Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00278: Binary words —rowmotion⟶ Binary words
St000392: Binary words ⟶ ℤ
Values
[1,0,1,0] => [2,1] => 1 => 1 => 1
[1,1,0,0] => [1,2] => 0 => 0 => 0
[1,0,1,0,1,0] => [3,2,1] => 11 => 11 => 2
[1,0,1,1,0,0] => [2,3,1] => 10 => 01 => 1
[1,1,0,0,1,0] => [3,1,2] => 10 => 01 => 1
[1,1,0,1,0,0] => [2,1,3] => 10 => 01 => 1
[1,1,1,0,0,0] => [1,2,3] => 00 => 00 => 0
[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] => 110 => 011 => 2
[1,0,1,1,0,0,1,0] => [4,2,3,1] => 110 => 011 => 2
[1,0,1,1,0,1,0,0] => [3,2,4,1] => 110 => 011 => 2
[1,0,1,1,1,0,0,0] => [2,3,4,1] => 100 => 001 => 1
[1,1,0,0,1,0,1,0] => [4,3,1,2] => 101 => 110 => 2
[1,1,0,0,1,1,0,0] => [3,4,1,2] => 100 => 001 => 1
[1,1,0,1,0,0,1,0] => [4,2,1,3] => 110 => 011 => 2
[1,1,0,1,0,1,0,0] => [3,2,1,4] => 110 => 011 => 2
[1,1,0,1,1,0,0,0] => [2,3,1,4] => 100 => 001 => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => 100 => 001 => 1
[1,1,1,0,0,1,0,0] => [3,1,2,4] => 100 => 001 => 1
[1,1,1,0,1,0,0,0] => [2,1,3,4] => 100 => 001 => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => 000 => 000 => 0
[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] => 1110 => 0111 => 3
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 1110 => 0111 => 3
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 1110 => 0111 => 3
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 1100 => 0011 => 2
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 1101 => 1110 => 3
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 1100 => 0011 => 2
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => 1110 => 0111 => 3
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 1110 => 0111 => 3
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 1100 => 0011 => 2
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 1100 => 0011 => 2
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 1100 => 0011 => 2
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 1100 => 0011 => 2
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1000 => 0001 => 1
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 1011 => 1101 => 2
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 1010 => 1100 => 2
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 1010 => 1100 => 2
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 1010 => 1100 => 2
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 1000 => 0001 => 1
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 1101 => 1110 => 3
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 1100 => 0011 => 2
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 1110 => 0111 => 3
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => 1110 => 0111 => 3
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => 1100 => 0011 => 2
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 1100 => 0011 => 2
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => 1100 => 0011 => 2
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => 1100 => 0011 => 2
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => 1000 => 0001 => 1
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 1001 => 0110 => 2
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 1000 => 0001 => 1
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 1010 => 1100 => 2
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => 1010 => 1100 => 2
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => 1000 => 0001 => 1
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 1100 => 0011 => 2
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => 1100 => 0011 => 2
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => 1100 => 0011 => 2
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => 1000 => 0001 => 1
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 1000 => 0001 => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => 1000 => 0001 => 1
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => 1000 => 0001 => 1
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => 1000 => 0001 => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 0000 => 0000 => 0
[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] => 11110 => 01111 => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => 11110 => 01111 => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => 11110 => 01111 => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => 11100 => 00111 => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => 11101 => 11110 => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => 11100 => 00111 => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => 11110 => 01111 => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => 11110 => 01111 => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => 11100 => 00111 => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => 11100 => 00111 => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => 11100 => 00111 => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => 11100 => 00111 => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 11000 => 00011 => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => 11011 => 11101 => 3
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => 11010 => 11100 => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => 11010 => 11100 => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => 11010 => 11100 => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => 11000 => 00011 => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => 11101 => 11110 => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => 11100 => 00111 => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => 11110 => 01111 => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => 11110 => 01111 => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => 11100 => 00111 => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => 11100 => 00111 => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => 11100 => 00111 => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => 11100 => 00111 => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 11000 => 00011 => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => 11001 => 01110 => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => 11000 => 00011 => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => 11010 => 11100 => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => 11010 => 11100 => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => 11000 => 00011 => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => 11100 => 00111 => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 11100 => 00111 => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => 11100 => 00111 => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 11000 => 00011 => 2
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => 11000 => 00011 => 2
>>> Load all 2225 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => 11000 => 00011 => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => 11000 => 00011 => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 11000 => 00011 => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 10000 => 00001 => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => 10111 => 11011 => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => 10110 => 11001 => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => 10110 => 11001 => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => 10110 => 11001 => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => 10100 => 11000 => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => 10101 => 11010 => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => 10100 => 11000 => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => 10110 => 11001 => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => 10110 => 11001 => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => 10100 => 11000 => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => 10100 => 11000 => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => 10100 => 11000 => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => 10100 => 11000 => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 10000 => 00001 => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => 11011 => 11101 => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => 11010 => 11100 => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => 11010 => 11100 => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => 11010 => 11100 => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => 11000 => 00011 => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => 11101 => 11110 => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => 11100 => 00111 => 3
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => 11110 => 01111 => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => 11110 => 01111 => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => 11100 => 00111 => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => 11100 => 00111 => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => 11100 => 00111 => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => 11100 => 00111 => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => 11000 => 00011 => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => 11001 => 01110 => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => 11000 => 00011 => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => 11010 => 11100 => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => 11010 => 11100 => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => 11000 => 00011 => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => 11100 => 00111 => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => 11100 => 00111 => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => 11100 => 00111 => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => 11000 => 00011 => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => 11000 => 00011 => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => 11000 => 00011 => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => 11000 => 00011 => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => 11000 => 00011 => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => 10000 => 00001 => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => 10011 => 01101 => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => 10010 => 01100 => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => 10010 => 01100 => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => 10010 => 01100 => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => 10000 => 00001 => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => 10101 => 11010 => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => 10100 => 11000 => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => 10110 => 11001 => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => 10110 => 11001 => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => 10100 => 11000 => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => 10100 => 11000 => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => 10100 => 11000 => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => 10100 => 11000 => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => 10000 => 00001 => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => 11001 => 01110 => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => 11000 => 00011 => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => 11010 => 11100 => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => 11010 => 11100 => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => 11000 => 00011 => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => 11100 => 00111 => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => 11100 => 00111 => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => 11100 => 00111 => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => 11000 => 00011 => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => 11000 => 00011 => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => 11000 => 00011 => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => 11000 => 00011 => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => 11000 => 00011 => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => 10000 => 00001 => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => 10001 => 00110 => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 10000 => 00001 => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => 10010 => 01100 => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => 10010 => 01100 => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => 10000 => 00001 => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => 10100 => 11000 => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => 10100 => 11000 => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => 10100 => 11000 => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => 10000 => 00001 => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => 11000 => 00011 => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => 11000 => 00011 => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => 11000 => 00011 => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => 11000 => 00011 => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => 10000 => 00001 => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 10000 => 00001 => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => 10000 => 00001 => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => 10000 => 00001 => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => 10000 => 00001 => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => 10000 => 00001 => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => 00000 => 00000 => 0
[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] => 111110 => 011111 => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => 111110 => 011111 => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => 111110 => 011111 => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => 111100 => 001111 => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => 111101 => 111110 => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => 111100 => 001111 => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => 111110 => 011111 => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => 111110 => 011111 => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => 111100 => 001111 => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => 111100 => 001111 => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => 111100 => 001111 => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => 111100 => 001111 => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => 111000 => 000111 => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => 111011 => 111101 => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => 111010 => 111100 => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => 111010 => 111100 => 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => 111010 => 111100 => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => 111000 => 000111 => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => 111101 => 111110 => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => 111100 => 001111 => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => 111110 => 011111 => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => 111110 => 011111 => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => 111100 => 001111 => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => 111100 => 001111 => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => 111100 => 001111 => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => 111100 => 001111 => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => 111000 => 000111 => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => 111001 => 011110 => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => 111000 => 000111 => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => 111010 => 111100 => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => 111010 => 111100 => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => 111000 => 000111 => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => 111100 => 001111 => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => 111100 => 001111 => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => 111100 => 001111 => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => 111000 => 000111 => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => 111000 => 000111 => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => 111000 => 000111 => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => 111000 => 000111 => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => 111000 => 000111 => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => 110000 => 000011 => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => 110111 => 111011 => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => 110110 => 111001 => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => 110110 => 111001 => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => 110110 => 111001 => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => 110100 => 111000 => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => 110101 => 111010 => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => 110100 => 111000 => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => 110110 => 111001 => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => 110110 => 111001 => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => 110100 => 111000 => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => 110100 => 111000 => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => 110100 => 111000 => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => 110100 => 111000 => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => 110000 => 000011 => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => 111011 => 111101 => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => 111010 => 111100 => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => 111010 => 111100 => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => 111010 => 111100 => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => 111000 => 000111 => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => 111101 => 111110 => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => 111100 => 001111 => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => 111110 => 011111 => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => 111110 => 011111 => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => 111100 => 001111 => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => 111100 => 001111 => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => 111100 => 001111 => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => 111100 => 001111 => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => 111000 => 000111 => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => 111001 => 011110 => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => 111000 => 000111 => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => 111010 => 111100 => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => 111010 => 111100 => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => 111000 => 000111 => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => 111100 => 001111 => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => 111100 => 001111 => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => 111100 => 001111 => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => 111000 => 000111 => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => 111000 => 000111 => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => 111000 => 000111 => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => 111000 => 000111 => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => 111000 => 000111 => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => 110000 => 000011 => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => 110011 => 011101 => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => 110010 => 011100 => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => 110010 => 011100 => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => 110010 => 011100 => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => 110000 => 000011 => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => 110101 => 111010 => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => 110100 => 111000 => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => 110110 => 111001 => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => 110110 => 111001 => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => 110100 => 111000 => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => 110100 => 111000 => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => 110100 => 111000 => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => 110100 => 111000 => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => 110000 => 000011 => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => 111001 => 011110 => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => 111000 => 000111 => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => 111010 => 111100 => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => 111010 => 111100 => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => 111000 => 000111 => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => 111100 => 001111 => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => 111100 => 001111 => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => 111100 => 001111 => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => 111000 => 000111 => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => 111000 => 000111 => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => 111000 => 000111 => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => 111000 => 000111 => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => 111000 => 000111 => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => 110000 => 000011 => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => 110001 => 001110 => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => 110000 => 000011 => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => 110010 => 011100 => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => 110010 => 011100 => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => 110000 => 000011 => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => 110100 => 111000 => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => 110100 => 111000 => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => 110100 => 111000 => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => 110000 => 000011 => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => 111000 => 000111 => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => 111000 => 000111 => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => 111000 => 000111 => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => 111000 => 000111 => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => 110000 => 000011 => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => 110000 => 000011 => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => 110000 => 000011 => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => 110000 => 000011 => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => 110000 => 000011 => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => 110000 => 000011 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 100000 => 000001 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => 101111 => 110111 => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => 101110 => 110011 => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => 101110 => 110011 => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => 101110 => 110011 => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => 101100 => 110001 => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => 101101 => 110110 => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => 101100 => 110001 => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => 101110 => 110011 => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => 101110 => 110011 => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => 101100 => 110001 => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => 101100 => 110001 => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => 101100 => 110001 => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => 101100 => 110001 => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => 101000 => 110000 => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => 101011 => 110101 => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => 101010 => 110100 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => 101010 => 110100 => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => 101010 => 110100 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => 101000 => 110000 => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => 101101 => 110110 => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => 101100 => 110001 => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => 101110 => 110011 => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => 101110 => 110011 => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => 101100 => 110001 => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => 101100 => 110001 => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => 101100 => 110001 => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => 101100 => 110001 => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => 101000 => 110000 => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => 101001 => 110010 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => 101000 => 110000 => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => 101010 => 110100 => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => 101010 => 110100 => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => 101000 => 110000 => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => 101100 => 110001 => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => 101100 => 110001 => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => 101100 => 110001 => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => 101000 => 110000 => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => 101000 => 110000 => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => 101000 => 110000 => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => 101000 => 110000 => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => 101000 => 110000 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => 100000 => 000001 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => 110111 => 111011 => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => 110110 => 111001 => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => 110110 => 111001 => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => 110110 => 111001 => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => 110100 => 111000 => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => 110101 => 111010 => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => 110100 => 111000 => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => 110110 => 111001 => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => 110110 => 111001 => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => 110100 => 111000 => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => 110100 => 111000 => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => 110100 => 111000 => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => 110100 => 111000 => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => 110000 => 000011 => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => 111011 => 111101 => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => 111010 => 111100 => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => 111010 => 111100 => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => 111010 => 111100 => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => 111000 => 000111 => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => 111101 => 111110 => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => 111100 => 001111 => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => 111110 => 011111 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => 111110 => 011111 => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => 111100 => 001111 => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => 111100 => 001111 => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => 111100 => 001111 => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => 111100 => 001111 => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => 111000 => 000111 => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => 111001 => 011110 => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => 111000 => 000111 => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => 111010 => 111100 => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => 111010 => 111100 => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => 111000 => 000111 => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => 111100 => 001111 => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => 111100 => 001111 => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => 111100 => 001111 => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => 111000 => 000111 => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => 111000 => 000111 => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => 111000 => 000111 => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => 111000 => 000111 => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => 111000 => 000111 => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => 110000 => 000011 => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => 110011 => 011101 => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => 110010 => 011100 => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => 110010 => 011100 => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => 110010 => 011100 => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => 110000 => 000011 => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => 110101 => 111010 => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => 110100 => 111000 => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => 110110 => 111001 => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => 110110 => 111001 => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => 110100 => 111000 => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => 110100 => 111000 => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => 110100 => 111000 => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => 110100 => 111000 => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => 110000 => 000011 => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => 111001 => 011110 => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => 111000 => 000111 => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => 111010 => 111100 => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => 111010 => 111100 => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => 111000 => 000111 => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => 111100 => 001111 => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => 111100 => 001111 => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => 111100 => 001111 => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => 111000 => 000111 => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => 111000 => 000111 => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => 111000 => 000111 => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => 111000 => 000111 => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => 111000 => 000111 => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => 110000 => 000011 => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => 110001 => 001110 => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => 110000 => 000011 => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => 110010 => 011100 => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => 110010 => 011100 => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => 110000 => 000011 => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => 110100 => 111000 => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => 110100 => 111000 => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => 110100 => 111000 => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => 110000 => 000011 => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => 111000 => 000111 => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => 111000 => 000111 => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => 111000 => 000111 => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => 111000 => 000111 => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => 110000 => 000011 => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => 110000 => 000011 => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => 110000 => 000011 => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => 110000 => 000011 => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => 110000 => 000011 => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => 110000 => 000011 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => 100000 => 000001 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => 100111 => 011011 => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => 100110 => 011001 => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => 100110 => 011001 => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => 100110 => 011001 => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => 100100 => 011000 => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => 100101 => 011010 => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => 100100 => 011000 => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => 100110 => 011001 => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => 100110 => 011001 => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => 100100 => 011000 => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => 100100 => 011000 => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => 100100 => 011000 => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => 100100 => 011000 => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => 100000 => 000001 => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => 101011 => 110101 => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => 101010 => 110100 => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => 101010 => 110100 => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => 101010 => 110100 => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => 101000 => 110000 => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => 101101 => 110110 => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => 101100 => 110001 => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => 101110 => 110011 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => 101110 => 110011 => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => 101100 => 110001 => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => 101100 => 110001 => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => 101100 => 110001 => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => 101100 => 110001 => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => 101000 => 110000 => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => 101001 => 110010 => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => 101000 => 110000 => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => 101010 => 110100 => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => 101010 => 110100 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => 101000 => 110000 => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => 101100 => 110001 => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => 101100 => 110001 => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => 101100 => 110001 => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => 101000 => 110000 => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => 101000 => 110000 => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => 101000 => 110000 => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => 101000 => 110000 => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => 101000 => 110000 => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => 100000 => 000001 => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => 110011 => 011101 => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => 110010 => 011100 => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => 110010 => 011100 => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => 110010 => 011100 => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => 110000 => 000011 => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => 110101 => 111010 => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => 110100 => 111000 => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => 110110 => 111001 => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => 110110 => 111001 => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => 110100 => 111000 => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => 110100 => 111000 => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => 110100 => 111000 => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => 110100 => 111000 => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => 110000 => 000011 => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => 111001 => 011110 => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => 111000 => 000111 => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => 111010 => 111100 => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => 111010 => 111100 => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => 111000 => 000111 => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => 111100 => 001111 => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => 111100 => 001111 => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => 111100 => 001111 => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => 111000 => 000111 => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => 111000 => 000111 => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => 111000 => 000111 => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => 111000 => 000111 => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => 111000 => 000111 => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => 110000 => 000011 => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => 110001 => 001110 => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => 110000 => 000011 => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => 110010 => 011100 => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => 110010 => 011100 => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => 110000 => 000011 => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => 110100 => 111000 => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => 110100 => 111000 => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => 110100 => 111000 => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => 110000 => 000011 => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => 111000 => 000111 => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => 111000 => 000111 => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => 111000 => 000111 => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => 111000 => 000111 => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => 110000 => 000011 => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => 110000 => 000011 => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => 110000 => 000011 => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => 110000 => 000011 => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => 110000 => 000011 => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => 110000 => 000011 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => 100000 => 000001 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => 100011 => 001101 => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => 100010 => 001100 => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => 100010 => 001100 => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => 100010 => 001100 => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => 100000 => 000001 => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => 100101 => 011010 => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => 100100 => 011000 => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => 100110 => 011001 => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => 100110 => 011001 => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => 100100 => 011000 => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => 100100 => 011000 => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => 100100 => 011000 => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => 100100 => 011000 => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => 100000 => 000001 => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => 101001 => 110010 => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => 101000 => 110000 => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => 101010 => 110100 => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => 101010 => 110100 => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => 101000 => 110000 => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => 101100 => 110001 => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => 101100 => 110001 => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => 101100 => 110001 => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => 101000 => 110000 => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => 101000 => 110000 => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => 101000 => 110000 => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => 101000 => 110000 => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => 101000 => 110000 => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => 100000 => 000001 => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => 110001 => 001110 => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => 110000 => 000011 => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => 110010 => 011100 => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => 110010 => 011100 => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => 110000 => 000011 => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => 110100 => 111000 => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => 110100 => 111000 => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => 110100 => 111000 => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => 110000 => 000011 => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => 111000 => 000111 => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => 111000 => 000111 => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => 111000 => 000111 => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => 111000 => 000111 => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => 110000 => 000011 => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => 110000 => 000011 => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => 110000 => 000011 => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => 110000 => 000011 => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => 110000 => 000011 => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => 110000 => 000011 => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => 100000 => 000001 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => 100001 => 000110 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => 100000 => 000001 => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => 100010 => 001100 => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => 100010 => 001100 => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => 100000 => 000001 => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => 100100 => 011000 => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => 100100 => 011000 => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => 100100 => 011000 => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => 100000 => 000001 => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => 101000 => 110000 => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => 101000 => 110000 => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => 101000 => 110000 => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => 101000 => 110000 => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => 100000 => 000001 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => 110000 => 000011 => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => 110000 => 000011 => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => 110000 => 000011 => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => 110000 => 000011 => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => 110000 => 000011 => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => 100000 => 000001 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => 100000 => 000001 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => 100000 => 000001 => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => 100000 => 000001 => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => 100000 => 000001 => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => 100000 => 000001 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => 100000 => 000001 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => 000000 => 000000 => 0
[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] => 1111110 => 0111111 => 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] => 1111110 => 0111111 => 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] => 1111110 => 0111111 => 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] => 1111100 => 0011111 => 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] => 1111101 => 1111110 => 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] => 1111100 => 0011111 => 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] => 1111110 => 0111111 => 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] => 1111110 => 0111111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111000 => 0001111 => 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] => 1111011 => 1111101 => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 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] => 1111000 => 0001111 => 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] => 1111101 => 1111110 => 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] => 1111110 => 0111111 => 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] => 1111110 => 0111111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111000 => 0001111 => 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] => 1111001 => 0111110 => 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] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 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] => 1111000 => 0001111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1110000 => 0000111 => 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] => 1110111 => 1111011 => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => 1110110 => 1111001 => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => 1110110 => 1111001 => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => 1110110 => 1111001 => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => 1110101 => 1111010 => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => 1110100 => 1111000 => 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] => 1110110 => 1111001 => 4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 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] => 1110000 => 0000111 => 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] => 1111011 => 1111101 => 5
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,2,1] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 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] => 1111000 => 0001111 => 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] => 1111101 => 1111110 => 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] => 1111100 => 0011111 => 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] => 1111110 => 0111111 => 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] => 1111110 => 0111111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111000 => 0001111 => 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] => 1111001 => 0111110 => 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] => 1111010 => 1111100 => 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] => 1111000 => 0001111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1110000 => 0000111 => 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] => 1110011 => 0111101 => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => 1110010 => 0111100 => 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] => 1110010 => 0111100 => 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] => 1110010 => 0111100 => 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] => 1110000 => 0000111 => 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] => 1110101 => 1111010 => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => 1110100 => 1111000 => 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] => 1110110 => 1111001 => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => 1111001 => 0111110 => 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] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1110000 => 0000111 => 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] => 1110001 => 0011110 => 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] => 1110000 => 0000111 => 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] => 1110010 => 0111100 => 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] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1100000 => 0000011 => 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] => 1101111 => 1110111 => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => 1101110 => 1110011 => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => 1101110 => 1110011 => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => 1101110 => 1110011 => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => 1101101 => 1110110 => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => 1101110 => 1110011 => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => 1101110 => 1110011 => 3
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => 1101100 => 1110001 => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => 1101100 => 1110001 => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,3,1] => 1101100 => 1110001 => 3
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => 1101000 => 1110000 => 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] => 1101011 => 1110101 => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => 1101010 => 1110100 => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => 1101010 => 1110100 => 3
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => 1101000 => 1110000 => 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] => 1101101 => 1110110 => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,3,1] => 1101110 => 1110011 => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,3,1] => 1101110 => 1110011 => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => 1101100 => 1110001 => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => 1101100 => 1110001 => 3
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => 1101100 => 1110001 => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => 1101001 => 1110010 => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => 1101000 => 1110000 => 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] => 1101010 => 1110100 => 3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 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] => 1100000 => 0000011 => 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] => 1110111 => 1111011 => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => 1110110 => 1111001 => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,4,1] => 1110110 => 1111001 => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => 1110110 => 1111001 => 4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => 1110100 => 1111000 => 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] => 1110101 => 1111010 => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => 1110110 => 1111001 => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => 1110110 => 1111001 => 4
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 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] => 1110000 => 0000111 => 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] => 1111011 => 1111101 => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,5,1] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 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] => 1111000 => 0001111 => 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] => 1111101 => 1111110 => 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] => 1111100 => 0011111 => 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] => 1111110 => 0111111 => 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] => 1111110 => 0111111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111000 => 0001111 => 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] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 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] => 1111000 => 0001111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1110000 => 0000111 => 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] => 1110011 => 0111101 => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => 1110010 => 0111100 => 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] => 1110010 => 0111100 => 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] => 1110010 => 0111100 => 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] => 1110000 => 0000111 => 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] => 1110101 => 1111010 => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => 1110100 => 1111000 => 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] => 1110110 => 1111001 => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => 1110110 => 1111001 => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 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] => 1110000 => 0000111 => 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] => 1111001 => 0111110 => 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] => 1111000 => 0001111 => 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] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1110000 => 0000111 => 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] => 1110010 => 0111100 => 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] => 1110010 => 0111100 => 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] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 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] => 1110000 => 0000111 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1100000 => 0000011 => 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] => 1100111 => 0111011 => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => 1100110 => 0111001 => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,4,1] => 1100110 => 0111001 => 3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => 1100100 => 0111000 => 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] => 1100101 => 0111010 => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,4,1] => 1100100 => 0111000 => 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] => 1100110 => 0111001 => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => 1100110 => 0111001 => 3
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => 1100100 => 0111000 => 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] => 1100100 => 0111000 => 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] => 1100100 => 0111000 => 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] => 1100000 => 0000011 => 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] => 1101011 => 1110101 => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,5,1] => 1101010 => 1110100 => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,5,1] => 1101010 => 1110100 => 3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => 1101000 => 1110000 => 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] => 1101101 => 1110110 => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => 1101110 => 1110011 => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => 1101110 => 1110011 => 3
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,8,1] => 1101100 => 1110001 => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,7,1] => 1101100 => 1110001 => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => 1101100 => 1110001 => 3
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => 1101100 => 1110001 => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,8,1] => 1101000 => 1110000 => 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] => 1101010 => 1110100 => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,8,1] => 1101010 => 1110100 => 3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => 1101000 => 1110000 => 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] => 1101100 => 1110001 => 3
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => 1101100 => 1110001 => 3
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 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] => 1100000 => 0000011 => 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] => 1110011 => 0111101 => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => 1110010 => 0111100 => 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] => 1110010 => 0111100 => 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] => 1110000 => 0000111 => 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] => 1110101 => 1111010 => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => 1110110 => 1111001 => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => 1110110 => 1111001 => 4
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 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] => 1111001 => 0111110 => 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] => 1111000 => 0001111 => 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] => 1111010 => 1111100 => 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] => 1111000 => 0001111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1100000 => 0000011 => 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] => 1100011 => 0011101 => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => 1100010 => 0011100 => 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] => 1100010 => 0011100 => 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] => 1100010 => 0011100 => 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] => 1100000 => 0000011 => 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] => 1100110 => 0111001 => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => 1100100 => 0111000 => 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] => 1100000 => 0000011 => 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] => 1101000 => 1110000 => 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] => 1101010 => 1110100 => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => 1101010 => 1110100 => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,7,1] => 1101100 => 1110001 => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => 1101100 => 1110001 => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => 1101100 => 1110001 => 3
