Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00130: Permutations —descent tops⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Images
[1,0] => [1] => =>
[1,0,1,0] => [1,2] => 0 => 1
[1,1,0,0] => [2,1] => 1 => 0
[1,0,1,0,1,0] => [1,2,3] => 00 => 11
[1,0,1,1,0,0] => [1,3,2] => 01 => 10
[1,1,0,0,1,0] => [2,1,3] => 10 => 01
[1,1,0,1,0,0] => [2,3,1] => 01 => 10
[1,1,1,0,0,0] => [3,2,1] => 11 => 00
[1,0,1,0,1,0,1,0] => [1,2,3,4] => 000 => 111
[1,0,1,0,1,1,0,0] => [1,2,4,3] => 001 => 110
[1,0,1,1,0,0,1,0] => [1,3,2,4] => 010 => 101
[1,0,1,1,0,1,0,0] => [1,3,4,2] => 001 => 110
[1,0,1,1,1,0,0,0] => [1,4,3,2] => 011 => 100
[1,1,0,0,1,0,1,0] => [2,1,3,4] => 100 => 011
[1,1,0,0,1,1,0,0] => [2,1,4,3] => 101 => 010
[1,1,0,1,0,0,1,0] => [2,3,1,4] => 010 => 101
[1,1,0,1,0,1,0,0] => [2,3,4,1] => 001 => 110
[1,1,0,1,1,0,0,0] => [2,4,3,1] => 011 => 100
[1,1,1,0,0,0,1,0] => [3,2,1,4] => 110 => 001
[1,1,1,0,0,1,0,0] => [3,2,4,1] => 011 => 100
[1,1,1,0,1,0,0,0] => [3,4,2,1] => 101 => 010
[1,1,1,1,0,0,0,0] => [4,3,2,1] => 111 => 000
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 0000 => 1111
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 0001 => 1110
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 0010 => 1101
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 0001 => 1110
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0011 => 1100
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 0100 => 1011
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 0101 => 1010
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 0010 => 1101
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 0001 => 1110
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 0011 => 1100
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 0110 => 1001
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0011 => 1100
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => 0101 => 1010
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 0111 => 1000
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 1000 => 0111
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 1001 => 0110
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 1010 => 0101
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 1001 => 0110
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 1011 => 0100
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 0100 => 1011
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 0101 => 1010
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 0010 => 1101
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 0001 => 1110
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => 0011 => 1100
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0110 => 1001
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => 0011 => 1100
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => 0101 => 1010
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => 0111 => 1000
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 1100 => 0011
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 1101 => 0010
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0110 => 1001
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0101 => 1010
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => 0111 => 1000
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => 1010 => 0101
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => 0011 => 1100
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => 1001 => 0110
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => 1011 => 0100
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 1110 => 0001
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 0111 => 1000
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => 1011 => 0100
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => 1101 => 0010
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 1111 => 0000
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 00000 => 11111
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 00001 => 11110
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 00010 => 11101
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 00001 => 11110
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 00011 => 11100
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 00100 => 11011
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 00101 => 11010
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => 00010 => 11101
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 00001 => 11110
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => 00011 => 11100
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 00110 => 11001
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 00011 => 11100
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => 00101 => 11010
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 00111 => 11000
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 01000 => 10111
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 01001 => 10110
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 01010 => 10101
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => 01001 => 10110
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 01011 => 10100
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => 00100 => 11011
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => 00101 => 11010
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => 00010 => 11101
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 00001 => 11110
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => 00011 => 11100
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => 00110 => 11001
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => 00011 => 11100
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => 00101 => 11010
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 00111 => 11000
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 01100 => 10011
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 01101 => 10010
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => 00110 => 11001
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 00101 => 11010
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 00111 => 11000
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => 01010 => 10101
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => 00011 => 11100
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => 01001 => 10110
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => 01011 => 10100
>>> Load all 2409 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 01110 => 10001
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 00111 => 11000
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => 01011 => 10100
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => 01101 => 10010
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 01111 => 10000
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => 10000 => 01111
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 10001 => 01110
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => 10010 => 01101
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => 10001 => 01110
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 10011 => 01100
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 10100 => 01011
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 10101 => 01010
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => 10010 => 01101
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => 10001 => 01110
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => 10011 => 01100
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 10110 => 01001
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => 10011 => 01100
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => 10101 => 01010
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 10111 => 01000
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => 01000 => 10111
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => 01001 => 10110
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => 01010 => 10101
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => 01001 => 10110
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => 01011 => 10100
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => 00100 => 11011
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => 00101 => 11010
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => 00010 => 11101
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 00001 => 11110
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => 00011 => 11100
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => 00110 => 11001
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => 00011 => 11100
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => 00101 => 11010
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => 00111 => 11000
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => 01100 => 10011
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => 01101 => 10010
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => 00110 => 11001
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => 00101 => 11010
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => 00111 => 11000
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => 01010 => 10101
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => 00011 => 11100
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => 01001 => 10110
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => 01011 => 10100
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 01110 => 10001
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => 00111 => 11000
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => 01011 => 10100
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => 01101 => 10010
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 01111 => 10000
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => 11000 => 00111
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 11001 => 00110
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 11010 => 00101
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => 11001 => 00110
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 11011 => 00100
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => 01100 => 10011
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => 01101 => 10010
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => 01010 => 10101
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 01001 => 10110
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => 01011 => 10100
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 01110 => 10001
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => 01011 => 10100
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => 01101 => 10010
