,9,8] => 00010101 => 00101010 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,9,8,10] => 000101010 => 001010100 => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,4,6,5,8,7,9] => 01001010 => 10010100 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [10,9,6,5,4,3,8,7,2,1] => 111110111 => 111111011 => 6
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7,10,9] => 110110101 => 111011010 => 3
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,10,9,8,7,6,5,3] => 000111111 => 001011111 => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7,10,9] => 000010101 => 000101010 => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,10,9] => 001010101 => 010101010 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,12,10] => 01010101001 => 10101010010 => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,1 1,8,4,1 1,21,15,4,1 1,57,53,16,4,1 1,157,186,64,16,4,1
$F_{2} = 1 + q$
$F_{3} = 1 + 3\ q + q^{2}$
$F_{4} = 1 + 8\ q + 4\ q^{2} + q^{3}$
$F_{5} = 1 + 21\ q + 15\ q^{2} + 4\ q^{3} + q^{4}$
$F_{6} = 1 + 57\ q + 53\ q^{2} + 16\ q^{3} + 4\ q^{4} + q^{5}$
$F_{7} = 1 + 157\ q + 186\ q^{2} + 64\ q^{3} + 16\ q^{4} + 4\ q^{5} + q^{6}$
Description
The length of the longest run of ones in a binary word.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
rowmotion
Description
Return the rowmotion of the binary word, regarded as an order ideal in the product of two chains.
In particular, this operation preserves the number of ones, and its order is the length of the word, see section 3.3 of [1].
In particular, this operation preserves the number of ones, and its order is the length of the word, see section 3.3 of [1].
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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