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,7,8,1] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 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] => 1100000 => 0000011 => 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] => 1110000 => 0000111 => 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] => 1110010 => 0111100 => 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] => 1110000 => 0000111 => 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] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 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] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1100000 => 0000011 => 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] => 1100001 => 0001110 => 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] => 1100000 => 0000011 => 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] => 1100010 => 0011100 => 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] => 1100000 => 0000011 => 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] => 1100100 => 0111000 => 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] => 1100100 => 0111000 => 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] => 1100100 => 0111000 => 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] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 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] => 1100000 => 0000011 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 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] => 1100000 => 0000011 => 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] => 1100000 => 0000011 => 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] => 1100000 => 0000011 => 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] => 1100000 => 0000011 => 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] => 1100000 => 0000011 => 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] => 1100000 => 0000011 => 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] => 1100000 => 0000011 => 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] => 1000000 => 0000001 => 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] => 1011111 => 1101111 => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => 1011110 => 1100111 => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => 1011110 => 1100111 => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => 1011110 => 1100111 => 3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => 1011101 => 1101110 => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => 1011110 => 1100111 => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => 1011110 => 1100111 => 3
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => 1011011 => 1101101 => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => 1011010 => 1101100 => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => 1011010 => 1101100 => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => 1011101 => 1101110 => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => 1011110 => 1100111 => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => 1011010 => 1101100 => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => 1011010 => 1101100 => 2
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => 1010000 => 1100000 => 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] => 1010111 => 1101011 => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => 1010110 => 1101001 => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => 1010110 => 1101001 => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => 1010100 => 1101000 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => 1010101 => 1101010 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => 1010100 => 1101000 => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => 1010110 => 1101001 => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => 1010110 => 1101001 => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => 1010100 => 1101000 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => 1010100 => 1101000 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => 1010100 => 1101000 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => 1010100 => 1101000 => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => 1010000 => 1100000 => 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] => 1011000 => 1100001 => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => 1011110 => 1100111 => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => 1011110 => 1100111 => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => 1011001 => 1100110 => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => 1010000 => 1100000 => 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] => 1010011 => 1100101 => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,1,2] => 1010010 => 1100100 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => 1010010 => 1100100 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,1,2] => 1010000 => 1100000 => 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] => 1010100 => 1101000 => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,1,2] => 1010110 => 1101001 => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,8,1,2] => 1010100 => 1101000 => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,8,1,2] => 1010000 => 1100000 => 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] => 1011001 => 1100110 => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,1,2] => 1011010 => 1101100 => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => 1011100 => 1100011 => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,8,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => 1010000 => 1100000 => 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] => 1010001 => 1100010 => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => 1010000 => 1100000 => 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] => 1010010 => 1100100 => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,1,2] => 1010100 => 1101000 => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => 1010100 => 1101000 => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,1,2] => 1010100 => 1101000 => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => 1010000 => 1100000 => 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] => 1011000 => 1100001 => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => 1011000 => 1100001 => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => 1010000 => 1100000 => 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] => 1010000 => 1100000 => 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] => 1010000 => 1100000 => 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] => 1010000 => 1100000 => 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] => 1010000 => 1100000 => 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] => 1010000 => 1100000 => 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] => 1000000 => 0000001 => 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] => 1101111 => 1110111 => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => 1101110 => 1110011 => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => 1101110 => 1110011 => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => 1101110 => 1110011 => 3
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,1,3] => 1101100 => 1110001 => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => 1101101 => 1110110 => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => 1101100 => 1110001 => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,1,3] => 1101110 => 1110011 => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => 1101110 => 1110011 => 3
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => 1101100 => 1110001 => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => 1101100 => 1110001 => 3
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,1,3] => 1101100 => 1110001 => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => 1101000 => 1110000 => 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] => 1101011 => 1110101 => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,1,3] => 1101010 => 1110100 => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,1,3] => 1101010 => 1110100 => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,1,3] => 1101110 => 1110011 => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => 1101110 => 1110011 => 3
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,1,3] => 1101100 => 1110001 => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,1,3] => 1101100 => 1110001 => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => 1101100 => 1110001 => 3
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => 1101000 => 1110000 => 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] => 1101001 => 1110010 => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,1,3] => 1101010 => 1110100 => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,1,3] => 1101010 => 1110100 => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 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] => 1100000 => 0000011 => 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] => 1110111 => 1111011 => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => 1110110 => 1111001 => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => 1110110 => 1111001 => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => 1110110 => 1111001 => 4
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => 1110100 => 1111000 => 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] => 1110101 => 1111010 => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => 1110100 => 1111000 => 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] => 1110110 => 1111001 => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => 1110110 => 1111001 => 4
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 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] => 1110000 => 0000111 => 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] => 1111011 => 1111101 => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 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] => 1111000 => 0001111 => 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] => 1111101 => 1111110 => 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] => 1111100 => 0011111 => 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] => 1111110 => 0111111 => 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 => 0111111 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => 1111100 => 0011111 => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 5
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => 1111100 => 0011111 => 5
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => 1111000 => 0001111 => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => 1111001 => 0111110 => 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] => 1111000 => 0001111 => 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] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 5
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => 1111000 => 0001111 => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,1,7] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 5
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => 1111100 => 0011111 => 5
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => 1111000 => 0001111 => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 4
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => 1111000 => 0001111 => 4
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => 1110000 => 0000111 => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => 1110011 => 0111101 => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,1,5] => 1110010 => 0111100 => 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] => 1110000 => 0000111 => 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] => 1110101 => 1111010 => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => 1110110 => 1111001 => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => 1110110 => 1111001 => 4
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => 1110100 => 1111000 => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 4
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,1,8] => 1110100 => 1111000 => 4
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => 1110000 => 0000111 => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,1,6] => 1111001 => 0111110 => 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] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 5
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => 1111000 => 0001111 => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => 1111100 => 0011111 => 5
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => 1111100 => 0011111 => 5
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => 1111000 => 0001111 => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 4
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => 1111000 => 0001111 => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => 1110001 => 0011110 => 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] => 1110000 => 0000111 => 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] => 1110010 => 0111100 => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 3
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => 1100000 => 0000011 => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => 1100111 => 0111011 => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => 1100110 => 0111001 => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => 1100110 => 0111001 => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => 1100110 => 0111001 => 3
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => 1100100 => 0111000 => 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] => 1100101 => 0111010 => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => 1100100 => 0111000 => 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] => 1100110 => 0111001 => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => 1100110 => 0111001 => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => 1100100 => 0111000 => 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] => 1100100 => 0111000 => 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] => 1100100 => 0111000 => 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] => 1100100 => 0111000 => 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] => 1100000 => 0000011 => 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] => 1101011 => 1110101 => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,1,5] => 1101010 => 1110100 => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,1,5] => 1101010 => 1110100 => 3
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => 1101000 => 1110000 => 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] => 1101110 => 1110011 => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => 1101110 => 1110011 => 3
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => 1101100 => 1110001 => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => 1101100 => 1110001 => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => 1101100 => 1110001 => 3
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => 1101000 => 1110000 => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => 1101001 => 1110010 => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => 1101000 => 1110000 => 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] => 1101010 => 1110100 => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => 1101010 => 1110100 => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => 1101000 => 1110000 => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => 1101100 => 1110001 => 3
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => 1101100 => 1110001 => 3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => 1101000 => 1110000 => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 3
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => 1101000 => 1110000 => 3
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => 1100000 => 0000011 => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => 1110011 => 0111101 => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => 1110010 => 0111100 => 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] => 1110000 => 0000111 => 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] => 1110101 => 1111010 => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => 1110110 => 1111001 => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => 1110110 => 1111001 => 4
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => 1110100 => 1111000 => 4
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => 1110000 => 0000111 => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => 1111001 => 0111110 => 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] => 1111000 => 0001111 => 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] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 5
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => 1111000 => 0001111 => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 5
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => 1111100 => 0011111 => 5
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => 1111000 => 0001111 => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => 1111000 => 0001111 => 4
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => 1111000 => 0001111 => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,1,6] => 1110001 => 0011110 => 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] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => 1110100 => 1111000 => 4
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => 1110000 => 0000111 => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 4
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => 1111000 => 0001111 => 4
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => 1110000 => 0000111 => 3
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => 1110000 => 0000111 => 3
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => 1110000 => 0000111 => 3
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => 1110000 => 0000111 => 3
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => 1100000 => 0000011 => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => 1100011 => 0011101 => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => 1100010 => 0011100 => 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] => 1100010 => 0011100 => 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] => 1100000 => 0000011 => 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] => 1100100 => 0111000 => 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] => 1100110 => 0111001 => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => 1100110 => 0111001 => 3
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => 1100100 => 0111000 => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,4,1,7] => 1100100 => 0111000 => 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] => 1100100 => 0111000 => 3
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => 1100100 => 0111000 => 3
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => 1100000 => 0000011 => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => 1101010 => 1110100 => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => 1101010 => 1110100 => 3
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => 1101000 => 1110000 => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,1,7] => 1101100 => 1110001 => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,1,8] => 1101100 => 1110001 => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 3
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => 1101000 => 1110000 => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => 1110010 => 0111100 => 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] => 1110010 => 0111100 => 4
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => 1110000 => 0000111 => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 4
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => 1110100 => 1111000 => 4
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => 1111000 => 0001111 => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,1,7] => 1110000 => 0000111 => 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] => 1100000 => 0000011 => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => 1100001 => 0001110 => 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] => 1100000 => 0000011 => 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] => 1100010 => 0011100 => 3