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 01111 => 10000
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => 10100 => 01011
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => 10101 => 01010
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => 00110 => 11001
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => 00101 => 11010
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => 00111 => 11000
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => 10010 => 01101
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => 00011 => 11100
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => 10001 => 01110
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => 10011 => 01100
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => 10110 => 01001
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => 00111 => 11000
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => 10011 => 01100
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => 10101 => 01010
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 10111 => 01000
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 11100 => 00011
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 11101 => 00010
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 01110 => 10001
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 01101 => 10010
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 01111 => 10000
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => 10110 => 01001
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => 00111 => 11000
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => 10101 => 01010
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 10111 => 01000
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => 11010 => 00101
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => 01011 => 10100
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => 10011 => 01100
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => 11001 => 00110
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 11011 => 00100
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 11110 => 00001
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 01111 => 10000
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 10111 => 01000
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 11011 => 00100
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 11101 => 00010
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 11111 => 00000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 000000 => 111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 000001 => 111110
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => 000010 => 111101
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 000001 => 111110
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 000011 => 111100
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => 000100 => 111011
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => 000101 => 111010
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => 000010 => 111101
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 000001 => 111110
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => 000011 => 111100
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => 000110 => 111001
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 000011 => 111100
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => 000101 => 111010
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => 000111 => 111000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => 001000 => 110111
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => 001001 => 110110
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => 001010 => 110101
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => 001001 => 110110
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => 001011 => 110100
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => 000100 => 111011
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => 000101 => 111010
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => 000010 => 111101
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 000001 => 111110
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => 000011 => 111100
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => 000110 => 111001
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => 000011 => 111100
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => 000101 => 111010
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => 000111 => 111000
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => 001100 => 110011
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => 001101 => 110010
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => 000110 => 111001
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 000101 => 111010
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => 000111 => 111000
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => 001010 => 110101
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => 000011 => 111100
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => 001001 => 110110
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => 001011 => 110100
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => 001110 => 110001
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => 000111 => 111000
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => 001011 => 110100
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => 001101 => 110010
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 001111 => 110000
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => 010000 => 101111
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => 010001 => 101110
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => 010010 => 101101
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => 010001 => 101110
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => 010011 => 101100
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => 010100 => 101011
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => 010101 => 101010
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => 010010 => 101101
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => 010001 => 101110
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => 010011 => 101100
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => 010110 => 101001
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => 010011 => 101100
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => 010101 => 101010
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => 010111 => 101000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => 001000 => 110111
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => 001001 => 110110
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => 001010 => 110101
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => 001001 => 110110
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => 001011 => 110100
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => 000100 => 111011
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => 000101 => 111010
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => 000010 => 111101
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 000001 => 111110
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => 000011 => 111100
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => 000110 => 111001
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => 000011 => 111100
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => 000101 => 111010
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => 000111 => 111000
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => 001100 => 110011
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => 001101 => 110010
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => 000110 => 111001
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => 000101 => 111010
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => 000111 => 111000
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => 001010 => 110101
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => 000011 => 111100
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => 001001 => 110110
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => 001011 => 110100
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => 001110 => 110001
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => 000111 => 111000
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => 001011 => 110100
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => 001101 => 110010
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 001111 => 110000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => 011000 => 100111
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => 011001 => 100110
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => 011010 => 100101
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => 011001 => 100110
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => 011011 => 100100
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => 001100 => 110011
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => 001101 => 110010
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => 001010 => 110101
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 001001 => 110110
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => 001011 => 110100
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => 001110 => 110001
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => 001011 => 110100
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => 001101 => 110010
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 001111 => 110000
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => 010100 => 101011
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => 010101 => 101010
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => 000110 => 111001
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => 000101 => 111010
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => 000111 => 111000
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => 010010 => 101101
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => 000011 => 111100
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => 010001 => 101110
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => 010011 => 101100
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => 010110 => 101001
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => 000111 => 111000
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => 010011 => 101100
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => 010101 => 101010
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => 010111 => 101000
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => 011100 => 100011
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => 011101 => 100010
