Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00234: Binary words —valleys-to-peaks⟶ Binary words
St000288: Binary words ⟶ ℤ
Values
[1,0,1,0] => [2,1] => 1 => 1 => 1
[1,1,0,0] => [1,2] => 0 => 1 => 1
[1,0,1,0,1,0] => [3,2,1] => 11 => 11 => 2
[1,0,1,1,0,0] => [2,3,1] => 01 => 10 => 1
[1,1,0,0,1,0] => [3,1,2] => 01 => 10 => 1
[1,1,0,1,0,0] => [2,1,3] => 10 => 11 => 2
[1,1,1,0,0,0] => [1,2,3] => 00 => 01 => 1
[1,0,1,0,1,0,1,0] => [4,3,2,1] => 111 => 111 => 3
[1,0,1,0,1,1,0,0] => [3,4,2,1] => 101 => 110 => 2
[1,0,1,1,0,0,1,0] => [4,2,3,1] => 011 => 101 => 2
[1,0,1,1,0,1,0,0] => [3,2,4,1] => 011 => 101 => 2
[1,0,1,1,1,0,0,0] => [2,3,4,1] => 001 => 010 => 1
[1,1,0,0,1,0,1,0] => [4,3,1,2] => 011 => 101 => 2
[1,1,0,0,1,1,0,0] => [3,4,1,2] => 001 => 010 => 1
[1,1,0,1,0,0,1,0] => [4,2,1,3] => 101 => 110 => 2
[1,1,0,1,0,1,0,0] => [3,2,1,4] => 110 => 111 => 3
[1,1,0,1,1,0,0,0] => [2,3,1,4] => 010 => 101 => 2
[1,1,1,0,0,0,1,0] => [4,1,2,3] => 001 => 010 => 1
[1,1,1,0,0,1,0,0] => [3,1,2,4] => 010 => 101 => 2
[1,1,1,0,1,0,0,0] => [2,1,3,4] => 100 => 101 => 2
[1,1,1,1,0,0,0,0] => [1,2,3,4] => 000 => 001 => 1
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 1111 => 1111 => 4
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 1101 => 1110 => 3
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 1011 => 1101 => 3
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 1011 => 1101 => 3
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 1001 => 1010 => 2
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 0111 => 1011 => 3
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 0101 => 1010 => 2
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => 0111 => 1011 => 3
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 0111 => 1011 => 3
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 0011 => 0101 => 2
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 0011 => 0101 => 2
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 0011 => 0101 => 2
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 0101 => 1010 => 2
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 0001 => 0010 => 1
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 0111 => 1011 => 3
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 0101 => 1010 => 2
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 0011 => 0101 => 2
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 0011 => 0101 => 2
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 0001 => 0010 => 1
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 1011 => 1101 => 3
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 1001 => 1010 => 2
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 1101 => 1110 => 3
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => 1110 => 1111 => 4
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => 1010 => 1101 => 3
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 0101 => 1010 => 2
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => 0110 => 1011 => 3
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => 0110 => 1011 => 3
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => 0010 => 0101 => 2
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 0011 => 0101 => 2
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 0001 => 0010 => 1
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 0101 => 1010 => 2
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => 0110 => 1011 => 3
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => 0010 => 0101 => 2
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 1001 => 1010 => 2
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => 1010 => 1101 => 3
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => 1100 => 1101 => 3
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => 0100 => 1001 => 2
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 0001 => 0010 => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => 0010 => 0101 => 2
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => 0100 => 1001 => 2
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => 1000 => 1001 => 2
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 0000 => 0001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 11111 => 11111 => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => 11101 => 11110 => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => 11011 => 11101 => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => 11011 => 11101 => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => 11001 => 11010 => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => 10111 => 11011 => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => 10101 => 11010 => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => 10111 => 11011 => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => 10111 => 11011 => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => 10011 => 10101 => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => 10011 => 10101 => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => 10011 => 10101 => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => 10101 => 11010 => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 10001 => 10010 => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => 01111 => 10111 => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => 01101 => 10110 => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => 01011 => 10101 => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => 01011 => 10101 => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => 01001 => 10010 => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => 01111 => 10111 => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => 01101 => 10110 => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => 01111 => 10111 => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => 01111 => 10111 => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => 01011 => 10101 => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => 00111 => 01011 => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => 00111 => 01011 => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => 00111 => 01011 => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 00011 => 00101 => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => 00111 => 01011 => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => 00101 => 01010 => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => 00111 => 01011 => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => 00111 => 01011 => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => 00011 => 00101 => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => 01011 => 10101 => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 01011 => 10101 => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => 01101 => 10110 => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 00101 => 01010 => 2
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => 00011 => 00101 => 2
>>> Load all 2149 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => 00011 => 00101 => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => 00101 => 01010 => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 01001 => 10010 => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 00001 => 00010 => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => 01111 => 10111 => 4
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => 01101 => 10110 => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => 01011 => 10101 => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => 01011 => 10101 => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => 01001 => 10010 => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => 00111 => 01011 => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => 00101 => 01010 => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => 00111 => 01011 => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => 00111 => 01011 => 3
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => 00011 => 00101 => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => 00011 => 00101 => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => 00011 => 00101 => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => 00101 => 01010 => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 00001 => 00010 => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => 10111 => 11011 => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => 10101 => 11010 => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => 10011 => 10101 => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => 10011 => 10101 => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => 10001 => 10010 => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => 11011 => 11101 => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => 11001 => 11010 => 3
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => 11101 => 11110 => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => 11110 => 11111 => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => 11010 => 11101 => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => 10101 => 11010 => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => 10110 => 11011 => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => 10110 => 11011 => 4
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => 10010 => 10101 => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => 01011 => 10101 => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => 01001 => 10010 => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => 01101 => 10110 => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => 01110 => 10111 => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => 01010 => 10101 => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => 01101 => 10110 => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => 01110 => 10111 => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => 01110 => 10111 => 4
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => 00110 => 01011 => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => 00101 => 01010 => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => 00110 => 01011 => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => 00110 => 01011 => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => 01010 => 10101 => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => 00010 => 00101 => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => 00111 => 01011 => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => 00101 => 01010 => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => 00011 => 00101 => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => 00011 => 00101 => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => 00001 => 00010 => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => 01011 => 10101 => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => 01001 => 10010 => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => 01101 => 10110 => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => 01110 => 10111 => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => 01010 => 10101 => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => 00101 => 01010 => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => 00110 => 01011 => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => 00110 => 01011 => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => 00010 => 00101 => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => 10011 => 10101 => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => 10001 => 10010 => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => 10101 => 11010 => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => 10110 => 11011 => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => 10010 => 10101 => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => 11001 => 11010 => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => 11010 => 11101 => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => 11100 => 11101 => 4
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => 10100 => 11001 => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => 01001 => 10010 => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => 01010 => 10101 => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => 01100 => 10101 => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => 01100 => 10101 => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => 00100 => 01001 => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => 00011 => 00101 => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 00001 => 00010 => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => 00101 => 01010 => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => 00110 => 01011 => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => 00010 => 00101 => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => 01001 => 10010 => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => 01010 => 10101 => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => 01100 => 10101 => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => 00100 => 01001 => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => 10001 => 10010 => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => 10010 => 10101 => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => 10100 => 11001 => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => 11000 => 11001 => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => 01000 => 10001 => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 00001 => 00010 => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => 00010 => 00101 => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => 00100 => 01001 => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => 01000 => 10001 => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => 10000 => 10001 => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => 00000 => 00001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => 111111 => 111111 => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => 111101 => 111110 => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => 111011 => 111101 => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => 111011 => 111101 => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => 111001 => 111010 => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => 110111 => 111011 => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => 110101 => 111010 => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => 110111 => 111011 => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => 110111 => 111011 => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => 110011 => 110101 => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => 110011 => 110101 => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => 110011 => 110101 => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => 110101 => 111010 => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => 110001 => 110010 => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => 101111 => 110111 => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => 101101 => 110110 => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => 101011 => 110101 => 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => 101011 => 110101 => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => 101001 => 110010 => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => 101111 => 110111 => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => 101101 => 110110 => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => 101111 => 110111 => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => 101111 => 110111 => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => 101011 => 110101 => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => 100111 => 101011 => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => 100111 => 101011 => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => 100111 => 101011 => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => 100011 => 100101 => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => 100111 => 101011 => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => 100101 => 101010 => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => 100111 => 101011 => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => 100111 => 101011 => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => 100011 => 100101 => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => 101011 => 110101 => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => 101011 => 110101 => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => 101101 => 110110 => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => 100101 => 101010 => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => 100011 => 100101 => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => 100011 => 100101 => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => 100101 => 101010 => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => 101001 => 110010 => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => 100001 => 100010 => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => 011111 => 101111 => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => 011101 => 101110 => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => 011011 => 101101 => 4
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => 011011 => 101101 => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => 011001 => 101010 => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => 010111 => 101011 => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => 010101 => 101010 => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => 010111 => 101011 => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => 010111 => 101011 => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => 010011 => 100101 => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => 010011 => 100101 => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => 010011 => 100101 => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => 010101 => 101010 => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => 010001 => 100010 => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => 011111 => 101111 => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => 011101 => 101110 => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => 011011 => 101101 => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => 011011 => 101101 => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => 011001 => 101010 => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => 011111 => 101111 => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => 011101 => 101110 => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => 011111 => 101111 => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => 011111 => 101111 => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => 011011 => 101101 => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => 010111 => 101011 => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => 010111 => 101011 => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => 010111 => 101011 => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => 010011 => 100101 => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => 001111 => 010111 => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => 001101 => 010110 => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => 001111 => 010111 => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => 001111 => 010111 => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => 001011 => 010101 => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => 001111 => 010111 => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => 001111 => 010111 => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => 001111 => 010111 => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => 000111 => 001011 => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => 000111 => 001011 => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => 000111 => 001011 => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => 000111 => 001011 => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => 001011 => 010101 => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => 000011 => 000101 => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => 001111 => 010111 => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => 001101 => 010110 => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => 001011 => 010101 => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => 001011 => 010101 => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => 001001 => 010010 => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => 001111 => 010111 => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => 001101 => 010110 => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => 001111 => 010111 => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => 001111 => 010111 => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => 001011 => 010101 => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => 000111 => 001011 => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => 000111 => 001011 => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => 000111 => 001011 => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => 000011 => 000101 => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => 010111 => 101011 => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => 010101 => 101010 => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => 010111 => 101011 => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => 010111 => 101011 => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => 010011 => 100101 => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => 011011 => 101101 => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => 011011 => 101101 => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => 011101 => 101110 => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => 010101 => 101010 => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => 001011 => 010101 => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => 001011 => 010101 => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => 001101 => 010110 => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => 001101 => 010110 => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => 000101 => 001010 => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => 000111 => 001011 => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => 000101 => 001010 => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => 000111 => 001011 => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => 000111 => 001011 => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => 000011 => 000101 => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => 001011 => 010101 => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => 001011 => 010101 => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => 001101 => 010110 => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => 000101 => 001010 => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => 010011 => 100101 => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => 010011 => 100101 => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => 010101 => 101010 => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => 011001 => 101010 => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => 001001 => 010010 => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => 000011 => 000101 => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => 000011 => 000101 => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => 000101 => 001010 => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => 001001 => 010010 => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => 010001 => 100010 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 000001 => 000010 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => 011111 => 101111 => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => 011101 => 101110 => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => 011011 => 101101 => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => 011011 => 101101 => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => 011001 => 101010 => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => 010111 => 101011 => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => 010101 => 101010 => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => 010111 => 101011 => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => 010111 => 101011 => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => 010011 => 100101 => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => 010011 => 100101 => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => 010011 => 100101 => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => 010101 => 101010 => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => 010001 => 100010 => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => 001111 => 010111 => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => 001101 => 010110 => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => 001011 => 010101 => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => 001011 => 010101 => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => 001001 => 010010 => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => 001111 => 010111 => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => 001101 => 010110 => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => 001111 => 010111 => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => 001111 => 010111 => 4
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => 001011 => 010101 => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => 000111 => 001011 => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => 000111 => 001011 => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => 000111 => 001011 => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => 000011 => 000101 => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => 000111 => 001011 => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => 000101 => 001010 => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => 000111 => 001011 => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => 000111 => 001011 => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => 000011 => 000101 => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => 001011 => 010101 => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => 001011 => 010101 => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => 001101 => 010110 => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => 000101 => 001010 => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => 000011 => 000101 => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => 000011 => 000101 => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => 000101 => 001010 => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => 001001 => 010010 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => 000001 => 000010 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => 101111 => 110111 => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => 101101 => 110110 => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => 101011 => 110101 => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => 101011 => 110101 => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => 101001 => 110010 => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => 100111 => 101011 => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => 100101 => 101010 => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => 100111 => 101011 => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => 100111 => 101011 => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => 100011 => 100101 => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => 100011 => 100101 => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => 100011 => 100101 => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => 100101 => 101010 => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => 100001 => 100010 => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => 110111 => 111011 => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => 110101 => 111010 => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => 110011 => 110101 => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => 110011 => 110101 => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => 110001 => 110010 => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => 111011 => 111101 => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => 111001 => 111010 => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => 111101 => 111110 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => 111110 => 111111 => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => 111010 => 111101 => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => 110101 => 111010 => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => 110110 => 111011 => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => 110110 => 111011 => 5
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => 110010 => 110101 => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => 101011 => 110101 => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => 101001 => 110010 => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => 101101 => 110110 => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => 101110 => 110111 => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => 101010 => 110101 => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => 101101 => 110110 => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => 101110 => 110111 => 5
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => 101110 => 110111 => 5
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => 100110 => 101011 => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => 100101 => 101010 => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => 100110 => 101011 => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => 100110 => 101011 => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => 101010 => 110101 => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => 100010 => 100101 => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => 010111 => 101011 => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => 010101 => 101010 => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => 010011 => 100101 => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => 010011 => 100101 => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => 010001 => 100010 => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => 011011 => 101101 => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => 011001 => 101010 => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => 011101 => 101110 => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => 011110 => 101111 => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => 011010 => 101101 => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => 010101 => 101010 => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => 010110 => 101011 => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => 010110 => 101011 => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => 010010 => 100101 => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => 011011 => 101101 => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => 011001 => 101010 => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => 011101 => 101110 => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => 011110 => 101111 => 5
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => 011010 => 101101 => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => 011101 => 101110 => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => 011110 => 101111 => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => 011110 => 101111 => 5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => 010110 => 101011 => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => 001101 => 010110 => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => 001110 => 010111 => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => 001110 => 010111 => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => 001110 => 010111 => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => 000110 => 001011 => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => 001011 => 010101 => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => 001001 => 010010 => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => 001101 => 010110 => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => 001110 => 010111 => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => 001010 => 010101 => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => 001101 => 010110 => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => 001110 => 010111 => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => 001110 => 010111 => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => 000110 => 001011 => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => 010101 => 101010 => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => 010110 => 101011 => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => 010110 => 101011 => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => 011010 => 101101 => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => 001010 => 010101 => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => 000101 => 001010 => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => 000110 => 001011 => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => 000110 => 001011 => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => 001010 => 010101 => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => 010010 => 100101 => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => 000010 => 000101 => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => 001111 => 010111 => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => 001101 => 010110 => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => 001011 => 010101 => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => 001011 => 010101 => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => 001001 => 010010 => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => 000111 => 001011 => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => 000101 => 001010 => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => 000111 => 001011 => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => 000111 => 001011 => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => 000011 => 000101 => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => 000011 => 000101 => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => 000011 => 000101 => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => 000101 => 001010 => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => 000001 => 000010 => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => 010111 => 101011 => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => 010101 => 101010 => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => 010011 => 100101 => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => 010011 => 100101 => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => 010001 => 100010 => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => 011011 => 101101 => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => 011001 => 101010 => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => 011101 => 101110 => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => 011110 => 101111 => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => 011010 => 101101 => 4
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => 010101 => 101010 => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => 010110 => 101011 => 4
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => 010110 => 101011 => 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => 010010 => 100101 => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => 001011 => 010101 => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => 001001 => 010010 => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => 001101 => 010110 => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => 001110 => 010111 => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => 001010 => 010101 => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => 001101 => 010110 => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => 001110 => 010111 => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => 001110 => 010111 => 4
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => 000110 => 001011 => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => 000101 => 001010 => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => 000110 => 001011 => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => 000110 => 001011 => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => 001010 => 010101 => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => 000010 => 000101 => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => 100111 => 101011 => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => 100101 => 101010 => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => 100011 => 100101 => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => 100011 => 100101 => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => 100001 => 100010 => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => 101011 => 110101 => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => 101001 => 110010 => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => 101101 => 110110 => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => 101110 => 110111 => 5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => 101010 => 110101 => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => 100101 => 101010 => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => 100110 => 101011 => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => 100110 => 101011 => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => 100010 => 100101 => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => 110011 => 110101 => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => 110001 => 110010 => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => 110101 => 111010 => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => 110110 => 111011 => 5
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => 110010 => 110101 => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => 111001 => 111010 => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => 111010 => 111101 => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => 111100 => 111101 => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => 110100 => 111001 => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => 101001 => 110010 => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => 101010 => 110101 => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => 101100 => 110101 => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => 101100 => 110101 => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => 100100 => 101001 => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => 010011 => 100101 => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => 010001 => 100010 => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => 010101 => 101010 => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => 010110 => 101011 => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => 010010 => 100101 => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => 011001 => 101010 => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => 011010 => 101101 => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => 011100 => 101101 => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => 010100 => 101001 => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => 011001 => 101010 => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => 011010 => 101101 => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => 011100 => 101101 => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => 011100 => 101101 => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => 001100 => 010101 => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => 001001 => 010010 => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => 001010 => 010101 => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => 001100 => 010101 => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => 001100 => 010101 => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => 010100 => 101001 => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => 000100 => 001001 => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => 000111 => 001011 => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => 000101 => 001010 => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => 000011 => 000101 => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => 000011 => 000101 => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => 000001 => 000010 => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => 001011 => 010101 => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => 001001 => 010010 => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => 001101 => 010110 => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => 001110 => 010111 => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => 001010 => 010101 => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => 000101 => 001010 => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => 000110 => 001011 => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => 000110 => 001011 => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => 000010 => 000101 => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => 010011 => 100101 => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => 010001 => 100010 => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => 010101 => 101010 => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => 010110 => 101011 => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => 010010 => 100101 => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => 011001 => 101010 => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => 011010 => 101101 => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => 011100 => 101101 => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => 010100 => 101001 => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => 001001 => 010010 => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => 001010 => 010101 => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => 001100 => 010101 => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => 001100 => 010101 => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => 000100 => 001001 => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => 100011 => 100101 => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => 100001 => 100010 => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => 100101 => 101010 => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => 100110 => 101011 => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => 100010 => 100101 => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => 101001 => 110010 => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => 101010 => 110101 => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => 101100 => 110101 => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => 100100 => 101001 => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => 110001 => 110010 => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => 110010 => 110101 => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => 110100 => 111001 => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => 111000 => 111001 => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => 101000 => 110001 => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => 010001 => 100010 => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => 010010 => 100101 => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => 010100 => 101001 => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => 011000 => 101001 => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => 011000 => 101001 => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => 001000 => 010001 => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => 000011 => 000101 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => 000001 => 000010 => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => 000101 => 001010 => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => 000110 => 001011 => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => 000010 => 000101 => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => 001001 => 010010 => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => 001010 => 010101 => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => 001100 => 010101 => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => 000100 => 001001 => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => 010001 => 100010 => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => 010010 => 100101 => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => 010100 => 101001 => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => 011000 => 101001 => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => 001000 => 010001 => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => 100001 => 100010 => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => 100010 => 100101 => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => 100100 => 101001 => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => 101000 => 110001 => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => 110000 => 110001 => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => 010000 => 100001 => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => 000001 => 000010 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => 000010 => 000101 => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => 000100 => 001001 => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => 001000 => 010001 => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => 010000 => 100001 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => 100000 => 100001 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => 000000 => 000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => 1111111 => 1111111 => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => 1111101 => 1111110 => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => 1111011 => 1111101 => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => 1111011 => 1111101 => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => 1111001 => 1111010 => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => 1110111 => 1111011 => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => 1110101 => 1111010 => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => 1110111 => 1111011 => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => 1110111 => 1111011 => 6
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => 1110011 => 1110101 => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => 1110011 => 1110101 => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => 1110011 => 1110101 => 5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => 1110101 => 1111010 => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => 1110001 => 1110010 => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => 1101111 => 1110111 => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => 1101101 => 1110110 => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => 1101011 => 1110101 => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,2,1] => 1101011 => 1110101 => 5
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,2,1] => 1101001 => 1110010 => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,2,1] => 1101111 => 1110111 => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,3,2,1] => 1101111 => 1110111 => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => 1101111 => 1110111 => 6
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => 1101011 => 1110101 => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,2,1] => 1100111 => 1101011 => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => 1100111 => 1101011 => 5
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => 1100111 => 1101011 => 5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => 1100011 => 1100101 => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => 1100111 => 1101011 => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,2,1] => 1100111 => 1101011 => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => 1100111 => 1101011 => 5
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => 1100011 => 1100101 => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,2,1] => 1101011 => 1110101 => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => 1101011 => 1110101 => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => 1101101 => 1110110 => 5
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => 1100101 => 1101010 => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => 1100011 => 1100101 => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => 1100011 => 1100101 => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => 1100101 => 1101010 => 4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => 1101001 => 1110010 => 4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => 1100001 => 1100010 => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => 1011111 => 1101111 => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => 1011101 => 1101110 => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => 1011011 => 1101101 => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => 1011011 => 1101101 => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => 1010111 => 1101011 => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => 1010101 => 1101010 => 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => 1010111 => 1101011 => 5
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => 1010011 => 1100101 => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => 1010011 => 1100101 => 4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => 1010101 => 1101010 => 4
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => 1010001 => 1100010 => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => 1011111 => 1101111 => 6
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,2,1] => 1011101 => 1101110 => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,2,1] => 1011011 => 1101101 => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => 1011011 => 1101101 => 5
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => 1011001 => 1101010 => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => 1011111 => 1101111 => 6
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => 1011101 => 1101110 => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => 1011111 => 1101111 => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => 1011111 => 1101111 => 6
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => 1011011 => 1101101 => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,2,1] => 1010111 => 1101011 => 5
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => 1010111 => 1101011 => 5
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => 1010011 => 1100101 => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,2,1] => 1001111 => 1010111 => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,7,2,1] => 1001111 => 1010111 => 5
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,2,1] => 1001011 => 1010101 => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,2,1] => 1001111 => 1010111 => 5
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => 1001111 => 1010111 => 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,2,1] => 1000111 => 1001011 => 4
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => 1000111 => 1001011 => 4
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => 1001011 => 1010101 => 4
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => 1000011 => 1000101 => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => 1001111 => 1010111 => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => 1001101 => 1010110 => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => 1001011 => 1010101 => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => 1001011 => 1010101 => 4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => 1001001 => 1010010 => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,6,2,1] => 1001111 => 1010111 => 5
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => 1001101 => 1010110 => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => 1001111 => 1010111 => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => 1010111 => 1101011 => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => 1010111 => 1101011 => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => 1010111 => 1101011 => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => 1011011 => 1101101 => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => 1011011 => 1101101 => 5
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => 1011101 => 1101110 => 5
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,2,1] => 1000101 => 1001010 => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => 1000111 => 1001011 => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => 1000101 => 1001010 => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => 1000111 => 1001011 => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => 1001011 => 1010101 => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => 1001011 => 1010101 => 4
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,2,1] => 1001101 => 1010110 => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => 1010011 => 1100101 => 4
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => 1011001 => 1101010 => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => 1000011 => 1000101 => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => 1000011 => 1000101 => 3
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => 1000101 => 1001010 => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => 1001001 => 1010010 => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => 1010001 => 1100010 => 3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => 1000001 => 1000010 => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => 0111111 => 1011111 => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => 0111101 => 1011110 => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => 0111011 => 1011101 => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => 0111011 => 1011101 => 5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => 0110111 => 1011011 => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => 0110111 => 1011011 => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => 0110111 => 1011011 => 5
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => 0110011 => 1010101 => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => 0110011 => 1010101 => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,3,1] => 0110011 => 1010101 => 4
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => 0110001 => 1010010 => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => 0101111 => 1010111 => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => 0101011 => 1010101 => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => 0101011 => 1010101 => 4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => 0101001 => 1010010 => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,3,1] => 0101111 => 1010111 => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,3,1] => 0101111 => 1010111 => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,3,1] => 0101111 => 1010111 => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => 0100111 => 1001011 => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => 0100111 => 1001011 => 4
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => 0100111 => 1001011 => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => 0100111 => 1001011 => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => 0100101 => 1001010 => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => 0100111 => 1001011 => 4
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => 0100011 => 1000101 => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => 0100011 => 1000101 => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => 0100001 => 1000010 => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => 0111111 => 1011111 => 6
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => 0111101 => 1011110 => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,4,1] => 0111011 => 1011101 => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => 0111011 => 1011101 => 5
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => 0111001 => 1011010 => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => 0110111 => 1011011 => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => 0110111 => 1011011 => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => 0110111 => 1011011 => 5
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => 0110011 => 1010101 => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => 0110011 => 1010101 => 4
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => 0110001 => 1010010 => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,5,1] => 0111111 => 1011111 => 6
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,5,1] => 0111101 => 1011110 => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,5,1] => 0111011 => 1011101 => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => 0111011 => 1011101 => 5
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,5,1] => 0111001 => 1011010 => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => 0111111 => 1011111 => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => 0111101 => 1011110 => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => 0111111 => 1011111 => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => 0111111 => 1011111 => 6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => 0111011 => 1011101 => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,7,1] => 0110111 => 1011011 => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,8,1] => 0110111 => 1011011 => 5
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => 0110111 => 1011011 => 5
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,8,1] => 0110011 => 1010101 => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,7,1] => 0101111 => 1010111 => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => 0101111 => 1010111 => 5
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,8,1] => 0101011 => 1010101 => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => 0101111 => 1010111 => 5
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,8,1] => 0101111 => 1010111 => 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => 0100111 => 1001011 => 4
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => 0100111 => 1001011 => 4
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => 0100011 => 1000101 => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => 0011111 => 0101111 => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => 0011101 => 0101110 => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => 0011011 => 0101101 => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => 0011011 => 0101101 => 4
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => 0011001 => 0101010 => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => 0011111 => 0101111 => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => 0011101 => 0101110 => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,7,1] => 0011111 => 0101111 => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => 0011111 => 0101111 => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => 0010111 => 0101011 => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => 0010111 => 0101011 => 4
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => 0010111 => 0101011 => 4
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,8,1] => 0010011 => 0100101 => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => 0011111 => 0101111 => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,6,1] => 0011101 => 0101110 => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => 0011111 => 0101111 => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => 0011111 => 0101111 => 5
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,7,1] => 0011111 => 0101111 => 5
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => 0011111 => 0101111 => 5
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => 0011111 => 0101111 => 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => 0001111 => 0010111 => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => 0001111 => 0010111 => 4
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => 0001111 => 0010111 => 4
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => 0001111 => 0010111 => 4
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => 0000111 => 0001011 => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => 0001111 => 0010111 => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,8,1] => 0001111 => 0010111 => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => 0001111 => 0010111 => 4
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => 0001111 => 0010111 => 4
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,8,1] => 0000111 => 0001011 => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,7,1] => 0010111 => 0101011 => 4
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => 0010111 => 0101011 => 4
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,8,1] => 0011011 => 0101101 => 4
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => 0001011 => 0010101 => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,7,1] => 0000111 => 0001011 => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => 0000111 => 0001011 => 3
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => 0000111 => 0001011 => 3
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,2,8,1] => 0010011 => 0100101 => 3
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => 0000011 => 0000101 => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => 0011111 => 0101111 => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => 0011011 => 0101101 => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,4,1] => 0011011 => 0101101 => 4
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => 0011001 => 0101010 => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => 0010111 => 0101011 => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,4,1] => 0010101 => 0101010 => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,4,1] => 0010111 => 0101011 => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => 0010111 => 0101011 => 4
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => 0010011 => 0100101 => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => 0010011 => 0100101 => 3
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,4,1] => 0010101 => 0101010 => 3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => 0010001 => 0100010 => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,5,1] => 0011111 => 0101111 => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,5,1] => 0011011 => 0101101 => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,5,1] => 0011011 => 0101101 => 4
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => 0011001 => 0101010 => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,3,6,1] => 0011111 => 0101111 => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => 0011111 => 0101111 => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => 0011111 => 0101111 => 5
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,8,1] => 0011011 => 0101101 => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,7,1] => 0010111 => 0101011 => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => 0010111 => 0101011 => 4
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => 0010111 => 0101011 => 4
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,8,1] => 0010011 => 0100101 => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,7,1] => 0001111 => 0010111 => 4
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,8,1] => 0001111 => 0010111 => 4
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => 0001011 => 0010101 => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,8,1] => 0001111 => 0010111 => 4
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => 0001111 => 0010111 => 4
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => 0000111 => 0001011 => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,8,1] => 0000111 => 0001011 => 3
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,8,1] => 0000111 => 0001011 => 3
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => 0001011 => 0010101 => 3
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => 0000011 => 0000101 => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => 0101111 => 1010111 => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => 0101101 => 1010110 => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => 0101011 => 1010101 => 4