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => 1100000 => 0000011 => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,1,7] => 1100100 => 0111000 => 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] => 1101000 => 1110000 => 3
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => 1100000 => 0000011 => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 3
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => 1110000 => 0000111 => 3
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => 1100000 => 0000011 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => 1100000 => 0000011 => 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] => 1100000 => 0000011 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => 1100000 => 0000011 => 2
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => 1100000 => 0000011 => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => 1100000 => 0000011 => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => 1100000 => 0000011 => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => 1000000 => 0000001 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => 1001111 => 0110111 => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => 1001110 => 0110011 => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,1,2,3] => 1001110 => 0110011 => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => 1001100 => 0110001 => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => 1001100 => 0110001 => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,1,2,3] => 1001110 => 0110011 => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,1,2,3] => 1001110 => 0110011 => 2
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => 1001100 => 0110001 => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => 1001100 => 0110001 => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => 1001100 => 0110001 => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => 1001100 => 0110001 => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => 1001000 => 0110000 => 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] => 1001011 => 0110101 => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => 1001010 => 0110100 => 2
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => 1001000 => 0110000 => 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] => 1001101 => 0110110 => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => 1001100 => 0110001 => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,1,2,3] => 1001110 => 0110011 => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => 1001110 => 0110011 => 2
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,1,2,3] => 1001100 => 0110001 => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,1,2,3] => 1001100 => 0110001 => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,1,2,3] => 1001100 => 0110001 => 2
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => 1001100 => 0110001 => 2
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,1,2,3] => 1001000 => 0110000 => 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] => 1001001 => 0110010 => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => 1001000 => 0110000 => 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] => 1001010 => 0110100 => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,1,2,3] => 1001010 => 0110100 => 2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => 1001000 => 0110000 => 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] => 1001100 => 0110001 => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => 1001100 => 0110001 => 2
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => 1001100 => 0110001 => 2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,1,2,3] => 1001000 => 0110000 => 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] => 1001000 => 0110000 => 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] => 1001000 => 0110000 => 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] => 1001000 => 0110000 => 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] => 1001000 => 0110000 => 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] => 1000000 => 0000001 => 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] => 1010111 => 1101011 => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,1,2,4] => 1010110 => 1101001 => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => 1010110 => 1101001 => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => 1010110 => 1101001 => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => 1010101 => 1101010 => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => 1010100 => 1101000 => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,1,2,4] => 1010110 => 1101001 => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => 1010110 => 1101001 => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => 1010100 => 1101000 => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => 1010100 => 1101000 => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => 1010100 => 1101000 => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => 1010000 => 1100000 => 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] => 1011011 => 1101101 => 2
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => 1011000 => 1100001 => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => 1011101 => 1101110 => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,1,2,6] => 1011100 => 1100011 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => 1011110 => 1100111 => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => 1011110 => 1100111 => 3
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => 1011100 => 1100011 => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => 1011100 => 1100011 => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => 1011010 => 1101100 => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => 1011010 => 1101100 => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,1,2,8] => 1011000 => 1100001 => 2
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => 1011000 => 1100001 => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => 1010000 => 1100000 => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => 1010011 => 1100101 => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => 1010010 => 1100100 => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => 1010010 => 1100100 => 2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => 1010000 => 1100000 => 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] => 1010101 => 1101010 => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,1,2,6] => 1010100 => 1101000 => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => 1010110 => 1101001 => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => 1010110 => 1101001 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => 1010100 => 1101000 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,1,2,8] => 1010100 => 1101000 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => 1010100 => 1101000 => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => 1011100 => 1100011 => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => 1011100 => 1100011 => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,1,2,7] => 1011000 => 1100001 => 2
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => 1011000 => 1100001 => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => 1010001 => 1100010 => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => 1010000 => 1100000 => 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] => 1010010 => 1100100 => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => 1010000 => 1100000 => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => 1010100 => 1101000 => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,1,2,8] => 1010100 => 1101000 => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => 1010000 => 1100000 => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => 1011000 => 1100001 => 2
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,1,2,8] => 1011000 => 1100001 => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => 1010000 => 1100000 => 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] => 1010000 => 1100000 => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,1,2,8] => 1010000 => 1100000 => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => 1000000 => 0000001 => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => 1100111 => 0111011 => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => 1100110 => 0111001 => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,1,3,4] => 1100110 => 0111001 => 3
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => 1100100 => 0111000 => 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] => 1100101 => 0111010 => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => 1100100 => 0111000 => 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] => 1100110 => 0111001 => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => 1100110 => 0111001 => 3
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => 1100100 => 0111000 => 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] => 1100100 => 0111000 => 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] => 1100100 => 0111000 => 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] => 1100100 => 0111000 => 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] => 1100000 => 0000011 => 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] => 1101011 => 1110101 => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,1,3,5] => 1101010 => 1110100 => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => 1101010 => 1110100 => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => 1101000 => 1110000 => 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] => 1101100 => 1110001 => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => 1101110 => 1110011 => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => 1101110 => 1110011 => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => 1101100 => 1110001 => 3
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => 1101100 => 1110001 => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,1,3,7] => 1101010 => 1110100 => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => 1101010 => 1110100 => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => 1101100 => 1110001 => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 3
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,1,3,8] => 1101000 => 1110000 => 3
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => 1100000 => 0000011 => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => 1110011 => 0111101 => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => 1110010 => 0111100 => 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] => 1110010 => 0111100 => 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] => 1110010 => 0111100 => 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] => 1110000 => 0000111 => 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] => 1110101 => 1111010 => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => 1110100 => 1111000 => 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] => 1110110 => 1111001 => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => 1110110 => 1111001 => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => 1110100 => 1111000 => 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] => 1111001 => 0111110 => 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] => 1111000 => 0001111 => 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] => 1111010 => 1111100 => 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] => 1111010 => 1111100 => 5
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => 1111000 => 0001111 => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => 1111100 => 0011111 => 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] => 1111100 => 0011111 => 5
[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 => 0011111 => 5
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => 1111000 => 0001111 => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 4
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => 1111000 => 0001111 => 4
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => 1110000 => 0000111 => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => 1110001 => 0011110 => 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] => 1110000 => 0000111 => 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] => 1110010 => 0111100 => 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] => 1110010 => 0111100 => 4
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => 1110000 => 0000111 => 3
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => 1110100 => 1111000 => 4
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => 1110000 => 0000111 => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,1,6,7] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 4
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => 1111000 => 0001111 => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 3
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => 1100000 => 0000011 => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => 1100011 => 0011101 => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => 1100010 => 0011100 => 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] => 1100010 => 0011100 => 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] => 1100010 => 0011100 => 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] => 1100000 => 0000011 => 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] => 1100101 => 0111010 => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => 1100110 => 0111001 => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => 1100110 => 0111001 => 3
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,1,4,8] => 1100100 => 0111000 => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => 1100100 => 0111000 => 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] => 1100100 => 0111000 => 3
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,1,4,8] => 1100100 => 0111000 => 3
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => 1100000 => 0000011 => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => 1101000 => 1110000 => 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] => 1101010 => 1110100 => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => 1101010 => 1110100 => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => 1101100 => 1110001 => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,1,6,7] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => 1110001 => 0011110 => 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] => 1110000 => 0000111 => 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] => 1110010 => 0111100 => 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] => 1110010 => 0111100 => 4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => 1110000 => 0000111 => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => 1110100 => 1111000 => 4
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => 1110000 => 0000111 => 3
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => 1111000 => 0001111 => 4
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => 1111000 => 0001111 => 4
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => 1110000 => 0000111 => 3
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => 1110000 => 0000111 => 3
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => 1100000 => 0000011 => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => 1100001 => 0001110 => 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] => 1100000 => 0000011 => 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] => 1100010 => 0011100 => 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] => 1100010 => 0011100 => 3
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => 1100000 => 0000011 => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => 1100100 => 0111000 => 3
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => 1100100 => 0111000 => 3
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => 1100000 => 0000011 => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => 1110000 => 0000111 => 3
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => 1110000 => 0000111 => 3
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => 1100000 => 0000011 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => 1100000 => 0000011 => 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] => 1100000 => 0000011 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => 1100000 => 0000011 => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => 1100000 => 0000011 => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => 1100000 => 0000011 => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => 1100000 => 0000011 => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => 1000000 => 0000001 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => 1000111 => 0011011 => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => 1000110 => 0011001 => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => 1000110 => 0011001 => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => 1000110 => 0011001 => 2
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => 1000100 => 0011000 => 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] => 1000101 => 0011010 => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => 1000100 => 0011000 => 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] => 1000110 => 0011001 => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => 1000110 => 0011001 => 2
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => 1000100 => 0011000 => 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] => 1000100 => 0011000 => 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] => 1000100 => 0011000 => 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] => 1000100 => 0011000 => 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] => 1000000 => 0000001 => 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] => 1001011 => 0110101 => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,1,2,3,5] => 1001010 => 0110100 => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,1,2,3,5] => 1001010 => 0110100 => 2
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => 1001000 => 0110000 => 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] => 1001101 => 0110110 => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => 1001100 => 0110001 => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => 1001110 => 0110011 => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => 1001110 => 0110011 => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => 1001100 => 0110001 => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,1,2,3,8] => 1001100 => 0110001 => 2
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => 1001000 => 0110000 => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,1,2,3,6] => 1001001 => 0110010 => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => 1001000 => 0110000 => 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] => 1001010 => 0110100 => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,1,2,3,8] => 1001010 => 0110100 => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,1,2,3,8] => 1001100 => 0110001 => 2
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => 1001000 => 0110000 => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => 1001000 => 0110000 => 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] => 1001000 => 0110000 => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => 1001000 => 0110000 => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => 1000000 => 0000001 => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => 1010011 => 1100101 => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => 1010010 => 1100100 => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => 1010010 => 1100100 => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => 1010010 => 1100100 => 2