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => 001110 => 110001
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => 001101 => 110010
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => 001111 => 110000
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => 010110 => 101001
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => 000111 => 111000
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => 010101 => 101010
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => 010111 => 101000
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => 011010 => 100101
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => 001011 => 110100
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => 010011 => 101100
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => 011001 => 100110
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => 011011 => 100100
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => 011110 => 100001
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => 001111 => 110000
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => 010111 => 101000
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => 011011 => 100100
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => 011101 => 100010
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 011111 => 100000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => 100000 => 011111
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => 100001 => 011110
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => 100010 => 011101
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => 100001 => 011110
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => 100011 => 011100
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => 100100 => 011011
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => 100101 => 011010
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => 100010 => 011101
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => 100001 => 011110
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => 100011 => 011100
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => 100110 => 011001
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => 100011 => 011100
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => 100101 => 011010
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => 100111 => 011000
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => 101000 => 010111
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => 101001 => 010110
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => 101010 => 010101
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => 101001 => 010110
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => 101011 => 010100
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => 100100 => 011011
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => 100101 => 011010
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => 100010 => 011101
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => 100001 => 011110
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => 100011 => 011100
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => 100110 => 011001
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => 100011 => 011100
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => 100101 => 011010
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => 100111 => 011000
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => 101100 => 010011
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => 101101 => 010010
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => 100110 => 011001
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => 100101 => 011010
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => 100111 => 011000
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => 101010 => 010101
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => 100011 => 011100
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => 101001 => 010110
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => 101011 => 010100
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => 101110 => 010001
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => 100111 => 011000
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => 101011 => 010100
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => 101101 => 010010
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 101111 => 010000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => 010000 => 101111
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => 010001 => 101110
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => 010010 => 101101
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => 010001 => 101110
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => 010011 => 101100
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => 010100 => 101011
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => 010101 => 101010
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => 010010 => 101101
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => 010001 => 101110
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => 010011 => 101100
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => 010110 => 101001
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => 010011 => 101100
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => 010101 => 101010
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => 010111 => 101000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => 001000 => 110111
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => 001001 => 110110
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => 001010 => 110101
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => 001001 => 110110
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => 001011 => 110100
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => 000100 => 111011
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => 000101 => 111010
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => 000010 => 111101
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 000001 => 111110
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => 000011 => 111100
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => 000110 => 111001
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => 000011 => 111100
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => 000101 => 111010
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => 000111 => 111000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => 001100 => 110011
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => 001101 => 110010
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => 000110 => 111001
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => 000101 => 111010
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => 000111 => 111000
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => 001010 => 110101
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => 000011 => 111100
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => 001001 => 110110
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => 001011 => 110100
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => 001110 => 110001
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => 000111 => 111000
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => 001011 => 110100
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => 001101 => 110010
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => 001111 => 110000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => 011000 => 100111
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => 011001 => 100110
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => 011010 => 100101
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => 011001 => 100110
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => 011011 => 100100
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => 001100 => 110011
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => 001101 => 110010
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => 001010 => 110101
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => 001001 => 110110
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => 001011 => 110100
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => 001110 => 110001
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => 001011 => 110100
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => 001101 => 110010
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => 001111 => 110000
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => 010100 => 101011
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => 010101 => 101010
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => 000110 => 111001
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => 000101 => 111010
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => 000111 => 111000
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => 010010 => 101101
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => 000011 => 111100
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => 010001 => 101110
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => 010011 => 101100
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => 010110 => 101001
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => 000111 => 111000
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => 010011 => 101100
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => 010101 => 101010
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => 010111 => 101000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => 011100 => 100011
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => 011101 => 100010
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => 001110 => 110001
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => 001101 => 110010
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => 001111 => 110000
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => 010110 => 101001
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => 000111 => 111000
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => 010101 => 101010
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => 010111 => 101000
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => 011010 => 100101
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => 001011 => 110100
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => 010011 => 101100
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => 011001 => 100110
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => 011011 => 100100
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => 011110 => 100001
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => 001111 => 110000
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => 010111 => 101000