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => 0101001 => 1010010 => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => 0101111 => 1010111 => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => 0101111 => 1010111 => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => 0101111 => 1010111 => 5
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => 0101011 => 1010101 => 4
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,8,1] => 0100111 => 1001011 => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => 0110111 => 1011011 => 5
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => 0110101 => 1011010 => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,7,1] => 0110111 => 1011011 => 5
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => 0110011 => 1010101 => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => 0111011 => 1011101 => 5
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => 0111011 => 1011101 => 5
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => 0111101 => 1011110 => 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,7,1] => 0101011 => 1010101 => 4
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => 0101101 => 1010110 => 4
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => 0100101 => 1001010 => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,6,1] => 0010101 => 0101010 => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => 0011011 => 0101101 => 4
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,8,1] => 0011101 => 0101110 => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => 0011011 => 0101101 => 4
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => 0011101 => 0101110 => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => 0001011 => 0010101 => 3
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => 0001101 => 0010110 => 3
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => 0010101 => 0101010 => 3
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => 0000101 => 0001010 => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => 0001111 => 0010111 => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => 0001101 => 0010110 => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => 0001011 => 0010101 => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,5,1] => 0001011 => 0010101 => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => 0001001 => 0010010 => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => 0001111 => 0010111 => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => 0000111 => 0001011 => 3
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,8,1] => 0000011 => 0000101 => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,6,1] => 0010101 => 0101010 => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => 0010111 => 0101011 => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => 0010111 => 0101011 => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,7,1] => 0011011 => 0101101 => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => 0011011 => 0101101 => 4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => 0011101 => 0101110 => 4
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,7,8,1] => 0010101 => 0101010 => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,7,1] => 0001011 => 0010101 => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,8,1] => 0001011 => 0010101 => 3
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => 0001101 => 0010110 => 3
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,8,1] => 0001101 => 0010110 => 3
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,8,1] => 0000101 => 0001010 => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => 0100101 => 1001010 => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => 0100111 => 1001011 => 4
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => 0100011 => 1000101 => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => 0101011 => 1010101 => 4
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,8,1] => 0101101 => 1010110 => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,7,1] => 0110011 => 1010101 => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => 0110011 => 1010101 => 4
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => 0111001 => 1011010 => 4
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,8,1] => 0101001 => 1010010 => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => 0010011 => 0100101 => 3
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => 0011001 => 0101010 => 3
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => 0011001 => 0101010 => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => 0001001 => 0010010 => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => 0000111 => 0001011 => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => 0000101 => 0001010 => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => 0000111 => 0001011 => 3
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => 0000011 => 0000101 => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,7,1] => 0001011 => 0010101 => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,8,1] => 0001011 => 0010101 => 3
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => 0001101 => 0010110 => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,7,1] => 0010011 => 0100101 => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,8,1] => 0010011 => 0100101 => 3
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => 0011001 => 0101010 => 3
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => 0001001 => 0010010 => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => 0100011 => 1000101 => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => 0100011 => 1000101 => 3
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => 0101001 => 1010010 => 3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => 0110001 => 1010010 => 3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => 0010001 => 0100010 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => 0000011 => 0000101 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => 0000011 => 0000101 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,8,1] => 0000101 => 0001010 => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => 0001001 => 0010010 => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => 0010001 => 0100010 => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => 0100001 => 1000010 => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0000001 => 0000010 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => 0111111 => 1011111 => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => 0111101 => 1011110 => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => 0111011 => 1011101 => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => 0111011 => 1011101 => 5
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => 0111001 => 1011010 => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => 0110111 => 1011011 => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => 0110101 => 1011010 => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => 0110111 => 1011011 => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => 0110111 => 1011011 => 5
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => 0110011 => 1010101 => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,1,2] => 0110011 => 1010101 => 4
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => 0110101 => 1011010 => 4
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => 0110001 => 1010010 => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => 0101111 => 1010111 => 5
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => 0101101 => 1010110 => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => 0101011 => 1010101 => 4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => 0101001 => 1010010 => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => 0101111 => 1010111 => 5
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => 0101111 => 1010111 => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,1,2] => 0100111 => 1001011 => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => 0100111 => 1001011 => 4
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => 0100111 => 1001011 => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => 0100101 => 1001010 => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => 0100111 => 1001011 => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => 0100111 => 1001011 => 4
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => 0100011 => 1000101 => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => 0101011 => 1010101 => 4
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => 0101101 => 1010110 => 4
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => 0100101 => 1001010 => 3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => 0101001 => 1010010 => 3
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => 0100001 => 1000010 => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => 0011111 => 0101111 => 5
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => 0011101 => 0101110 => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => 0011011 => 0101101 => 4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => 0011001 => 0101010 => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => 0010111 => 0101011 => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => 0010101 => 0101010 => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => 0010111 => 0101011 => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => 0010111 => 0101011 => 4
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => 0010011 => 0100101 => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => 0010011 => 0100101 => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => 0010011 => 0100101 => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => 0010101 => 0101010 => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => 0010001 => 0100010 => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,1,2] => 0011001 => 0101010 => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => 0011101 => 0101110 => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => 0011111 => 0101111 => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => 0011111 => 0101111 => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,1,2] => 0010111 => 0101011 => 4
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,1,2] => 0010111 => 0101011 => 4
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => 0010011 => 0100101 => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => 0001111 => 0010111 => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => 0001101 => 0010110 => 3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => 0001011 => 0010101 => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => 0001111 => 0010111 => 4
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,1,2] => 0001111 => 0010111 => 4
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,1,2] => 0001111 => 0010111 => 4
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => 0000111 => 0001011 => 3
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,1,2] => 0001011 => 0010101 => 3
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => 0000011 => 0000101 => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => 0001111 => 0010111 => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,1,2] => 0001101 => 0010110 => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => 0001011 => 0010101 => 3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,1,2] => 0001001 => 0010010 => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => 0001101 => 0010110 => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,1,2] => 0001111 => 0010111 => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,8,1,2] => 0000111 => 0001011 => 3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,8,1,2] => 0000011 => 0000101 => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,1,2] => 0010111 => 0101011 => 4
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => 0010101 => 0101010 => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,1,2] => 0010111 => 0101011 => 4
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => 0011011 => 0101101 => 4
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,1,2] => 0011011 => 0101101 => 4
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => 0011101 => 0101110 => 4
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => 0010101 => 0101010 => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,8,1,2] => 0001011 => 0010101 => 3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => 0001101 => 0010110 => 3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => 0000101 => 0001010 => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => 0000111 => 0001011 => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => 0000101 => 0001010 => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => 0000111 => 0001011 => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,1,2] => 0001011 => 0010101 => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => 0001011 => 0010101 => 3
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,1,2] => 0001101 => 0010110 => 3
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => 0000101 => 0001010 => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => 0010011 => 0100101 => 3
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => 0010101 => 0101010 => 3
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => 0011001 => 0101010 => 3
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => 0001001 => 0010010 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => 0000011 => 0000101 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => 0000011 => 0000101 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => 0000101 => 0001010 => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => 0001001 => 0010010 => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => 0010001 => 0100010 => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => 0000001 => 0000010 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => 1011111 => 1101111 => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => 1011101 => 1101110 => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => 1011011 => 1101101 => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => 1011011 => 1101101 => 5
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,1,3] => 1011001 => 1101010 => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => 1010111 => 1101011 => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => 1010101 => 1101010 => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,1,3] => 1010111 => 1101011 => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => 1010111 => 1101011 => 5
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => 1010011 => 1100101 => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => 1010011 => 1100101 => 4
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,1,3] => 1010101 => 1101010 => 4
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => 1010001 => 1100010 => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => 1001111 => 1010111 => 5
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,1,3] => 1001011 => 1010101 => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,1,3] => 1001011 => 1010101 => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,1,3] => 1001111 => 1010111 => 5
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => 1001111 => 1010111 => 5
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,1,3] => 1001011 => 1010101 => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,1,3] => 1000111 => 1001011 => 4
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => 1000111 => 1001011 => 4
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => 1000011 => 1000101 => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,1,3] => 1000111 => 1001011 => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,1,3] => 1000111 => 1001011 => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,1,3] => 1000111 => 1001011 => 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => 1000011 => 1000101 => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,2,1,3] => 1000011 => 1000101 => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => 1001001 => 1010010 => 3
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => 1000001 => 1000010 => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => 1101111 => 1110111 => 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => 1101101 => 1110110 => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => 1101011 => 1110101 => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => 1101011 => 1110101 => 5
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => 1101001 => 1110010 => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => 1100111 => 1101011 => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => 1100101 => 1101010 => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => 1100111 => 1101011 => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => 1100111 => 1101011 => 5
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => 1100011 => 1100101 => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => 1100011 => 1100101 => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,1,4] => 1100011 => 1100101 => 4
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => 1100101 => 1101010 => 4
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => 1100001 => 1100010 => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => 1110111 => 1111011 => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => 1110101 => 1111010 => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => 1110011 => 1110101 => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => 1110011 => 1110101 => 5
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => 1110001 => 1110010 => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => 1111011 => 1111101 => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => 1111001 => 1111010 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => 1111101 => 1111110 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => 1111110 => 1111111 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => 1111010 => 1111101 => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => 1110101 => 1111010 => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => 1110110 => 1111011 => 6
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => 1110110 => 1111011 => 6
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => 1110010 => 1110101 => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => 1101011 => 1110101 => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,1,6] => 1101001 => 1110010 => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => 1101101 => 1110110 => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => 1101110 => 1110111 => 6
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => 1101010 => 1110101 => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,1,7] => 1101101 => 1110110 => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => 1101110 => 1110111 => 6
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => 1101110 => 1110111 => 6
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => 1100110 => 1101011 => 5
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => 1100101 => 1101010 => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => 1100110 => 1101011 => 5
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => 1101010 => 1110101 => 5
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => 1100010 => 1100101 => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => 1010111 => 1101011 => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,1,5] => 1010101 => 1101010 => 4
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => 1010001 => 1100010 => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,1,6] => 1011011 => 1101101 => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => 1011101 => 1101110 => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => 1011110 => 1101111 => 6
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => 1011010 => 1101101 => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => 1010101 => 1101010 => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => 1010110 => 1101011 => 5
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,1,8] => 1010110 => 1101011 => 5
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => 1010010 => 1100101 => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,1,6] => 1011011 => 1101101 => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,1,7] => 1011101 => 1101110 => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => 1011110 => 1101111 => 6
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => 1011010 => 1101101 => 5
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => 1011110 => 1101111 => 6
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => 1011110 => 1101111 => 6
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => 1010110 => 1101011 => 5
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => 1001101 => 1010110 => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,1,8] => 1001110 => 1010111 => 5
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => 1001110 => 1010111 => 5
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => 1001011 => 1010101 => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,1,6] => 1001001 => 1010010 => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => 1001110 => 1010111 => 5
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => 1010101 => 1101010 => 4