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => 1010000 => 1100000 => 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] => 1010101 => 1101010 => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => 1010100 => 1101000 => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => 1010100 => 1101000 => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,1,2,4,8] => 1010100 => 1101000 => 2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => 1010000 => 1100000 => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => 1011000 => 1100001 => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => 1011010 => 1101100 => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => 1011010 => 1101100 => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => 1011100 => 1100011 => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => 1011100 => 1100011 => 2
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => 1011000 => 1100001 => 2
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => 1011000 => 1100001 => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => 1011000 => 1100001 => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => 1010001 => 1100010 => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => 1010000 => 1100000 => 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] => 1010010 => 1100100 => 2
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => 1010000 => 1100000 => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => 1010100 => 1101000 => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,1,2,6,8] => 1010100 => 1101000 => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => 1010000 => 1100000 => 2
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,1,2,7,8] => 1011000 => 1100001 => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => 1011000 => 1100001 => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,1,2,6,7] => 1010000 => 1100000 => 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] => 1010000 => 1100000 => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => 1000000 => 0000001 => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => 1100011 => 0011101 => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => 1100010 => 0011100 => 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] => 1100010 => 0011100 => 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] => 1100000 => 0000011 => 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] => 1100101 => 0111010 => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => 1100100 => 0111000 => 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] => 1100110 => 0111001 => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => 1100110 => 0111001 => 3
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,1,3,4,8] => 1100100 => 0111000 => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => 1100100 => 0111000 => 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] => 1100100 => 0111000 => 3
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => 1100000 => 0000011 => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => 1101001 => 1110010 => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => 1101000 => 1110000 => 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] => 1101010 => 1110100 => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => 1101010 => 1110100 => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => 1101100 => 1110001 => 3
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => 1101100 => 1110001 => 3
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => 1101000 => 1110000 => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => 1101000 => 1110000 => 3
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => 1101000 => 1110000 => 3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => 1101000 => 1110000 => 3
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => 1110001 => 0011110 => 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] => 1110000 => 0000111 => 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] => 1110010 => 0111100 => 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] => 1110010 => 0111100 => 4
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => 1110000 => 0000111 => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => 1110100 => 1111000 => 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] => 1110100 => 1111000 => 4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => 1110100 => 1111000 => 4
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => 1110000 => 0000111 => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => 1111000 => 0001111 => 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] => 1111000 => 0001111 => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => 1111000 => 0001111 => 4
[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 => 0001111 => 4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => 1110000 => 0000111 => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 3
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => 1110000 => 0000111 => 3
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => 1110000 => 0000111 => 3
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => 1100001 => 0001110 => 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] => 1100000 => 0000011 => 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] => 1100010 => 0011100 => 3
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => 1100000 => 0000011 => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => 1100100 => 0111000 => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 3
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => 1110000 => 0000111 => 3
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => 1110000 => 0000111 => 3
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => 1100000 => 0000011 => 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] => 1100000 => 0000011 => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => 1000000 => 0000001 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => 1000011 => 0001101 => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => 1000010 => 0001100 => 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] => 1000010 => 0001100 => 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] => 1000010 => 0001100 => 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] => 1000000 => 0000001 => 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] => 1000101 => 0011010 => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => 1000100 => 0011000 => 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] => 1000110 => 0011001 => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => 1000110 => 0011001 => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => 1000100 => 0011000 => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => 1000100 => 0011000 => 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] => 1000100 => 0011000 => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => 1000100 => 0011000 => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => 1000000 => 0000001 => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => 1001001 => 0110010 => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,8,4,1,2,3,5,6] => 1001000 => 0110000 => 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] => 1001100 => 0110001 => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => 1001100 => 0110001 => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [8,4,5,1,2,3,6,7] => 1001000 => 0110000 => 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] => 1001000 => 0110000 => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => 1000000 => 0000001 => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => 1010000 => 1100000 => 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] => 1010000 => 1100000 => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => 1010100 => 1101000 => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => 1010100 => 1101000 => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => 1011000 => 1100001 => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => 1011000 => 1100001 => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => 1011000 => 1100001 => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => 1010000 => 1100000 => 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] => 1010000 => 1100000 => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => 1010000 => 1100000 => 2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => 1010000 => 1100000 => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => 1000000 => 0000001 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => 1100001 => 0001110 => 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] => 1100000 => 0000011 => 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] => 1100100 => 0111000 => 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] => 1100000 => 0000011 => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => 1101000 => 1110000 => 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] => 1101000 => 1110000 => 3
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => 1101000 => 1110000 => 3
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => 1110000 => 0000111 => 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] => 1110000 => 0000111 => 3
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,4,5,7,8] => 1110000 => 0000111 => 3
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => 1110000 => 0000111 => 3
[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 => 0000111 => 3
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => 1100000 => 0000011 => 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] => 1100000 => 0000011 => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => 1000000 => 0000001 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => 1000001 => 0000110 => 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] => 1000000 => 0000001 => 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] => 1000010 => 0001100 => 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] => 1000010 => 0001100 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => 1000000 => 0000001 => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => 1000100 => 0011000 => 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] => 1000100 => 0011000 => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => 1001000 => 0110000 => 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] => 1001000 => 0110000 => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => 1001000 => 0110000 => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => 1001000 => 0110000 => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => 1000000 => 0000001 => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => 1010000 => 1100000 => 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] => 1010000 => 1100000 => 2
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => 1010000 => 1100000 => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => 1010000 => 1100000 => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => 1010000 => 1100000 => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => 1000000 => 0000001 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => 1100000 => 0000011 => 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] => 1100000 => 0000011 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,3,4,5,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => 1100000 => 0000011 => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => 1100000 => 0000011 => 2
[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 => 0000011 => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => 1000000 => 0000001 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => 1000000 => 0000001 => 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] => 1000000 => 0000001 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => 1000000 => 0000001 => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => 1000000 => 0000001 => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => 1000000 => 0000001 => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => 1000000 => 0000001 => 1
[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 => 0000001 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => 0000000 => 0000000 => 0
[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] => 10000000 => 00000001 => 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] => 10000000 => 00000001 => 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] => 100000000 => 000000001 => 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] => 11000000 => 00000011 => 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] => 11000000 => 00000011 => 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] => 100000000 => 000000001 => 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] => 1000000000 => 0000000001 => 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] => 110000000 => 000000011 => 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] => 10100000 => 11000000 => 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] => 11000000 => 00000011 => 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] => 11000000 => 00000011 => 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] => 11000000 => 00000011 => 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] => 110000000 => 000000011 => 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] => 1000000000 => 0000000001 => 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] => 10000000000 => 00000000001 => 1
[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] => 101000000 => 110000000 => 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] => 110000000 => 000000011 => 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] => 10010000 => 01100000 => 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] => 11000000 => 00000011 => 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] => 11100000 => 00000111 => 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] => 110000000 => 000000011 => 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] => 100100000 => 011000000 => 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] => 110000000 => 000000011 => 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] => 10100000 => 11000000 => 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] => 11000000 => 00000011 => 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] => 11000000 => 00000011 => 2
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,10,1] => 111000000 => 000000111 => 3
[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] => 110000000 => 000000011 => 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] => 10000100 => 00011000 => 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] => 11000000 => 00000011 => 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] => 110000000 => 000000011 => 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] => 11010000 => 11100000 => 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] => 110000000 => 000000011 => 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] => 110000000 => 000000011 => 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] => 100001000 => 000110000 => 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] => 110000000 => 000000011 => 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] => 10000010 => 00001100 => 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] => 11000000 => 00000011 => 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] => 10000000 => 00000001 => 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] => 11000000 => 00000011 => 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] => 11110000 => 00001111 => 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] => 10000000 => 00000001 => 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] => 11000000 => 00000011 => 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] => 100000100 => 000011000 => 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] => 110000000 => 000000011 => 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] => 10000001 => 00000110 => 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] => 11000000 => 00000011 => 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] => 11000000 => 00000011 => 2
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,6,7,8,9,10,1] => 111100000 => 000001111 => 4
[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] => 10100000 => 11000000 => 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] => 11000000 => 00000011 => 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] => 110000000 => 000000011 => 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] => 100000000 => 000000001 => 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] => 11100000 => 00000111 => 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] => 110000000 => 000000011 => 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] => 10100000 => 11000000 => 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] => 10100000 => 11000000 => 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] => 100000000 => 000000001 => 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] => 110000000 => 000000011 => 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] => 100000001 => 000000110 => 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] => 110000000 => 000000011 => 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] => 11010000 => 11100000 => 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] => 11100000 => 00000111 => 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] => 11011000 => 11100001 => 3
[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] => 11000000 => 00000011 => 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] => 101000000 => 110000000 => 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] => 110000000 => 000000011 => 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 => 01111111 => 7
[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] => 11111100 => 00111111 => 6
[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] => 11111100 => 00111111 => 6
[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] => 11111100 => 00111111 => 6
[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] => 11111000 => 00011111 => 5
[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] => 11111010 => 11111100 => 6
[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] => 11111100 => 00111111 => 6
[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] => 11111100 => 00111111 => 6
[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] => 11111000 => 00011111 => 5
[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] => 11111000 => 00011111 => 5
[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] => 11111000 => 00011111 => 5
[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] => 11110110 => 11111001 => 5
[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] => 11111010 => 11111100 => 6
[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] => 11111000 => 00011111 => 5
[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] => 11110110 => 11111001 => 5
[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] => 11111100 => 00111111 => 6
[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] => 11111000 => 00011111 => 5
[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] => 11000000 => 00000011 => 2
[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] => 11011110 => 11100111 => 3
[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] => 11111100 => 00111111 => 6
[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] => 11110000 => 00001111 => 4
[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] => 11111000 => 00011111 => 5
[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] => 11000000 => 00000011 => 2
[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] => 11000000 => 00000011 => 2
[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] => 11000000 => 00000011 => 2
[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] => 10000000 => 00000001 => 1
[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] => 10111110 => 11001111 => 4
[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] => 10101000 => 11010000 => 2
[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] => 10100000 => 11000000 => 2