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => 011011 => 100100
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => 011101 => 100010
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => 011111 => 100000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => 110000 => 001111
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => 110001 => 001110
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => 110010 => 001101
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => 110001 => 001110
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => 110011 => 001100
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => 110100 => 001011
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => 110101 => 001010
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => 110010 => 001101
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => 110001 => 001110
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => 110011 => 001100
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => 110110 => 001001
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => 110011 => 001100
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => 110101 => 001010
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => 110111 => 001000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => 011000 => 100111
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => 011001 => 100110
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => 011010 => 100101
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => 011001 => 100110
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => 011011 => 100100
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => 010100 => 101011
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => 010101 => 101010
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => 010010 => 101101
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => 010001 => 101110
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => 010011 => 101100
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => 010110 => 101001
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => 010011 => 101100
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => 010101 => 101010
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => 010111 => 101000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => 011100 => 100011
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => 011101 => 100010
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => 010110 => 101001
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => 010101 => 101010
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => 010111 => 101000
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => 011010 => 100101
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => 010011 => 101100
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => 011001 => 100110
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => 011011 => 100100
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => 011110 => 100001
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => 010111 => 101000
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => 011011 => 100100
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => 011101 => 100010
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => 011111 => 100000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => 101000 => 010111
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => 101001 => 010110
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => 101010 => 010101
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => 101001 => 010110
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => 101011 => 010100
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => 001100 => 110011
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => 001101 => 110010
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => 001010 => 110101
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => 001001 => 110110
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => 001011 => 110100
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => 001110 => 110001
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => 001011 => 110100
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => 001101 => 110010
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => 001111 => 110000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => 100100 => 011011
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => 100101 => 011010
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => 000110 => 111001
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => 000101 => 111010
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => 000111 => 111000
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => 100010 => 011101
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => 000011 => 111100
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => 100001 => 011110
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => 100011 => 011100
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => 100110 => 011001
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => 000111 => 111000
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => 100011 => 011100
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => 100101 => 011010
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => 100111 => 011000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => 101100 => 010011
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => 101101 => 010010
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => 001110 => 110001
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => 001101 => 110010
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => 001111 => 110000
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => 100110 => 011001
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => 000111 => 111000
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => 100101 => 011010
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => 100111 => 011000
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => 101010 => 010101
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => 001011 => 110100
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => 100011 => 011100
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => 101001 => 010110
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => 101011 => 010100
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => 101110 => 010001
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => 001111 => 110000
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => 100111 => 011000
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => 101011 => 010100
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => 101101 => 010010
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => 101111 => 010000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => 111000 => 000111
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => 111001 => 000110
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => 111010 => 000101
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => 111001 => 000110
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => 111011 => 000100
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => 011100 => 100011
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => 011101 => 100010
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => 011010 => 100101
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => 011001 => 100110
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => 011011 => 100100
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => 011110 => 100001
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => 011011 => 100100
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => 011101 => 100010
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => 011111 => 100000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => 101100 => 010011
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => 101101 => 010010
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => 001110 => 110001
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => 001101 => 110010
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => 001111 => 110000
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => 101010 => 010101
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => 001011 => 110100
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => 101001 => 010110
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => 101011 => 010100
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => 101110 => 010001
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => 001111 => 110000
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => 101011 => 010100
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => 101101 => 010010
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => 101111 => 010000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => 110100 => 001011
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => 110101 => 001010
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => 010110 => 101001
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => 010101 => 101010
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => 010111 => 101000
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => 100110 => 011001
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => 000111 => 111000
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => 100101 => 011010
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => 100111 => 011000
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => 110010 => 001101
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => 010011 => 101100
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => 100011 => 011100
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => 110001 => 001110
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => 110011 => 001100
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => 110110 => 001001
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => 010111 => 101000
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => 100111 => 011000
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => 110011 => 001100
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => 110101 => 001010
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => 110111 => 001000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => 111100 => 000011
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 111101 => 000010
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => 011110 => 100001
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => 011101 => 100010
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => 011111 => 100000
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => 101110 => 010001