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => 1011010 => 1101101 => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => 1000101 => 1001010 => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => 1000110 => 1001011 => 4
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => 1000010 => 1000101 => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => 0101111 => 1010111 => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => 0101101 => 1010110 => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => 0101011 => 1010101 => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => 0101011 => 1010101 => 4
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => 0101001 => 1010010 => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => 0100111 => 1001011 => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => 0100101 => 1001010 => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,1,4] => 0100111 => 1001011 => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => 0100111 => 1001011 => 4
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => 0100011 => 1000101 => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,1,4] => 0100011 => 1000101 => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => 0100011 => 1000101 => 3
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,1,4] => 0100101 => 1001010 => 3
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => 0100001 => 1000010 => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => 0110111 => 1011011 => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,1,5] => 0110011 => 1010101 => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,1,5] => 0110011 => 1010101 => 4
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => 0110001 => 1010010 => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => 0111101 => 1011110 => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => 0111110 => 1011111 => 6
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => 0111010 => 1011101 => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => 0110101 => 1011010 => 4
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => 0110110 => 1011011 => 5
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => 0110010 => 1010101 => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => 0101011 => 1010101 => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => 0101001 => 1010010 => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,1,7] => 0101101 => 1010110 => 4
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => 0101110 => 1010111 => 5
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => 0101010 => 1010101 => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => 0101110 => 1010111 => 5
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => 0101110 => 1010111 => 5
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => 0100110 => 1001011 => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => 0100101 => 1001010 => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,1,8] => 0100110 => 1001011 => 4
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => 0101010 => 1010101 => 4
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => 0100010 => 1000101 => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => 0110111 => 1011011 => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => 0110011 => 1010101 => 4
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => 0110001 => 1010010 => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => 0111011 => 1011101 => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => 0111101 => 1011110 => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => 0111110 => 1011111 => 6
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => 0110110 => 1011011 => 5
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => 0110010 => 1010101 => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => 0111011 => 1011101 => 5
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => 0111001 => 1011010 => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,1,7] => 0111101 => 1011110 => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => 0111110 => 1011111 => 6
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => 0111010 => 1011101 => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => 0111101 => 1011110 => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => 0111110 => 1011111 => 6
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => 0111110 => 1011111 => 6
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => 0110110 => 1011011 => 5
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => 0101110 => 1010111 => 5
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => 0101110 => 1010111 => 5
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,1,6] => 0011011 => 0101101 => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => 0011001 => 0101010 => 3
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => 0011010 => 0101101 => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => 0011110 => 0101111 => 5
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => 0010110 => 0101011 => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => 0011101 => 0101110 => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => 0011110 => 0101111 => 5
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => 0011110 => 0101111 => 5
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => 0001110 => 0010111 => 4
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => 0001110 => 0010111 => 4
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => 0001110 => 0010111 => 4
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => 0010110 => 0101011 => 4
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => 0000110 => 0001011 => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => 0010111 => 0101011 => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => 0010011 => 0100101 => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,1,5] => 0010011 => 0100101 => 3
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => 0010001 => 0100010 => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => 0011001 => 0101010 => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => 0011101 => 0101110 => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => 0011110 => 0101111 => 5
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => 0011010 => 0101101 => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,4,1,7] => 0010101 => 0101010 => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => 0010110 => 0101011 => 4
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => 0010110 => 0101011 => 4
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => 0010010 => 0100101 => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => 0011101 => 0101110 => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => 0011110 => 0101111 => 5
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => 0011010 => 0101101 => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,1,7] => 0011101 => 0101110 => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,1,8] => 0011110 => 0101111 => 5
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => 0001101 => 0010110 => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => 0001110 => 0010111 => 4
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => 0001110 => 0010111 => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => 0101101 => 1010110 => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => 0101110 => 1010111 => 5
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => 0101010 => 1010101 => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => 0101101 => 1010110 => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => 0101110 => 1010111 => 5
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => 0101110 => 1010111 => 5
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => 0111010 => 1011101 => 5
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,1,7] => 0010101 => 0101010 => 3
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,1,8] => 0001010 => 0010101 => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => 0001011 => 0010101 => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => 0001001 => 0010010 => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => 0001110 => 0010111 => 4
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => 0001010 => 0010101 => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,1,7] => 0001101 => 0010110 => 3
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => 0011010 => 0101101 => 4
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => 0001010 => 0010101 => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => 0100101 => 1001010 => 3
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,1,8] => 0100110 => 1001011 => 4
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => 0110010 => 1010101 => 4
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => 0010010 => 0100101 => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => 0000101 => 0001010 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => 0000110 => 0001011 => 3
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => 0000110 => 0001011 => 3
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => 0001010 => 0010101 => 3
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => 0010010 => 0100101 => 3
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => 0100010 => 1000101 => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => 0000010 => 0000101 => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => 0011111 => 0101111 => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => 0011101 => 0101110 => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,1,2,3] => 0011011 => 0101101 => 4
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => 0011001 => 0101010 => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => 0010101 => 0101010 => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,1,2,3] => 0010111 => 0101011 => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,1,2,3] => 0010111 => 0101011 => 4
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => 0010011 => 0100101 => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => 0010011 => 0100101 => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => 0010011 => 0100101 => 3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => 0010101 => 0101010 => 3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => 0010001 => 0100010 => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => 0001111 => 0010111 => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => 0001011 => 0010101 => 3
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => 0001001 => 0010010 => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => 0001111 => 0010111 => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => 0001101 => 0010110 => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,1,2,3] => 0001111 => 0010111 => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => 0001111 => 0010111 => 4
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,1,2,3] => 0001011 => 0010101 => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,1,2,3] => 0000111 => 0001011 => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,1,2,3] => 0000111 => 0001011 => 3
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => 0000111 => 0001011 => 3
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,1,2,3] => 0000011 => 0000101 => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => 0000111 => 0001011 => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => 0000101 => 0001010 => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,1,2,3] => 0000111 => 0001011 => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,1,2,3] => 0000111 => 0001011 => 3
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => 0000011 => 0000101 => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,1,2,3] => 0001011 => 0010101 => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => 0001011 => 0010101 => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => 0001101 => 0010110 => 3
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,1,2,3] => 0000101 => 0001010 => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => 0000011 => 0000101 => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,1,2,3] => 0000011 => 0000101 => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,1,2,3] => 0000101 => 0001010 => 2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => 0001001 => 0010010 => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => 0000001 => 0000010 => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => 0101111 => 1010111 => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,1,2,4] => 0101101 => 1010110 => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => 0101011 => 1010101 => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => 0101011 => 1010101 => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => 0100111 => 1001011 => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => 0100101 => 1001010 => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,1,2,4] => 0100111 => 1001011 => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => 0100111 => 1001011 => 4
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => 0100011 => 1000101 => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => 0100011 => 1000101 => 3
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => 0100101 => 1001010 => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => 0100001 => 1000010 => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => 0110111 => 1011011 => 5
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => 0110001 => 1010010 => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => 0111011 => 1011101 => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,1,2,6] => 0111001 => 1011010 => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => 0111101 => 1011110 => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => 0111110 => 1011111 => 6
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => 0111010 => 1011101 => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => 0110110 => 1011011 => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => 0101101 => 1010110 => 4
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => 0101110 => 1010111 => 5
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,1,2,8] => 0100110 => 1001011 => 4
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => 0101010 => 1010101 => 4
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => 0100010 => 1000101 => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => 0010111 => 0101011 => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => 0010101 => 0101010 => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => 0010011 => 0100101 => 3
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => 0010001 => 0100010 => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => 0011011 => 0101101 => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,1,2,6] => 0011001 => 0101010 => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => 0011101 => 0101110 => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => 0011110 => 0101111 => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => 0010101 => 0101010 => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,1,2,8] => 0010110 => 0101011 => 4
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => 0010110 => 0101011 => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => 0011101 => 0101110 => 4
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => 0011110 => 0101111 => 5
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,1,2,7] => 0001101 => 0010110 => 3
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => 0001110 => 0010111 => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => 0001011 => 0010101 => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => 0001001 => 0010010 => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => 0001101 => 0010110 => 3
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => 0001010 => 0010101 => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => 0001101 => 0010110 => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,1,2,8] => 0001110 => 0010111 => 4
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => 0000110 => 0001011 => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => 0010101 => 0101010 => 3
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,1,2,8] => 0010110 => 0101011 => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => 0000101 => 0001010 => 2
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => 0000110 => 0001011 => 3
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,1,2,8] => 0010010 => 0100101 => 3
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => 0000010 => 0000101 => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => 1001111 => 1010111 => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => 1001101 => 1010110 => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,1,3,4] => 1001011 => 1010101 => 4
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => 1001001 => 1010010 => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => 1000111 => 1001011 => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => 1000101 => 1001010 => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => 1000111 => 1001011 => 4
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => 1000111 => 1001011 => 4
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => 1000011 => 1000101 => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,1,3,4] => 1000011 => 1000101 => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => 1000011 => 1000101 => 3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => 1000101 => 1001010 => 3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => 1000001 => 1000010 => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => 1010111 => 1101011 => 5
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,1,3,5] => 1010101 => 1101010 => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => 1010011 => 1100101 => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => 1010001 => 1100010 => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => 1011001 => 1101010 => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => 1011101 => 1101110 => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => 1011110 => 1101111 => 6
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => 1010101 => 1101010 => 4
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => 1010110 => 1101011 => 5
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,1,3,7] => 1001101 => 1010110 => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => 1001110 => 1010111 => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => 1001110 => 1010111 => 5
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => 1000101 => 1001010 => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,1,3,8] => 1000110 => 1001011 => 4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,1,3,8] => 1001010 => 1010101 => 4
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => 1000010 => 1000101 => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => 1100111 => 1101011 => 5
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => 1100101 => 1101010 => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => 1100011 => 1100101 => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => 1100011 => 1100101 => 4
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => 1100001 => 1100010 => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => 1101011 => 1110101 => 5
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => 1101001 => 1110010 => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => 1101101 => 1110110 => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => 1101110 => 1110111 => 6
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => 1100101 => 1101010 => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => 1110011 => 1110101 => 5
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => 1110001 => 1110010 => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => 1110101 => 1111010 => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => 1110110 => 1111011 => 6
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => 1110010 => 1110101 => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => 1111001 => 1111010 => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => 1111010 => 1111101 => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => 1111100 => 1111101 => 6
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => 1110100 => 1111001 => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => 1101001 => 1110010 => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => 1101010 => 1110101 => 5
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => 1101100 => 1110101 => 5
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => 1100100 => 1101001 => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => 1010011 => 1100101 => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => 1010001 => 1100010 => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => 1010101 => 1101010 => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => 1010110 => 1101011 => 5
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => 1010010 => 1100101 => 4
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => 1011100 => 1101101 => 5
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => 1010100 => 1101001 => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,1,6,7] => 1011001 => 1101010 => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => 1011010 => 1101101 => 5
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => 1011100 => 1101101 => 5