[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] => 10000000 => 00000001 => 1
[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] => 11011110 => 11100111 => 3
[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] => 11101110 => 11110011 => 4
[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] => 11110110 => 11111001 => 5
[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] => 11111010 => 11111100 => 6
[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] => 11111100 => 00111111 => 6
[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 => 00111111 => 6
[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] => 11111000 => 00011111 => 5
[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] => 11111000 => 00011111 => 5
[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] => 11110010 => 01111100 => 5
[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] => 11100110 => 01111001 => 4
[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] => 11000000 => 00000011 => 2
[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] => 11001110 => 01110011 => 3
[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] => 11111000 => 00011111 => 5
[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] => 11110000 => 00001111 => 4
[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] => 11000000 => 00000011 => 2
[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] => 11000000 => 00000011 => 2
[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] => 10000000 => 00000001 => 1
[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] => 10011110 => 01100111 => 3
[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] => 10000000 => 00000001 => 1
[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] => 10111000 => 11000011 => 2
[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] => 10000000 => 00000001 => 1
[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] => 11101100 => 11110001 => 4
[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] => 11110000 => 00001111 => 4
[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 => 00011111 => 5
[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] => 11110000 => 00001111 => 4
[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] => 11000000 => 00000011 => 2
[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] => 11110000 => 00001111 => 4
[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] => 11100000 => 00000111 => 3
[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] => 11000000 => 00000011 => 2
[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] => 10000000 => 00000001 => 1
[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] => 10000000 => 00000001 => 1
[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] => 10101010 => 11010100 => 2
[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] => 10111000 => 11000011 => 2
[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] => 10111000 => 11000011 => 2
[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] => 10100000 => 11000000 => 2
[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] => 11010100 => 11101000 => 3
[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 => 00001111 => 4
[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] => 11100000 => 00000111 => 3
[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] => 11000000 => 00000011 => 2
[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] => 11100000 => 00000111 => 3
[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] => 11000000 => 00000011 => 2
[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] => 11000000 => 00000011 => 2
[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] => 10000000 => 00000001 => 1
[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] => 10000000 => 00000001 => 1
[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] => 10000000 => 00000001 => 1
[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] => 10101000 => 11010000 => 2
[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] => 10110000 => 11000001 => 2
[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] => 10100000 => 11000000 => 2
[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] => 10000000 => 00000001 => 1
[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] => 11000000 => 00000011 => 2
[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 => 00000111 => 3
[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] => 11000000 => 00000011 => 2
[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] => 11000000 => 00000011 => 2
[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] => 11000000 => 00000011 => 2
[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] => 11000000 => 00000011 => 2
[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] => 10000000 => 00000001 => 1
[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] => 10000000 => 00000001 => 1
[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] => 10010000 => 01100000 => 2
[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] => 10100000 => 11000000 => 2
[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] => 10100000 => 11000000 => 2
[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] => 10100000 => 11000000 => 2
[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] => 10000000 => 00000001 => 1
[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] => 11000000 => 00000011 => 2
[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 => 00000011 => 2
[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] => 10000000 => 00000001 => 1
[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] => 10000000 => 00000001 => 1
[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] => 10000000 => 00000001 => 1
[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] => 10000000 => 00000001 => 1
[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] => 10000000 => 00000001 => 1
[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] => 10000000 => 00000001 => 1
[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] => 10000000 => 00000001 => 1
[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 => 00000001 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => 00000000 => 00000000 => 0
[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] => 11111110 => 01111111 => 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] => 11111110 => 01111111 => 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] => 11111110 => 01111111 => 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] => 11111110 => 01111111 => 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] => 11111110 => 01111111 => 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] => 11111110 => 01111111 => 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] => 11111110 => 01111111 => 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] => 111111110 => 011111111 => 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] => 11111100 => 00111111 => 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] => 111111110 => 011111111 => 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] => 11111100 => 00111111 => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => 111111110 => 011111111 => 8
[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] => 11111010 => 11111100 => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => 111111110 => 011111111 => 8
[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] => 11110110 => 11111001 => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => 111111110 => 011111111 => 8
[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] => 11101110 => 11110011 => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => 111111110 => 011111111 => 8
[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] => 11011110 => 11100111 => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => 111111110 => 011111111 => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => 111111110 => 011111111 => 8
[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 => 011111111 => 8
[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] => 1111111110 => 0111111111 => 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] => 111111100 => 001111111 => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,9,11,8,7,6,5,4,3,2,1] => 1111111110 => 0111111111 => 9
[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] => 11111100 => 00111111 => 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] => 11111000 => 00011111 => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,1,2,10] => 101111110 => 110011111 => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => 1111111110 => 0111111111 => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110 => 0111111111 => 9
[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] => 111111100 => 001111111 => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => 111111000 => 000111111 => 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] => 11111000 => 00011111 => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,2,1,3,10] => 110111110 => 111001111 => 4
[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] => 11110000 => 00001111 => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,3,2,1,4,10] => 111011110 => 111100111 => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => 111110000 => 000011111 => 5
[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] => 11111100 => 00111111 => 6
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,1,5,10] => 111101110 => 111110011 => 5
[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] => 11111100 => 00111111 => 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] => 11110000 => 00001111 => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,4,3,2,1,6,10] => 111110110 => 111111001 => 6
[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] => 11100000 => 00000111 => 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] => 11111000 => 00011111 => 5
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,7,8,9,10,4,3,2,1] => 111110000 => 000011111 => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9,8,6,5,4,3,2,1,7,10] => 111111010 => 111111100 => 7
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => 111100000 => 000001111 => 4
[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] => 100001110 => 000110011 => 2
[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] => 111111100 => 001111111 => 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] => 111111100 => 001111111 => 7
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,8,9,10,1] => 111111000 => 000111111 => 6
[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] => 11111110 => 01111111 => 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] => 11111100 => 00111111 => 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] => 11111100 => 00111111 => 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] => 11111011 => 11111101 => 6
[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] => 11111000 => 00011111 => 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] => 11110111 => 11111011 => 5
[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] => 11110100 => 11111000 => 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] => 11110000 => 00001111 => 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] => 11110011 => 01111101 => 5
[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] => 11110000 => 00001111 => 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] => 11101111 => 11110111 => 4
[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] => 11101000 => 11110000 => 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] => 11100000 => 00000111 => 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] => 11100000 => 00000111 => 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] => 11011111 => 11101111 => 4
[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] => 11011110 => 11100111 => 3
[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] => 11010111 => 11101011 => 3
[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] => 11010100 => 11101000 => 3
[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] => 11010000 => 11100000 => 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] => 11010000 => 11100000 => 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] => 11000000 => 00000011 => 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] => 11001111 => 01110111 => 3
[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] => 11000000 => 00000011 => 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] => 11000000 => 00000011 => 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] => 11000001 => 00001110 => 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] => 11000000 => 00000011 => 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] => 10111111 => 11011111 => 5
[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] => 10111110 => 11001111 => 4
[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] => 10111110 => 11001111 => 4
[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] => 10110000 => 11000001 => 2
[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] => 10100000 => 11000000 => 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] => 10101111 => 11010111 => 3
[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] => 10101011 => 11010101 => 2
[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] => 10101010 => 11010100 => 2
[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] => 10101000 => 11010000 => 2
[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] => 10100000 => 11000000 => 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] => 10100000 => 11000000 => 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] => 10100001 => 11000010 => 2
[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] => 10100000 => 11000000 => 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] => 10100000 => 11000000 => 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] => 10011111 => 01101111 => 4
[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] => 10010111 => 01101011 => 2
[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] => 10010100 => 01101000 => 2
[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] => 10010011 => 01100101 => 2
[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] => 10010000 => 01100000 => 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] => 10000000 => 00000001 => 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] => 10001111 => 00110111 => 3
[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] => 10001011 => 00110101 => 2
[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] => 10001010 => 00110100 => 2
[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] => 10001001 => 00110010 => 2
[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] => 10001000 => 00110000 => 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] => 10001000 => 00110000 => 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] => 10000000 => 00000001 => 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] => 10000111 => 00011011 => 2
[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] => 10000100 => 00011000 => 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] => 10000101 => 00011010 => 2
[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] => 10000100 => 00011000 => 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] => 10000000 => 00000001 => 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] => 10000011 => 00001101 => 2
[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] => 10000010 => 00001100 => 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] => 10000000 => 00000001 => 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] => 111111110 => 011111111 => 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] => 111111100 => 001111111 => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [10,9,8,6,7,5,4,3,2,1] => 111111011 => 111111101 => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,4,3,2,1] => 111110111 => 111111011 => 6
[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] => 111110100 => 111111000 => 6
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => 111000000 => 000000111 => 3
[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] => 111010100 => 111101000 => 4
[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] => 111000000 => 000000111 => 3
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,2,1] => 111000000 => 000000111 => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,3,1] => 110111111 => 111011111 => 5
[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] => 110101010 => 111010100 => 3
[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] => 110101000 => 111010000 => 3
[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] => 110100000 => 111000000 => 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] => 110000000 => 000000011 => 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] => 110010000 => 011100000 => 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] => 110000000 => 000000011 => 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] => 110000000 => 000000011 => 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] => 110000001 => 000001110 => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,1,2] => 101111111 => 110111111 => 6
[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] => 101111110 => 110011111 => 5
[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] => 101011111 => 110101111 => 4
[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] => 101010111 => 110101011 => 2
[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] => 101010101 => 110101010 => 2
[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] => 101010100 => 110101000 => 2
[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] => 101010000 => 110100000 => 2
[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] => 101010000 => 110100000 => 2
[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] => 101000000 => 110000000 => 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] => 101000001 => 110000010 => 2
[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] => 101000000 => 110000000 => 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] => 101000000 => 110000000 => 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] => 100111111 => 011011111 => 5
[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] => 100101111 => 011010111 => 3
[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] => 100101010 => 011010100 => 2
[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] => 100100100 => 011001000 => 2
[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] => 100100000 => 011000000 => 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] => 100000000 => 000000001 => 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] => 100011111 => 001101111 => 4
[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] => 100010100 => 001101000 => 2
[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] => 100010000 => 001100000 => 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] => 100010000 => 001100000 => 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] => 100010001 => 001100010 => 2
[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] => 100010000 => 001100000 => 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] => 100000000 => 000000001 => 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] => 100001111 => 000110111 => 3
[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] => 100001010 => 000110100 => 2
[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] => 100001000 => 000110000 => 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] => 100000000 => 000000001 => 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] => 100000111 => 000011011 => 2
[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] => 100000100 => 000011000 => 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] => 100000000 => 000000001 => 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] => 100000011 => 000001101 => 2