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => 001111 => 110000
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => 101101 => 010010
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => 101111 => 010000
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => 110110 => 001001
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => 010111 => 101000
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => 100111 => 011000
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => 110101 => 001010
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => 110111 => 001000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => 111010 => 000101
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => 011011 => 100100
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => 101011 => 010100
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => 110011 => 001100
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => 111001 => 000110
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => 111011 => 000100
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => 111110 => 000001
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => 011111 => 100000
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => 101111 => 010000
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => 110111 => 001000
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => 111011 => 000100
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => 111101 => 000010
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => 111111 => 000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => 0000000 => 1111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => 0000001 => 1111110
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => 0000010 => 1111101
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => 0000001 => 1111110
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => 0000011 => 1111100
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => 0000100 => 1111011
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => 0000101 => 1111010
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => 0000010 => 1111101
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => 0000001 => 1111110
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => 0000011 => 1111100
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => 0000110 => 1111001
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => 0000011 => 1111100
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => 0000101 => 1111010
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => 0000111 => 1111000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => 0001000 => 1110111
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => 0001001 => 1110110
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => 0001010 => 1110101
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => 0001001 => 1110110
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => 0001011 => 1110100
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => 0000100 => 1111011
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => 0000101 => 1111010
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => 0000010 => 1111101
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => 0000001 => 1111110
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => 0000011 => 1111100
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => 0000110 => 1111001
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => 0000011 => 1111100
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => 0000101 => 1111010
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => 0000111 => 1111000
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => 0001100 => 1110011
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => 0001101 => 1110010
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => 0000110 => 1111001
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => 0000101 => 1111010
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => 0000111 => 1111000
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,5,4,8] => 0001010 => 1110101
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => 0000011 => 1111100
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => 0001001 => 1110110
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => 0001011 => 1110100
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => 0001110 => 1110001
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => 0000111 => 1111000
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => 0001011 => 1110100
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => 0001101 => 1110010
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => 0001111 => 1110000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => 0010000 => 1101111
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => 0010001 => 1101110
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => 0010010 => 1101101
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => 0010001 => 1101110
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => 0010011 => 1101100
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => 0010100 => 1101011
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => 0010101 => 1101010
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => 0010010 => 1101101
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => 0010001 => 1101110
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => 0010011 => 1101100
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => 0010011 => 1101100
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => 0010101 => 1101010
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => 0010111 => 1101000
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => 0001010 => 1110101
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => 0001001 => 1110110
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => 0001011 => 1110100
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => 0000100 => 1111011
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => 0000101 => 1111010
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => 0000010 => 1111101
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => 0000001 => 1111110
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => 0000011 => 1111100
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,6,3] => 0000101 => 1111010
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => 0000111 => 1111000
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => 0001100 => 1110011
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,4,6,5,7,8,3] => 0000101 => 1111010
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => 0000111 => 1111000
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,4,6,7,5,3,8] => 0001010 => 1110101
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => 0001001 => 1110110
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => 0001011 => 1110100
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => 0000111 => 1111000
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,7,6,8,5,3] => 0001011 => 1110100
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,6,5,3] => 0001101 => 1110010
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => 0001111 => 1110000
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => 0011000 => 1100111
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => 0011001 => 1100110
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => 0011001 => 1100110
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => 0011011 => 1100100
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => 0001010 => 1110101
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => 0001001 => 1110110
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => 0001011 => 1110100
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => 0001011 => 1110100
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,7,8,6,3] => 0001101 => 1110010
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => 0001111 => 1110000
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,4,3,7,8] => 0010100 => 1101011
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,4,7,3,8] => 0000110 => 1111001
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => 0000101 => 1111010
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,5,6,7,4,3,8] => 0010010 => 1101101
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => 0000011 => 1111100
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => 0010001 => 1101110
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => 0010011 => 1101100
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,6,4,3,8] => 0010110 => 1101001
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,6,4,8,3] => 0000111 => 1111000
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,6,8,4,3] => 0010011 => 1101100
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,7,6,4,3] => 0010111 => 1101000
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => 0011100 => 1100011
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => 0001101 => 1110010
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => 0001111 => 1110000
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,5,7,8,4,3] => 0010101 => 1101010
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,5,8,7,4,3] => 0010111 => 1101000
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,5,4,3,8] => 0011010 => 1100101
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => 0011001 => 1100110
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => 0011110 => 1100001
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => 0001111 => 1110000
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,6,5,8,4,3] => 0010111 => 1101000
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => 0011011 => 1100100
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => 0011101 => 1100010
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => 0011111 => 1100000
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => 0100000 => 1011111
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => 0100001 => 1011110
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => 0100010 => 1011101
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => 0100001 => 1011110
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => 0100011 => 1011100
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => 0100100 => 1011011
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => 0100101 => 1011010
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => 0100001 => 1011110
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => 0100011 => 1011100
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => 0100110 => 1011001
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => 0100011 => 1011100