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => 1001001 => 1010010 => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => 1001010 => 1010101 => 4
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => 1000100 => 1001001 => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => 0100111 => 1001011 => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => 0100101 => 1001010 => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,1,4,5] => 0100011 => 1000101 => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => 0100011 => 1000101 => 3
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => 0100001 => 1000010 => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,3,1,4,6] => 0101011 => 1010101 => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => 0101101 => 1010110 => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => 0101110 => 1010111 => 5
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,1,4,8] => 0101010 => 1010101 => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => 0100101 => 1001010 => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => 0100110 => 1001011 => 4
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,1,4,8] => 0100110 => 1001011 => 4
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => 0100010 => 1000101 => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => 0110001 => 1010010 => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => 0110101 => 1011010 => 4
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => 0110110 => 1011011 => 5
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => 0111010 => 1011101 => 5
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,1,6,7] => 0101001 => 1010010 => 3
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => 0101100 => 1010101 => 4
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => 0110011 => 1010101 => 4
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => 0110001 => 1010010 => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => 0110101 => 1011010 => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => 0110110 => 1011011 => 5
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => 0110010 => 1010101 => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => 0111010 => 1011101 => 5
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => 0110100 => 1011001 => 4
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => 0111100 => 1011101 => 5
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => 0111100 => 1011101 => 5
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => 0101100 => 1010101 => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => 0011100 => 0101101 => 4
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => 0001100 => 0010101 => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => 0010011 => 0100101 => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => 0010001 => 0100010 => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,1,5,7] => 0010101 => 0101010 => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => 0010110 => 0101011 => 4
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => 0010010 => 0100101 => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => 0011001 => 0101010 => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => 0011010 => 0101101 => 4
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => 0011100 => 0101101 => 4
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => 0010100 => 0101001 => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => 0011001 => 0101010 => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => 0011010 => 0101101 => 4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => 0101100 => 1010101 => 4
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => 0110100 => 1011001 => 4
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => 0010100 => 0101001 => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => 0001001 => 0010010 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => 0001010 => 0010101 => 3
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => 0001100 => 0010101 => 3
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => 0001100 => 0010101 => 3
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => 0010100 => 0101001 => 3
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => 0100100 => 1001001 => 3
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => 0000100 => 0001001 => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => 0001111 => 0010111 => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => 0001101 => 0010110 => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => 0001011 => 0010101 => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => 0001011 => 0010101 => 3
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => 0001001 => 0010010 => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => 0000111 => 0001011 => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => 0000101 => 0001010 => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => 0000111 => 0001011 => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => 0000111 => 0001011 => 3
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => 0000011 => 0000101 => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => 0000011 => 0000101 => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => 0000011 => 0000101 => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => 0000101 => 0001010 => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => 0000001 => 0000010 => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => 0010111 => 0101011 => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,1,2,3,5] => 0010101 => 0101010 => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,1,2,3,5] => 0010011 => 0100101 => 3
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => 0010001 => 0100010 => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => 0011011 => 0101101 => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => 0011001 => 0101010 => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => 0011101 => 0101110 => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => 0011110 => 0101111 => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => 0010101 => 0101010 => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,1,2,3,8] => 0010110 => 0101011 => 4
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => 0010010 => 0100101 => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,1,2,3,6] => 0001011 => 0010101 => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => 0001001 => 0010010 => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => 0001101 => 0010110 => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,1,2,3,8] => 0001110 => 0010111 => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,1,2,3,8] => 0001110 => 0010111 => 4
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => 0000110 => 0001011 => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => 0000101 => 0001010 => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => 0000110 => 0001011 => 3
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => 0001010 => 0010101 => 3
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => 0000010 => 0000101 => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => 0100111 => 1001011 => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => 0100101 => 1001010 => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => 0100011 => 1000101 => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => 0100011 => 1000101 => 3
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => 0100001 => 1000010 => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => 0101011 => 1010101 => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => 0101001 => 1010010 => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => 0100101 => 1001010 => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,1,2,4,8] => 0100110 => 1001011 => 4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => 0100010 => 1000101 => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => 0110001 => 1010010 => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => 0110101 => 1011010 => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => 0110110 => 1011011 => 5
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => 0111010 => 1011101 => 5
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => 0111100 => 1011101 => 5
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => 0110100 => 1011001 => 4
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => 0101100 => 1010101 => 4
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => 0101100 => 1010101 => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => 0010011 => 0100101 => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => 0010001 => 0100010 => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,1,2,5,7] => 0010101 => 0101010 => 3
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => 0010010 => 0100101 => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => 0011001 => 0101010 => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,1,2,6,8] => 0011010 => 0101101 => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => 0010100 => 0101001 => 3
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,1,2,7,8] => 0011100 => 0101101 => 4
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => 0011100 => 0101101 => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,1,2,6,7] => 0001001 => 0010010 => 2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => 0010100 => 0101001 => 3
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => 0000100 => 0001001 => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => 1000111 => 1001011 => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => 1000101 => 1001010 => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => 1000011 => 1000101 => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => 1000001 => 1000010 => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => 1001011 => 1010101 => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => 1001001 => 1010010 => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => 1001101 => 1010110 => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => 1001110 => 1010111 => 5
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,1,3,4,8] => 1001010 => 1010101 => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => 1000101 => 1001010 => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => 1000110 => 1001011 => 4
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => 1000010 => 1000101 => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => 1010011 => 1100101 => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => 1010001 => 1100010 => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => 1010101 => 1101010 => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => 1010110 => 1101011 => 5
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => 1011001 => 1101010 => 4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => 1011100 => 1101101 => 5
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => 1010100 => 1101001 => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => 1001010 => 1010101 => 4
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => 1001100 => 1010101 => 4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => 1001100 => 1010101 => 4
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => 1000100 => 1001001 => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => 1100011 => 1100101 => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => 1100001 => 1100010 => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => 1100101 => 1101010 => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => 1100110 => 1101011 => 5
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => 1100010 => 1100101 => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => 1101001 => 1110010 => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => 1101010 => 1110101 => 5
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => 1101100 => 1110101 => 5
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => 1100100 => 1101001 => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => 1110001 => 1110010 => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => 1110010 => 1110101 => 5
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => 1110100 => 1111001 => 5
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => 1111000 => 1111001 => 5
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => 1101000 => 1110001 => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => 1010001 => 1100010 => 3
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,1,5,7,8] => 1010100 => 1101001 => 4
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => 1011000 => 1101001 => 4
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => 1011000 => 1101001 => 4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => 1001000 => 1010001 => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => 0100011 => 1000101 => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => 0100001 => 1000010 => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,1,4,5,8] => 0100110 => 1001011 => 4
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => 0100010 => 1000101 => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => 0101010 => 1010101 => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => 0110001 => 1010010 => 3
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => 0111000 => 1011001 => 4
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => 0101000 => 1010001 => 3
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => 0111000 => 1011001 => 4
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => 0111000 => 1011001 => 4
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => 0011000 => 0101001 => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => 0010001 => 0100010 => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => 0010010 => 0100101 => 3
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => 0011000 => 0101001 => 3
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => 0011000 => 0101001 => 3
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => 0101000 => 1010001 => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => 0001000 => 0010001 => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => 0000111 => 0001011 => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => 0000101 => 0001010 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => 0000011 => 0000101 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => 0000011 => 0000101 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => 0000001 => 0000010 => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => 0001011 => 0010101 => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => 0001001 => 0010010 => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => 0001101 => 0010110 => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => 0001110 => 0010111 => 4
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => 0001010 => 0010101 => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => 0000101 => 0001010 => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => 0000110 => 0001011 => 3
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => 0000110 => 0001011 => 3
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => 0000010 => 0000101 => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => 0010011 => 0100101 => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,8,4,1,2,3,5,6] => 0010001 => 0100010 => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4,1,2,3,6,7] => 0011001 => 0101010 => 3
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => 0011100 => 0101101 => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [8,4,5,1,2,3,6,7] => 0001001 => 0010010 => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => 0001010 => 0010101 => 3
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => 0000100 => 0001001 => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => 0100001 => 1000010 => 2
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => 0100010 => 1000101 => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => 0101001 => 1010010 => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => 0101010 => 1010101 => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => 0110010 => 1010101 => 4
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => 0110100 => 1011001 => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => 0111000 => 1011001 => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => 0010001 => 0100010 => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => 0010010 => 0100101 => 3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => 0011000 => 0101001 => 3
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => 0011000 => 0101001 => 3
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => 0001000 => 0010001 => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => 1000011 => 1000101 => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => 1000001 => 1000010 => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => 1001001 => 1010010 => 3
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => 1000100 => 1001001 => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => 1010001 => 1100010 => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => 1010100 => 1101001 => 4
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => 1011000 => 1101001 => 4
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => 1001000 => 1010001 => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => 1100001 => 1100010 => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => 1100010 => 1100101 => 4
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,4,5,7,8] => 1100100 => 1101001 => 4
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => 1101000 => 1110001 => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => 1110000 => 1110001 => 4
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => 1010000 => 1100001 => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => 0100001 => 1000010 => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => 0100010 => 1000101 => 3
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => 0100100 => 1001001 => 3
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => 0101000 => 1010001 => 3
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => 0110000 => 1010001 => 3
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => 0110000 => 1010001 => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => 0010000 => 0100001 => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => 0000011 => 0000101 => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => 0000001 => 0000010 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => 0000101 => 0001010 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => 0000110 => 0001011 => 3
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => 0000010 => 0000101 => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => 0001001 => 0010010 => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => 0001010 => 0010101 => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => 0010001 => 0100010 => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => 0010010 => 0100101 => 3
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => 0010100 => 0101001 => 3
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => 0011000 => 0101001 => 3
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => 0001000 => 0010001 => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => 0100001 => 1000010 => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => 0100010 => 1000101 => 3
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => 0100100 => 1001001 => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => 0101000 => 1010001 => 3
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => 0110000 => 1010001 => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => 0010000 => 0100001 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => 1000001 => 1000010 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => 1000010 => 1000101 => 3
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,3,4,5,7,8] => 1000100 => 1001001 => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => 1001000 => 1010001 => 3
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => 1010000 => 1100001 => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => 1100000 => 1100001 => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => 0100000 => 1000001 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => 0000001 => 0000010 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => 0000010 => 0000101 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => 0000100 => 0001001 => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => 0001000 => 0010001 => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => 0010000 => 0100001 => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => 0100000 => 1000001 => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => 1000000 => 1000001 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => 0000000 => 0000001 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => 00000001 => 00000010 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 00000001 => 00000010 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => 000000001 => 000000010 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,3,4,5,6,7,8] => 10000001 => 10000010 => 2
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => 01000001 => 10000010 => 2
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => 000000001 => 000000010 => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => 0000000001 => 0000000010 => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => 100000001 => 100000010 => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1,2,4,5,6,7,8] => 01000001 => 10000010 => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,1,4,5,6,7,8] => 01000001 => 10000010 => 2