[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] => 100000010 => 000001100 => 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] => 100000000 => 000000001 => 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 => 000000000 => 0
[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] => 11011111 => 11101111 => 4
[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] => 11101111 => 11110111 => 4
[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] => 11110111 => 11111011 => 5
[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] => 11111011 => 11111101 => 6
[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] => 11111101 => 11111110 => 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] => 11111110 => 01111111 => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,1,3] => 110111111 => 111011111 => 5
[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] => 11001111 => 01110111 => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,2,1,4] => 111011111 => 111101111 => 4
[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] => 11100111 => 01111011 => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,3,2,1,5] => 111101111 => 111110111 => 5
[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] => 11110011 => 01111101 => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,4,3,2,1,6] => 111110111 => 111111011 => 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] => 11111001 => 01111110 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [10,9,8,6,5,4,3,2,1,7] => 111111011 => 111111101 => 7
[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] => 11111100 => 00111111 => 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] => 111111101 => 111111110 => 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] => 111111110 => 011111111 => 8
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,4,3,2,1,7,8,9,10] => 111100000 => 000001111 => 4
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,1,2,7,8,9,10] => 101110000 => 110000011 => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1,8,9,10,11] => 1111100000 => 0000011111 => 5
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [6,7,5,4,3,2,1,8,9,10] => 111110000 => 000011111 => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,1,2,8,9,10] => 101111000 => 110000111 => 3
[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] => 10111110 => 11001111 => 4
[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] => 111111100 => 001111111 => 7
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => 100000000 => 000000001 => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => 100000000 => 000000001 => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10,11] => 1000000000 => 0000000001 => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9,10] => 110000000 => 000000011 => 2
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9,10] => 101000000 => 110000000 => 2
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => 1000000000 => 0000000001 => 1
[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] => 101111110 => 110011111 => 5
[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] => 11011110 => 11100111 => 3
[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] => 11011110 => 11100111 => 3
[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] => 11011110 => 11100111 => 3
[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] => 11111100 => 00111111 => 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] => 11111001 => 01111110 => 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] => 11110011 => 01111101 => 5
[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] => 11100111 => 01111011 => 4
[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] => 11001111 => 01110111 => 3
[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] => 100000000 => 000000001 => 1
[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] => 100000000 => 000000001 => 1
[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] => 1000000000 => 0000000001 => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,2,1,3,4,5,6,7,8,10] => 110000000 => 000000011 => 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] => 10000101 => 00011010 => 2
[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] => 10001011 => 00110101 => 2
[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] => 10010111 => 01101011 => 2
[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] => 10101111 => 11010111 => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => 100000000 => 000000001 => 1
[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] => 100000000 => 000000001 => 1
[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] => 100000000 => 000000001 => 1
[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] => 100000000 => 000000001 => 1
[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] => 100000000 => 000000001 => 1
[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] => 100000000 => 000000001 => 1
[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] => 11111000 => 00011111 => 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] => 10111100 => 11000111 => 3
[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] => 11111100 => 00111111 => 6
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,1,10] => 111111100 => 001111111 => 7
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000 => 0000000001 => 1
[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] => 11000000 => 00000011 => 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] => 11000000 => 00000011 => 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] => 11000000 => 00000011 => 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] => 11000000 => 00000011 => 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] => 11110111 => 11111011 => 5
[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] => 11110111 => 11111011 => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [10,9,7,6,8,5,4,3,2,1] => 111111101 => 111111110 => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [10,8,7,6,9,5,4,3,2,1] => 111111110 => 011111111 => 8
[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] => 11110110 => 11111001 => 5
[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] => 10110111 => 11011011 => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,5,1,10] => 111101110 => 111110011 => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,5,2,1,10] => 111101110 => 111110011 => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,5,3,2,1,10] => 111101110 => 111110011 => 5
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,7,8,9,10,1] => 111110000 => 000011111 => 5
[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] => 11011100 => 11100011 => 3
[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] => 10111110 => 11001111 => 4
[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] => 11111100 => 00111111 => 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] => 11111100 => 00111111 => 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] => 10111110 => 11001111 => 4
[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] => 11111000 => 00011111 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7,8,9,6,5,4,3,2,1,10] => 111111000 => 000111111 => 6
[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] => 11110000 => 00001111 => 4
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7,6,8,9,5,4,3,2,1,10] => 111111000 => 000111111 => 6
[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] => 11101000 => 11110000 => 4
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,6,5,8,9,4,3,2,1,10] => 111111000 => 000111111 => 6
[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] => 11011000 => 11100001 => 3
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,8,9,3,2,1,10] => 111111000 => 000111111 => 6
[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] => 10111000 => 11000011 => 2
[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] => 111111000 => 000111111 => 6
[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] => 111111000 => 000111111 => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => 111111000 => 000111111 => 6
[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] => 10100000 => 11000000 => 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] => 11000000 => 00000011 => 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] => 10010000 => 01100000 => 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] => 11000000 => 00000011 => 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] => 10001000 => 00110000 => 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] => 10000010 => 00001100 => 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] => 100000000 => 000000001 => 1
[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] => 10000100 => 00011000 => 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] => 100000000 => 000000001 => 1
[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] => 100000000 => 000000001 => 1
[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] => 10010000 => 01100000 => 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] => 100000000 => 000000001 => 1
[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] => 100000000 => 000000001 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => 111110110 => 111111001 => 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] => 11111010 => 11111100 => 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] => 11010100 => 11101000 => 3
[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] => 11010100 => 11101000 => 3
[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] => 110101000 => 111010000 => 3
[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] => 110101010 => 111010100 => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,7,9,6,5,4,3,2,1,10] => 111111100 => 001111111 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,6,9,5,4,3,2,1,10] => 111111100 => 001111111 => 7
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,9,3,2,1,10] => 111111100 => 001111111 => 7
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1,10] => 111111100 => 001111111 => 7
[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 => 001111111 => 7
[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] => 100000000 => 000000001 => 1
[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] => 100000000 => 000000001 => 1
[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] => 100000000 => 000000001 => 1
[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] => 100000000 => 000000001 => 1
[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] => 111110000 => 000011111 => 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] => 110101010 => 111010100 => 3
[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 => 0000000000 => 0
[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] => 1000000000 => 0000000001 => 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] => 111111100 => 001111111 => 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] => 11111000 => 00011111 => 5
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9,10] => 110000000 => 000000011 => 2
[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] => 1000000000 => 0000000001 => 1
[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] => 1000000000 => 0000000001 => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => 111110000 => 000011111 => 5
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [5,4,6,7,8,9,10,3,2,1] => 111100000 => 000001111 => 4
[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] => 11101111 => 11110111 => 4
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => 110000000 => 000000011 => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [11,9,10,8,7,6,5,4,3,2,1] => 1111111110 => 0111111111 => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,9,2,1] => 111111110 => 011111111 => 8
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => 111100000 => 000001111 => 4
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => 111000000 => 000000111 => 3
[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] => 1111111110 => 0111111111 => 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] => 11111110 => 01111111 => 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] => 11100000 => 00000111 => 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] => 100000000 => 000000001 => 1
[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] => 100000000 => 000000001 => 1
[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] => 100000000 => 000000001 => 1
[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] => 1111100000 => 0000011111 => 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] => 11110000 => 00001111 => 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] => 111101110 => 111110011 => 5
[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] => 11111100 => 00111111 => 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] => 111111100 => 001111111 => 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] => 10001101 => 00110110 => 2
[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] => 10101010 => 11010100 => 2
[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] => 110010100 => 011101000 => 3
[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] => 10100000 => 11000000 => 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] => 11110000 => 00001111 => 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] => 11110000 => 00001111 => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [11,10,1,2,3,4,5,6,7,8,9] => 1000000001 => 0000000110 => 2
[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] => 10010001 => 01100010 => 2
[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] => 11111011 => 11111101 => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [10,9,8,6,5,7,4,3,2,1] => 111111011 => 111111101 => 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] => 110000000 => 000000011 => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,9,1] => 111111110 => 011111111 => 8
[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] => 11111100 => 00111111 => 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] => 11111101 => 11111110 => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,8,3,2,1] => 111111101 => 111111110 => 8
[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] => 11111101 => 11111110 => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,3,8,2,1] => 111111101 => 111111110 => 8
[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] => 100100000 => 011000000 => 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] => 11000000 => 00000011 => 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] => 10101000 => 11010000 => 2
[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] => 101010100 => 110101000 => 2
[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] => 101111110 => 110011111 => 5
[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] => 11111110 => 01111111 => 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] => 11100000 => 00000111 => 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] => 11111001 => 01111110 => 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] => 11000000 => 00000011 => 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] => 10100000 => 11000000 => 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] => 100000000 => 000000001 => 1
[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] => 11000000 => 00000011 => 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] => 111111100 => 001111111 => 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] => 110101010 => 111010100 => 3
[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] => 11111001 => 01111110 => 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] => 11110000 => 00001111 => 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] => 111100000 => 000001111 => 4
[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] => 111111100 => 001111111 => 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] => 11000000 => 00000011 => 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] => 11000000 => 00000011 => 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] => 11110000 => 00001111 => 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] => 110101000 => 111010000 => 3
[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] => 110000000 => 000000011 => 2
[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] => 101010100 => 110101000 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [10,8,9,6,5,4,3,2,1,7] => 111111010 => 111111100 => 7
[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] => 11111000 => 00011111 => 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] => 101010000 => 110100000 => 2
[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] => 10000000000 => 00000000001 => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11,12] => 10000000000 => 00000000001 => 1
[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] => 11010000 => 11100000 => 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] => 11001000 => 01110000 => 3
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [10,4,5,6,7,8,9,2,1,3] => 110100000 => 111000000 => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [11,8,9,10,1,2,3,4,5,6,7] => 1000000100 => 0000011000 => 2
[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] => 11110010 => 01111100 => 5
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [10,4,3,5,6,7,8,9,2,1] => 111100000 => 000001111 => 4
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [10,3,2,4,5,6,7,8,9,1] => 111000000 => 000000111 => 3
[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] => 11000000 => 00000011 => 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] => 1000000000 => 0000000001 => 1
[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] => 1000000000 => 0000000001 => 1
[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] => 110000000 => 000000011 => 2
[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] => 111100000 => 000001111 => 4
[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] => 100100000 => 011000000 => 2
[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] => 110111110 => 111001111 => 4
[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] => 11110001 => 00111110 => 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] => 10101010 => 11010100 => 2
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,7,8,9,10,1,2] => 101110000 => 110000011 => 2
[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] => 110010100 => 011101000 => 3
[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] => 111111010 => 111111100 => 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] => 11010000 => 11100000 => 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] => 111100000 => 000001111 => 4
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8,9,10] => 110000000 => 000000011 => 2
[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] => 11001010 => 01110100 => 3
[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] => 110010100 => 011101000 => 3
[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] => 10100000 => 11000000 => 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] => 11111111110 => 01111111111 => 10
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,1 1,6,6,1 1,10,21,9,1 1,15,61,42,12,1 1,21,170,152,69,15,1
$F_{2} = 1 + q$
$F_{3} = 1 + 3\ q + q^{2}$
$F_{4} = 1 + 6\ q + 6\ q^{2} + q^{3}$
$F_{5} = 1 + 10\ q + 21\ q^{2} + 9\ q^{3} + q^{4}$
$F_{6} = 1 + 15\ q + 61\ q^{2} + 42\ q^{3} + 12\ q^{4} + q^{5}$
$F_{7} = 1 + 21\ q + 170\ q^{2} + 152\ q^{3} + 69\ q^{4} + 15\ q^{5} + q^{6}$
Description
The length of the longest run of ones in a binary word.
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
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].
Map
rowmotion
Description
Return the rowmotion of the binary word, regarded as an order ideal in the product of two chains.
In particular, this operation preserves the number of ones, and its order is the length of the word, see section 3.3 of [1].
In particular, this operation preserves the number of ones, and its order is the length of the word, see section 3.3 of [1].
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