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => 0100111 => 1011000
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => 0101000 => 1010111
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 0101010 => 1010101
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => 0101001 => 1010110
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => 0101011 => 1010100
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => 0100100 => 1011011
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => 0100101 => 1011010
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => 0100010 => 1011101
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => 0100001 => 1011110
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => 0100011 => 1011100
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => 0100110 => 1011001
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => 0100011 => 1011100
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => 0100101 => 1011010
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => 0100111 => 1011000
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => 0101100 => 1010011
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => 0101101 => 1010010
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => 0100110 => 1011001
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => 0100101 => 1011010
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => 0100111 => 1011000
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,5,4,8] => 0101010 => 1010101
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => 0100011 => 1011100
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,5,4] => 0101001 => 1010110
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,7,5,4] => 0101011 => 1010100
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => 0101110 => 1010001
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => 0100111 => 1011000
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,6,8,5,4] => 0101011 => 1010100
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => 0101111 => 1010000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => 0010000 => 1101111
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => 0010001 => 1101110
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => 0010010 => 1101101
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => 0010001 => 1101110
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => 0010011 => 1101100
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => 0010101 => 1101010
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => 0010010 => 1101101
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => 0010001 => 1101110
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => 0010011 => 1101100
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => 0010011 => 1101100
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,6,5] => 0010101 => 1101010
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => 0010111 => 1101000
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => 0001000 => 1110111
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,5,2,6,8,7] => 0001001 => 1110110
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => 0001010 => 1110101
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => 0001001 => 1110110
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => 0001011 => 1110100
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => 0000100 => 1111011
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => 0000101 => 1111010
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => 0000010 => 1111101
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => 0000001 => 1111110
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => 0000011 => 1111100
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => 0000110 => 1111001
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => 0000011 => 1111100
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => 0000101 => 1111010
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => 0000111 => 1111000
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => 0000110 => 1111001
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => 0000101 => 1111010
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,5,2,8] => 0001010 => 1110101
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,5,8,2] => 0000011 => 1111100
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => 0001001 => 1110110
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => 0000111 => 1111000
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,7,6,8,5,2] => 0001011 => 1110100
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => 0001111 => 1110000
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => 0011000 => 1100111
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => 0011001 => 1100110
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => 0011010 => 1100101
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => 0011001 => 1100110
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,3,5,4,6,2,7,8] => 0001100 => 1110011
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,4,6,7,2,8] => 0001010 => 1110101
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => 0001001 => 1110110
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => 0001110 => 1110001
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => 0001011 => 1110100
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,4,7,8,6,2] => 0001101 => 1110010
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => 0001111 => 1110000
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,4,2,7,8] => 0010100 => 1101011
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,4,7,2,8] => 0000110 => 1111001
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,5,6,4,7,8,2] => 0000101 => 1111010
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,4,2,8] => 0010010 => 1101101
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,4,8,2] => 0000011 => 1111100
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => 0010001 => 1101110
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,7,4,2] => 0010011 => 1101100
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => 0010110 => 1101001
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,6,4,8,2] => 0000111 => 1111000
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,6,8,4,2] => 0010011 => 1101100
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => 0010101 => 1101010
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => 0010111 => 1101000
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => 0011101 => 1100010
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => 0001110 => 1110001
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => 0001111 => 1110000
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,5,7,4,2,8] => 0010110 => 1101001
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,5,7,4,8,2] => 0000111 => 1111000
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => 0010101 => 1101010
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,6,7,5,4,2,8] => 0011010 => 1100101
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => 0010011 => 1101100
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => 0011001 => 1100110
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,6,8,7,5,4,2] => 0011011 => 1100100
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => 0011110 => 1100001
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,6,5,4,2] => 0011101 => 1100010
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => 0011111 => 1100000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => 0110000 => 1001111
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => 0110001 => 1001110
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => 0110010 => 1001101
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => 0110001 => 1001110
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => 0110011 => 1001100
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => 0110010 => 1001101
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => 0110001 => 1001110
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => 0110011 => 1001100
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 0110110 => 1001001
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => 0110011 => 1001100
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => 0110111 => 1001000
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => 0011010 => 1100101
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3,5,2,7,8,6] => 0011001 => 1100110
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3,5,2,8,7,6] => 0011011 => 1100100
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => 0010100 => 1101011
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => 0010001 => 1101110
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => 0010110 => 1101001
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,7,8,6,2] => 0010101 => 1101010
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => 0010111 => 1101000
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => 0011100 => 1100011
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => 0010110 => 1101001
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => 0010101 => 1101010
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => 0010111 => 1101000
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,3,6,7,5,8,2] => 0010011 => 1101100
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,6,7,8,5,2] => 0011001 => 1100110
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,6,8,7,5,2] => 0011011 => 1100100
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => 0011011 => 1100100
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => 0011101 => 1100010
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => 0011111 => 1100000
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,3,2,6,7,8] => 0101000 => 1010111
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,5,3,2,6,8,7] => 0101001 => 1010110
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,3,2,7,6,8] => 0101010 => 1010101
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,3,2,7,8,6] => 0101001 => 1010110
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,3,2,8,7,6] => 0101011 => 1010100
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,3,6,2,7,8] => 0001100 => 1110011
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,3,6,7,2,8] => 0001010 => 1110101
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => 0001001 => 1110110
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,3,6,8,7,2] => 0001011 => 1110100
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,3,7,8,6,2] => 0001101 => 1110010
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,3,8,7,6,2] => 0001111 => 1110000