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => 00100001 => 01000010 => 2
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,1] => 00100001 => 01000010 => 2
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => 010000001 => 100000010 => 2
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000001 => 0000000010 => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => 00000000001 => 00000000010 => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,1,3,4,5,6,7,8,9,10] => 1000000001 => 1000000010 => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [10,3,1,2,4,5,6,7,8,9] => 010000001 => 100000010 => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,1,4,5,6,7,8,9] => 010000001 => 100000010 => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [9,4,1,2,3,5,6,7,8] => 00100001 => 01000010 => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,1,5,6,7,8] => 00100001 => 01000010 => 2
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,1] => 01100001 => 10100010 => 3
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,10,1] => 001000001 => 010000010 => 2
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,11,1] => 0100000001 => 1000000010 => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [11,3,1,2,4,5,6,7,8,9,10] => 0100000001 => 1000000010 => 2
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [10,4,1,2,3,5,6,7,8,9] => 001000001 => 010000010 => 2
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,1,5,6,7,8,9] => 001000001 => 010000010 => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [9,3,4,1,2,5,6,7,8] => 00100001 => 01000010 => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,1,6,7,8] => 00010001 => 00100010 => 2
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [4,5,2,3,6,7,8,9,1] => 00010001 => 00100010 => 2
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,1,6,7,8,9] => 000100001 => 001000010 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [9,6,1,2,3,4,5,7,8] => 00001001 => 00010010 => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,1,7,8] => 00001001 => 00010010 => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [6,2,3,4,5,7,8,9,10,1] => 000010001 => 000100010 => 2
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,3,6,7,8,9,1] => 00110001 => 01010010 => 3
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [4,5,2,3,6,7,8,9,10,1] => 000100001 => 001000010 => 2
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,2,7,8,9,10,1] => 000010001 => 000100010 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [10,6,1,2,3,4,5,7,8,9] => 000010001 => 000100010 => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,1,7,8,9] => 000010001 => 000100010 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => 00000101 => 00001010 => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,1,8] => 00000101 => 00001010 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => 00000001 => 00000010 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => 00000011 => 00000101 => 2
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,7,8,9,1] => 01110001 => 10110010 => 4
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => 00000001 => 00000010 => 1
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,1] => 00000011 => 00000101 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [10,7,1,2,3,4,5,6,8,9] => 000001001 => 000010010 => 2
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,1,8,9] => 000001001 => 000010010 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => 00000011 => 00000101 => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1] => 00000011 => 00000101 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,1,3,4,5,6,7] => 10000001 => 10000010 => 2
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,1,2] => 00100001 => 01000010 => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => 10000001 => 10000010 => 2
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,1,9] => 000000101 => 000001010 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => 000000001 => 000000010 => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,4,5,6,7,8,1] => 01000011 => 10000101 => 3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => 000000011 => 000000101 => 2
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [5,3,4,6,7,8,9,1,2] => 00010001 => 00100010 => 2
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [4,5,3,6,7,8,9,1,2] => 00010001 => 00100010 => 2
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => 000000001 => 000000010 => 1
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,10,1] => 000000011 => 000000101 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => 000000011 => 000000101 => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,9,1] => 000000011 => 000000101 => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [9,4,2,3,5,6,7,8,1] => 00100011 => 01000101 => 3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [9,3,4,2,5,6,7,8,1] => 00100011 => 01000101 => 3
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [6,5,4,2,3,7,8,9,1] => 00111001 => 01011010 => 4
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,6,7,2,3,4,8,9,1] => 00000101 => 00001010 => 2
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,3,5,6,7,8,9,10,1,2] => 001000001 => 010000010 => 2
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => 100000001 => 100000010 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => 11111110 => 11111111 => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => 11111010 => 11111101 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8,6,7,5,4,3,2,1,9] => 11110110 => 11111011 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,1,9] => 11110110 => 11111011 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [6,7,8,5,4,3,2,1,9] => 11110010 => 11110101 => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,7,5,6,4,3,2,1,9] => 11101110 => 11110111 => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [8,6,5,7,4,3,2,1,9] => 11101110 => 11110111 => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7,6,5,8,4,3,2,1,9] => 11101110 => 11110111 => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [6,7,5,8,4,3,2,1,9] => 11100110 => 11101011 => 6
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [8,5,6,7,4,3,2,1,9] => 11100110 => 11101011 => 6
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [6,5,7,8,4,3,2,1,9] => 11101010 => 11110101 => 6
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => 11011110 => 11101111 => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,6,3,2,1,9] => 11011110 => 11101111 => 7
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1,9] => 11011010 => 11101101 => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,3,5,2,1,9] => 10111110 => 11011111 => 7
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,8,2,1,9] => 10111110 => 11011111 => 7
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,7,8,2,1,9] => 10111010 => 11011101 => 6
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1,9] => 10000010 => 10000101 => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,1,9] => 01111110 => 10111111 => 7
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,1,9] => 01111110 => 10111111 => 7
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9] => 00011110 => 00101111 => 5
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,8,1,9] => 01111010 => 10111101 => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,1,9] => 00000110 => 00001011 => 3
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,1,9] => 00100010 => 01000101 => 3
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1,9] => 01000010 => 10000101 => 3
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => 00000010 => 00000101 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => 01111110 => 10111111 => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7,8,5,6,3,4,1,2,9] => 00101010 => 01010101 => 4
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,3,4,5,6,8,1,2,9] => 00000110 => 00001011 => 3
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => 00000010 => 00000101 => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,1,3,9] => 10111110 => 11011111 => 7
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,2,1,4,9] => 11011110 => 11101111 => 7
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,3,2,1,5,9] => 11101110 => 11110111 => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,2,1,6,9] => 11110110 => 11111011 => 7
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,1,7,9] => 11111010 => 11111101 => 7
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => 11111100 => 11111101 => 7
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,4,3,2,1,8,9] => 11110100 => 11111001 => 6
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,6,4,3,2,1,7,9] => 11101010 => 11110101 => 6
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8,7,4,5,3,2,1,6,9] => 11010110 => 11101011 => 6
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8,7,6,3,4,2,1,5,9] => 10101110 => 11010111 => 6
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8,9] => 10000100 => 10001001 => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,2,3,1,4,9] => 01011110 => 10101111 => 6
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,1,8,9] => 01111100 => 10111101 => 6
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,4,3,2,7,1,8,9] => 01101100 => 10110101 => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [7,8,2,3,4,5,1,6,9] => 00010010 => 00100101 => 3
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,2,3,4,5,6,1,8,9] => 00001100 => 00010101 => 3
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => 00000100 => 00001001 => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,1,2,3,9] => 00111110 => 01011111 => 6
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => 00000010 => 00000101 => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,7,1,2,8,9] => 00111100 => 01011101 => 5
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8,9] => 00000100 => 00001001 => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [7,6,5,3,2,1,4,8,9] => 11011100 => 11101101 => 6
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [6,7,4,3,2,1,5,8,9] => 11100100 => 11101001 => 5
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => 11111000 => 11111001 => 6
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,4,3,2,1,7,8,9] => 11101000 => 11110001 => 5
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8,9] => 10001000 => 10010001 => 3
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,1,7,8,9] => 01111000 => 10111001 => 5
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,5,2,6,1,7,8,9] => 00111000 => 01011001 => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [6,2,3,4,5,1,7,8,9] => 00011000 => 00101001 => 3
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => 00001000 => 00010001 => 2
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => 00000010 => 00000101 => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [8,7,5,3,1,2,4,6,9] => 01010110 => 10101011 => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [7,5,4,3,1,2,6,8,9] => 01110100 => 10111001 => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1,2,7,8,9] => 01111000 => 10111001 => 5
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,6,3,4,1,2,7,8,9] => 00101000 => 01010001 => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [8,6,4,2,1,3,5,7,9] => 10101010 => 11010101 => 5
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => 11110000 => 11110001 => 5
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,5,3,2,1,6,7,8,9] => 11010000 => 11100001 => 4
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8,9] => 10010000 => 10100001 => 3
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,1,6,7,8,9] => 01110000 => 10110001 => 4
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9] => 00110000 => 01010001 => 3
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,2,3,4,1,6,7,8,9] => 00110000 => 01010001 => 3
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => 00010000 => 00100001 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [6,7,8,1,2,3,4,5,9] => 00000010 => 00000101 => 2
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => 00001000 => 00010001 => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1,2,4,6,8,9] => 01010100 => 10101001 => 4
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1,2,6,7,8,9] => 01110000 => 10110001 => 4
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [4,3,5,1,2,6,7,8,9] => 00110000 => 01010001 => 3
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8,9] => 00010000 => 00100001 => 2
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [4,5,2,1,3,6,7,8,9] => 10010000 => 10100001 => 3
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => 11100000 => 11100001 => 4
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9] => 10100000 => 11000001 => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,1,4,5,6,7,9] => 01000010 => 10000101 => 3
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,1,5,6,7,8,9] => 01100000 => 10100001 => 3
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9] => 01100000 => 10100001 => 3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => 00100000 => 01000001 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,8,1,2,3,4,5,6,9] => 00000010 => 00000101 => 2
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1,2,3,6,7,8,9] => 00110000 => 01010001 => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [8,3,1,2,4,5,6,7,9] => 01000010 => 10000101 => 3
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1,2,4,6,7,8,9] => 01010000 => 10100001 => 3
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9] => 01100000 => 10100001 => 3
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => 00100000 => 01000001 => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,3,4,5,6,7,9] => 10000010 => 10000101 => 3
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => 11000000 => 11000001 => 3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => 01000000 => 10000001 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => 00000010 => 00000101 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => 00000100 => 00001001 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => 00001000 => 00010001 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => 00010000 => 00100001 => 2
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => 00100000 => 01000001 => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => 01000000 => 10000001 => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => 10000000 => 10000001 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => 00000000 => 00000001 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => 11111111 => 11111111 => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,2,1] => 11111101 => 11111110 => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => 11111011 => 11111101 => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,4,3,2,1] => 11110111 => 11111011 => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,2,1] => 11101111 => 11110111 => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,3,2,1] => 11011111 => 11101111 => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,2,1] => 10111111 => 11011111 => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => 01111111 => 10111111 => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => 111111111 => 111111111 => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => 111111101 => 111111110 => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => 11111001 => 11111010 => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,2,1] => 111111011 => 111111101 => 8
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [8,6,7,9,5,4,3,2,1] => 11110011 => 11110101 => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [8,7,5,6,9,4,3,2,1] => 11100111 => 11101011 => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,9,3,2,1] => 11001111 => 11010111 => 6
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,4,9,2,1] => 10011111 => 10101111 => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,9,1] => 00111111 => 01011111 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => 111111110 => 111111111 => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => 1111111101 => 1111111110 => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => 111111001 => 111111010 => 7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [7,6,8,9,5,4,3,2,1] => 11110101 => 11111010 => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => 11110001 => 11110010 => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,7,9,10,6,5,4,3,2,1] => 111110101 => 111111010 => 7
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,6,9,2,1] => 10110111 => 11011011 => 6
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,4,3,2,1] => 11101001 => 11110010 => 5
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => 11100001 => 11100010 => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => 01111011 => 10111101 => 6
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,9,1] => 01111101 => 10111110 => 6
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => 11010001 => 11100010 => 4
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => 11000001 => 11000010 => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,8,9,1] => 01111001 => 10111010 => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,1,2,3,4,5,10] => 000011110 => 000101111 => 5
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,10,1] => 011111101 => 101111110 => 7
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,7,6,5,4,3,2,1,8,10] => 111111010 => 111111101 => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,2,1] => 11111011 => 11111101 => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [8,9,6,7,5,4,3,2,1] => 11110101 => 11111010 => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [9,6,7,8,5,4,3,2,1] => 11110011 => 11110101 => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,4,3,2,1] => 11101111 => 11110111 => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,4,3,2,1] => 11101001 => 11110010 => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,3,2,1] => 11011111 => 11101111 => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,3,2,1] => 11010101 => 11101010 => 5
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,5,3,2,1] => 11010001 => 11100010 => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,3,2,1] => 11001111 => 11010111 => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,3,2,1] => 11001001 => 11010010 => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,2,1] => 10111111 => 11011111 => 7
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,3,4,2,1] => 10101001 => 11010010 => 4
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,4,2,1] => 10100001 => 11000010 => 3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,2,1] => 10000011 => 10000101 => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,3,1] => 01111111 => 10111111 => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,3,1] => 01111101 => 10111110 => 6
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,2,3,1] => 01011111 => 10101111 => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,2,3,1] => 01010101 => 10101010 => 4
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,5,2,3,1] => 01010001 => 10100010 => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,2,3,1] => 01001001 => 10010010 => 3
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,3,1] => 01000001 => 10000010 => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,3,4,1] => 00111111 => 01011111 => 6
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,3,4,1] => 00100001 => 01000010 => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,5,1] => 00010001 => 00100010 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [9,8,2,3,4,5,6,7,1] => 00000111 => 00001011 => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,6,7,1] => 00000101 => 00001010 => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,1,2] => 01111111 => 10111111 => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,1,2] => 01111101 => 10111110 => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,1,2] => 01111011 => 10111101 => 6
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,3,1,2] => 01001001 => 10010010 => 3
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,1,2] => 01000001 => 10000010 => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,1,2] => 00111111 => 01011111 => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => 00101111 => 01010111 => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,1,2] => 00101011 => 01010101 => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,3,4,1,2] => 00101001 => 01010010 => 3
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,4,1,2] => 00100001 => 01000010 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,3,4,5,1,2] => 00010001 => 00100010 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [9,8,3,4,5,6,7,1,2] => 00000111 => 00001011 => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [8,9,3,4,5,6,7,1,2] => 00000101 => 00001010 => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,1,2] => 00000011 => 00000101 => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => 00111111 => 01011111 => 6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => 00011111 => 00101111 => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => 00010101 => 00101010 => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => 00001111 => 00010111 => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => 00001001 => 00010010 => 2
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => 00000001 => 00000010 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => 00011111 => 00101111 => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => 00001111 => 00010111 => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => 00001011 => 00010101 => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => 00000111 => 00001011 => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => 00000101 => 00001010 => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => 00000011 => 00000101 => 2
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => 00000001 => 00000010 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => 00001111 => 00010111 => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [7,8,9,6,1,2,3,4,5] => 00001001 => 00010010 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => 00000111 => 00001011 => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => 00000011 => 00000101 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => 00000001 => 00000010 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => 00000111 => 00001011 => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => 00000011 => 00000101 => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => 00000001 => 00000010 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [10,8,9,7,6,5,4,3,2,1] => 111111011 => 111111101 => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [9,10,7,8,6,5,4,3,2,1] => 111110101 => 111111010 => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,4,3,2,1] => 111010101 => 111101010 => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,2,1] => 101010101 => 110101010 => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,3,4,5,6,2,1] => 100010001 => 100100010 => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,2,3,1] => 010101011 => 101010101 => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [8,9,10,6,7,4,5,2,3,1] => 010101001 => 101010010 => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,4,5,6,2,3,1] => 010010001 => 100100010 => 3
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,2,3,1] => 010000001 => 100000010 => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,2,3,4,1] => 001001001 => 010010010 => 3
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,2,3,4,1] => 001000001 => 010000010 => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,2,3,4,5,1] => 000100001 => 001000010 => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [10,9,2,3,4,5,6,7,8,1] => 000000111 => 000001011 => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,1,2] => 011111101 => 101111110 => 7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,1,2] => 001111111 => 010111111 => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,3,4,1,2] => 001011111 => 010101111 => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [10,9,7,8,5,6,3,4,1,2] => 001010111 => 010101011 => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,1,2] => 001010101 => 010101010 => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,5,6,3,4,1,2] => 001010001 => 010100010 => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,3,4,1,2] => 001001001 => 010010010 => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,3,4,5,6,1,2] => 000010001 => 000100010 => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [10,9,3,4,5,6,7,8,1,2] => 000000111 => 000001011 => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [9,10,3,4,5,6,7,8,1,2] => 000000101 => 000001010 => 2
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,1,2] => 000000011 => 000000101 => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,1,2,3] => 001111111 => 010111111 => 7
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,1,2,3] => 000111111 => 001011111 => 6
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,1,2,3] => 000101011 => 001010101 => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => 000010101 => 000101010 => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,4,5,6,1,2,3] => 000010001 => 000100010 => 2
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => 000000001 => 000000010 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => 000111111 => 001011111 => 6
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => 000010101 => 000101010 => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,5,6,1,2,3,4] => 000010001 => 000100010 => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => 000001001 => 000010010 => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => 000000111 => 000001011 => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => 000000101 => 000001010 => 2
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => 000000001 => 000000010 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => 000011111 => 000101111 => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => 000001011 => 000010101 => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => 000000011 => 000000101 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => 000000001 => 000000010 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => 000001111 => 000010111 => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => 000000011 => 000000101 => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => 000000001 => 000000010 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => 000000111 => 000001011 => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => 000000011 => 000000101 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => 000000001 => 000000010 => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 000000001 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,1,3] => 10111111 => 11011111 => 7
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,1,4] => 11011111 => 11101111 => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,2,1,5] => 11101111 => 11110111 => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,4,3,2,1,6] => 11110111 => 11111011 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,3,2,1,7] => 11111011 => 11111101 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,1,8] => 11111101 => 11111110 => 7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,3,1,4] => 01011111 => 10101111 => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,3,4,2,1,5] => 10101111 => 11010111 => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,3,2,1,6] => 11010111 => 11101011 => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [9,8,5,6,4,3,2,1,7] => 11101011 => 11110101 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [9,6,7,5,4,3,2,1,8] => 11110101 => 11111010 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,3,2,1,8] => 111111011 => 111111101 => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,1,9] => 111111101 => 111111110 => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,1,2] => 01111011 => 10111101 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => 111111010 => 111111101 => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,1,2] => 011111011 => 101111101 => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,2,1,3] => 10111011 => 11011101 => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,2,3,1] => 01111011 => 10111101 => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,1,3] => 10111101 => 11011110 => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,1,7,8] => 11111001 => 11111010 => 6
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [9,8,5,4,3,2,1,6,7] => 11110011 => 11110101 => 6
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,3,2,1,5,6] => 11100111 => 11101011 => 6
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,3,2,1,4,5] => 11001111 => 11010111 => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,1,3,4] => 10011111 => 10101111 => 6
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => 000000010 => 000000101 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => 000000010 => 000000101 => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => 0000000010 => 0000000101 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [9,8,6,1,2,3,4,5,7] => 00001011 => 00010101 => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,1,2,3,4,6] => 00010111 => 00101011 => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,1,2,3,5] => 00101111 => 01010111 => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,1,2,4] => 01011111 => 10101111 => 6
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => 001000000 => 010000001 => 2
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => 000100000 => 001000001 => 2
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => 000010000 => 000100001 => 2
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => 000001000 => 000010001 => 2
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => 000000100 => 000001001 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [8,9,5,4,3,2,1,6,7] => 11110001 => 11110010 => 5
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,8,9,1,2] => 00111101 => 01011110 => 5
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,7,1,8] => 01111101 => 10111110 => 6
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,1,3] => 10000001 => 10000010 => 2
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,1,3,4] => 10000001 => 10000010 => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,1,3,4,5] => 10000001 => 10000010 => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,1,3,4,5,6] => 10000001 => 10000010 => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,2,5,1] => 01111111 => 10111111 => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,5,2,1] => 10111111 => 11011111 => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [8,9,7,6,4,3,2,1,5] => 11101101 => 11110110 => 6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,5,1,2] => 00111111 => 01011111 => 6
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,2,3,8,9,1] => 00111101 => 01011110 => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,1,2,8] => 01111101 => 10111110 => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,9,1] => 01111011 => 10111101 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,9,6,5,4,3,2,1,7] => 11111001 => 11111010 => 6
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,1,2] => 00111111 => 01011111 => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [7,8,9,5,4,3,2,1,6] => 11110001 => 11110010 => 5
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,3,2,1,5] => 11100001 => 11100010 => 4
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,3,2,1,4] => 11001001 => 11010010 => 4
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [6,5,4,7,8,9,2,1,3] => 10011001 => 10101010 => 4
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,7,8,9,1,2] => 00111001 => 01011010 => 4
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,8,9,2,1,10] => 101111010 => 110111101 => 7
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,8,9,1,10] => 011111010 => 101111101 => 7
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,3,9,1,2] => 00000011 => 00000101 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,1,6,7] => 00010001 => 00100010 => 2
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [5,6,7,4,8,9,1,2,3] => 00000101 => 00001010 => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,3,1,4,5,6] => 01000001 => 10000010 => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,1,2,3,4] => 00001001 => 00010010 => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,9,1,2,3,4,5,6] => 00000011 => 00000101 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => 000000100 => 000001001 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [7,6,8,9,1,2,3,4,5] => 00000101 => 00001010 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => 000001000 => 000010001 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => 000010000 => 000100001 => 2
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,9,1,2,3] => 00010001 => 00100010 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => 000100000 => 001000001 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => 001000000 => 010000001 => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,3,4,2,1] => 10110111 => 11011011 => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [9,7,8,5,4,3,2,1,6] => 11110011 => 11110101 => 6
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [9,6,7,4,5,2,3,1,8] => 01010101 => 10101010 => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,2,1,3] => 10010101 => 10101010 => 4
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [9,10,6,7,4,5,2,3,1,8] => 010101001 => 101010010 => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,2,1,3] => 100101011 => 101010101 => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => 111111100 => 111111101 => 8
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => 001000000 => 010000001 => 2
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => 000010000 => 000100001 => 2
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => 000000100 => 000001001 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5,10] => 000000010 => 000000101 => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [6,5,7,4,8,3,9,2,10,1] => 000011111 => 000101111 => 5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [10,8,6,4,2,1,3,5,7,9] => 101010101 => 110101010 => 5
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000 => 0000000001 => 1
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => 0000000001 => 0000000010 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [10,7,6,5,4,3,2,1,8,9] => 111111001 => 111111010 => 7
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,5,4,3,2,1,6,7,8] => 11110001 => 11110010 => 5
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => 0000000010 => 0000000101 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,11,1,2,3,4,5,6,7,8,9] => 0000000001 => 0000000010 => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,4,1] => 01111111 => 10111111 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [11,9,8,7,6,5,4,3,2,1,10] => 1111111101 => 1111111110 => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,8,1] => 01111111 => 10111111 => 7
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,2,1,4] => 11000001 => 11000010 => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => 000000010 => 000000101 => 2
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4,10] => 000000010 => 000000101 => 2
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => 000000010 => 000000101 => 2
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,5,7,8,9,10,11,4,3,2,1] => 1110100001 => 1111000010 => 5
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,3,9,2,1] => 10010011 => 10100101 => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,4,3,2,1,5,9] => 111011101 => 111101110 => 7
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [7,6,8,5,9,4,3,2,1] => 11100111 => 11101011 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,10,7,6,5,4,3,2,1,8] => 111111001 => 111111010 => 7
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,1,2,3,4,7] => 00011011 => 00101101 => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [8,7,9,5,6,3,4,1,2] => 00101011 => 01010101 => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,2,1,3,4] => 100010101 => 100101010 => 4
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,3,4,1,2,5] => 00100001 => 01000010 => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,3,2,1,6] => 11010001 => 11100010 => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [8,9,4,5,6,3,2,1,7] => 11001001 => 11010010 => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [9,8,4,1,2,3,5,6,7] => 00100011 => 01000101 => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,4,6,3,2,1] => 11011111 => 11101111 => 7
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,2,1,3,4,5,6] => 100000001 => 100000010 => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,9,1] => 01110111 => 10111011 => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,3,7,2,1] => 10111111 => 11011111 => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,7,3,2,1] => 11011111 => 11101111 => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [8,9,10,4,5,6,1,2,3,7] => 000010001 => 000100010 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [7,8,2,3,4,5,6,9,1] => 00000011 => 00000101 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [8,9,5,6,3,4,1,2,7] => 00101001 => 01010010 => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [10,7,8,5,6,3,4,1,2,9] => 001010101 => 010101010 => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,1,2,9] => 011111101 => 101111110 => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,8,2,1] => 10111111 => 11011111 => 7
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,2,1,8] => 10000101 => 10001010 => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [9,8,5,4,6,7,3,2,1] => 11010111 => 11101011 => 6
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,3,4,1,5,6] => 00100001 => 01000010 => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,1,2,8] => 00000101 => 00001010 => 2
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9,10] => 000000100 => 000001001 => 2
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,1,5] => 00100001 => 01000010 => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,10,1] => 011111011 => 101111101 => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [9,8,10,6,7,4,5,2,3,1] => 010101011 => 101010101 => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [9,8,5,4,6,3,7,2,1] => 10011111 => 10101111 => 6
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1] => 00001111 => 00010111 => 4
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9,10] => 000111100 => 001011101 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [10,7,8,6,5,4,3,2,1,9] => 111110101 => 111111010 => 7
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,1,4,5] => 01000001 => 10000010 => 2
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,3,1,4] => 01000001 => 10000010 => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [9,4,3,5,6,7,8,2,1] => 10100011 => 11000101 => 4
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,4,5,2,3,10,1] => 000101011 => 001010101 => 4
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,1,10] => 000000110 => 000001011 => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,3,1,2,4,6,8,10] => 010101010 => 101010101 => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [11,12,9,10,7,8,5,6,3,4,1,2] => 00101010101 => 01010101010 => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [8,9,5,6,4,3,2,1,7] => 11101001 => 11110010 => 5
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [7,8,5,6,3,4,1,2,9,10] => 001010100 => 010101001 => 4
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [11,12,1,2,3,4,5,6,7,8,9,10] => 00000000001 => 00000000010 => 1
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => 1000000001 => 1000000010 => 2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [9,4,5,6,7,8,2,1,3] => 10000011 => 10000101 => 3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,2,1,3,4] => 10000011 => 10000101 => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [9,7,8,4,3,2,1,5,6] => 11100011 => 11100101 => 5
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,3,4,5,1,6] => 00010001 => 00100010 => 2
[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2,11] => 0000000010 => 0000000101 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5,11] => 0000000010 => 0000000101 => 2
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9,10] => 001100000 => 010100001 => 3
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1,10] => 000011110 => 000101111 => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7,8,9,4,5,6,1,2,3,10] => 000010010 => 000100101 => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,2,1,3,9] => 101111101 => 110111110 => 7
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [9,8,4,3,5,6,7,2,1] => 10100111 => 11001011 => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1,2,4,6,8] => 01010101 => 10101010 => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [8,7,9,10,5,6,2,1,3,4] => 100010101 => 100101010 => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [10,8,6,5,4,3,2,1,7,9] => 111110101 => 111111010 => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [8,9,4,5,6,2,3,1,7] => 01001001 => 10010010 => 3
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [6,4,5,7,3,8,2,9,1,10] => 000011110 => 000101111 => 5
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [9,7,5,2,3,1,4,6,8] => 01010101 => 10101010 => 4
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,2,3,1,4,6,8,10] => 010101010 => 101010101 => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [7,8,9,3,4,5,1,2,6] => 00010001 => 00100010 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [12,10,9,8,7,6,5,4,3,2,1,11] => 11111111101 => 11111111110 => 10
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
3,2 4,8,2 5,20,15,2 6,40,60,24,2 7,70,175,140,35,2
F2=2 q
F3=3 q+2 q2
F4=4 q+8 q2+2 q3
F5=5 q+20 q2+15 q3+2 q4
F6=6 q+40 q2+60 q3+24 q4+2 q5
F7=7 q+70 q2+175 q3+140 q4+35 q5+2 q6
Description
The number of ones in a binary word.
This is also known as the Hamming weight of the word.
This is also known as the Hamming weight of the word.
Map
valleys-to-peaks
Description
Return the binary word with every valley replaced by a peak.
A valley in a binary word is a subsequence 01, or a trailing 0. A peak is a subsequence 10 or a trailing 1. This map replaces every valley with a peak.
A valley in a binary word is a subsequence 01, or a trailing 0. A peak is a subsequence 10 or a trailing 1. This map replaces every valley with a peak.
Map
descent tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!