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,3,2,7,8] => 0100100 => 1011011
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,3,7,2,8] => 0000110 => 1111001
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,5,6,3,8,7,2] => 0000111 => 1111000
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => 0100010 => 1011101
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => 0000011 => 1111100
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => 0100001 => 1011110
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,4,5,7,8,6,3,2] => 0100101 => 1011010
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,7,6,3,2] => 0100111 => 1011000
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,5,3,2,7,8] => 0101100 => 1010011
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,5,3,8,7,2] => 0001111 => 1110000
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,5,7,3,2,8] => 0100110 => 1011001
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,5,7,3,8,2] => 0000111 => 1111000
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,5,8,7,3,2] => 0100111 => 1011000
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,5,3,2,8] => 0101010 => 1010101
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,5,3,8,2] => 0001011 => 1110100
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,5,8,3,2] => 0100011 => 1011100
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,5,3,2] => 0101001 => 1010110
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => 0101011 => 1010100
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,6,5,3,2,8] => 0101110 => 1010001
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,6,5,8,3,2] => 0100111 => 1011000
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,6,5,3,2] => 0101101 => 1010010
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => 0101111 => 1010000
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => 0111000 => 1000111
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => 0111010 => 1000101
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => 0111001 => 1000110
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => 0111011 => 1000100
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => 0011100 => 1100011
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => 0011010 => 1100101
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => 0011001 => 1100110
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => 0011011 => 1100100
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => 0011111 => 1100000
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,4,6,3,2,7,8] => 0101100 => 1010011
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,4,6,3,2,8,7] => 0101101 => 1010010
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,4,6,3,7,2,8] => 0001110 => 1110001
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,4,6,3,7,8,2] => 0001101 => 1110010
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,4,6,7,3,2,8] => 0101010 => 1010101
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => 0001011 => 1110100
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => 0101001 => 1010110
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,4,6,8,7,3,2] => 0101011 => 1010100
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,4,7,6,3,2,8] => 0101110 => 1010001
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,4,7,8,6,3,2] => 0101101 => 1010010
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,4,3,2,7,8] => 0110100 => 1001011
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,4,3,2,8,7] => 0110101 => 1001010
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,4,3,8,7,2] => 0010111 => 1101000
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,5,6,4,7,3,2,8] => 0100110 => 1011001
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,4,7,3,8,2] => 0000111 => 1111000
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,4,7,8,3,2] => 0100101 => 1011010
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,5,6,7,4,3,2,8] => 0110010 => 1001101
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,4,3,8,2] => 0010011 => 1101100
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => 0110001 => 1001110
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,6,8,4,3,2] => 0110011 => 1001100
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => 0110111 => 1001000
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => 0111100 => 1000011
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => 0111101 => 1000010
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => 0011101 => 1100010
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => 0011111 => 1100000
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,5,4,7,8,3,2] => 0101101 => 1010010
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,6,5,4,8,7,3,2] => 0101111 => 1010000
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,5,7,4,3,2,8] => 0110110 => 1001001
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => 0010111 => 1101000
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,5,7,8,4,3,2] => 0110101 => 1001010
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,5,8,7,4,3,2] => 0110111 => 1001000
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,5,4,3,2,8] => 0111010 => 1000101
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,7,5,4,3,8,2] => 0011011 => 1100100
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => 0110011 => 1001100
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => 0111001 => 1000110
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => 0111011 => 1000100
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => 0111110 => 1000001
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => 0011111 => 1100000
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => 0101111 => 1010000
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => 0110111 => 1001000
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => 0111011 => 1000100
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => 0111101 => 1000010
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 0111111 => 1000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => 1000000 => 0111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => 1000001 => 0111110
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => 1000010 => 0111101
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => 1000001 => 0111110
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => 1000011 => 0111100
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => 1000100 => 0111011
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => 1000101 => 0111010
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,4,6,7,5,8] => 1000010 => 0111101
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => 1000001 => 0111110
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => 1000011 => 0111100
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,6,5] => 1000101 => 0111010
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => 1000111 => 0111000
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => 1001000 => 0110111
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => 1001001 => 0110110
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => 1001001 => 0110110
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => 1001011 => 0110100
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => 1000101 => 0111010
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => 1000001 => 0111110
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,6,8,4] => 1000011 => 0111100
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => 1001101 => 0110010
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => 1000111 => 0111000
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,5,4,8] => 1001010 => 0110101
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,5,4] => 1001001 => 0110110
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,6,8,7,5,4] => 1001011 => 0110100
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,6,5,4] => 1001101 => 0110010
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => 1001111 => 0110000
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => 1010000 => 0101111
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => 1010001 => 0101110
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => 1010001 => 0101110
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => 1010011 => 0101100
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => 1010100 => 0101011
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 1010101 => 0101010
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => 1010010 => 0101101
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => 1010001 => 0101110
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => 1010011 => 0101100
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => 1010011 => 0101100
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => 1010101 => 0101010
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 1010111 => 0101000
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => 1001000 => 0110111
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => 1001001 => 0110110
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => 1001011 => 0110100
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => 1000101 => 0111010
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => 1000010 => 0111101
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => 1000001 => 0111110
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => 1000011 => 0111100
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => 1000101 => 0111010
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => 1000111 => 0111000
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => 1001100 => 0110011
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => 1001101 => 0110010
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => 1000111 => 0111000
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,4,6,7,5,3,8] => 1001010 => 0110101
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,5,8,3] => 1000011 => 0111100
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,5,3] => 1001001 => 0110110
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => 1001011 => 0110100
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => 1000111 => 0111000
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,7,6,8,5,3] => 1001011 => 0110100
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,6,5,3] => 1001101 => 0110010
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => 1001111 => 0110000
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => 1011000 => 0100111
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => 1011001 => 0100110
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => 1011010 => 0100101
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => 1011011 => 0100100
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => 1001101 => 0110010
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => 1001010 => 0110101
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => 1001001 => 0110110
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => 1001011 => 0110100
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => 1001011 => 0110100
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,7,8,6,3] => 1001101 => 0110010
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => 1001111 => 0110000
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,4,3,7,8] => 1010100 => 0101011
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => 1010101 => 0101010
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,4,7,8,3] => 1000101 => 0111010
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => 1000111 => 0111000
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,5,6,7,4,3,8] => 1010010 => 0101101
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,4,8,3] => 1000011 => 0111100
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => 1010001 => 0101110
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,7,4,3] => 1010011 => 0101100
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,6,4,8,3] => 1000111 => 0111000
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => 1010011 => 0101100
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => 1010101 => 0101010
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,7,6,4,3] => 1010111 => 0101000
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 1011101 => 0100010
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => 1001111 => 0110000
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => 1000111 => 0111000
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => 1010101 => 0101010
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => 1010111 => 0101000
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,6,7,5,4,3,8] => 1011010 => 0100101
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,5,4,8,3] => 1001011 => 0110100
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => 1010011 => 0101100
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => 1011001 => 0100110
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,7,5,4,3] => 1011011 => 0100100
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => 1011110 => 0100001
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => 1001111 => 0110000
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => 1010111 => 0101000
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => 1011011 => 0100100
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,6,5,4,3] => 1011101 => 0100010
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 1011111 => 0100000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => 0100000 => 1011111
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => 0100001 => 1011110
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => 0100010 => 1011101
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => 0100001 => 1011110
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => 0100101 => 1011010
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => 0100010 => 1011101
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => 0100001 => 1011110
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => 0100011 => 1011100
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,6,5] => 0100101 => 1011010
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => 0100111 => 1011000
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => 0101000 => 1010111
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => 0101010 => 1010101
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => 0100100 => 1011011
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => 0100010 => 1011101
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => 0100001 => 1011110
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => 0100011 => 1011100
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,6,4] => 0100101 => 1011010
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => 0101100 => 1010011
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => 0101101 => 1010010
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => 0100110 => 1011001
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => 0100111 => 1011000
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,6,7,5,4,8] => 0101010 => 1010101
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,5,8,4] => 0100011 => 1011100
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,5,4] => 0101001 => 1010110
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,7,5,4] => 0101011 => 1010100
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => 0100111 => 1011000
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,6,8,5,4] => 0101011 => 1010100
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => 0101101 => 1010010
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => 0101111 => 1010000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => 0010000 => 1101111
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => 0010001 => 1101110
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => 0010010 => 1101101
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => 0010001 => 1101110
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => 0010011 => 1101100
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => 0010100 => 1101011
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => 0010101 => 1101010
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => 0010010 => 1101101
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => 0010001 => 1101110
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => 0010011 => 1101100
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => 0010110 => 1101001
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => 0010011 => 1101100
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => 0010101 => 1101010
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => 0010111 => 1101000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => 0001000 => 1110111
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => 0001001 => 1110110
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => 0001010 => 1110101
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => 0001001 => 1110110
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => 0001011 => 1110100
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => 0000100 => 1111011
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => 0000101 => 1111010
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => 0000010 => 1111101
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 0000001 => 1111110
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => 0000011 => 1111100
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => 0000110 => 1111001
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => 0000011 => 1111100
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => 0000101 => 1111010
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => 0000111 => 1111000
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => 0001100 => 1110011
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => 0000110 => 1111001
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => 0000101 => 1111010
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => 0000111 => 1111000
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => 0001010 => 1110101
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => 0000011 => 1111100
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => 0001001 => 1110110
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,7,5,1] => 0001011 => 1110100
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => 0001110 => 1110001
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => 0000111 => 1111000
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => 0001011 => 1110100
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,6,5,1] => 0001101 => 1110010
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => 0001111 => 1110000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => 0011000 => 1100111
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => 0011001 => 1100110
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => 0011010 => 1100101
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => 0011011 => 1100100
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => 0001100 => 1110011
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => 0001010 => 1110101
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => 0001001 => 1110110
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => 0001011 => 1110100
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,7,8,6,1] => 0001101 => 1110010
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => 0001111 => 1110000
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,4,1,7,8] => 0010100 => 1101011
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,5,6,4,1,8,7] => 0010101 => 1101010
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,4,7,1,8] => 0000110 => 1111001
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => 0000101 => 1111010
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,4,8,7,1] => 0000111 => 1111000
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,4,1,8] => 0010010 => 1101101
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => 0000011 => 1111100
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => 0010001 => 1101110
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => 0010011 => 1101100
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,5,7,6,4,1,8] => 0010110 => 1101001
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,6,4,8,1] => 0000111 => 1111000
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,6,8,4,1] => 0010011 => 1101100
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => 0010101 => 1101010
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,8,7,6,4,1] => 0010111 => 1101000
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => 0011100 => 1100011
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => 0011101 => 1100010
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => 0001101 => 1110010
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,6,5,7,4,1,8] => 0010110 => 1101001
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => 0010111 => 1101000
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,6,7,5,4,1,8] => 0011010 => 1100101
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,5,4,1] => 0011001 => 1100110
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => 0011110 => 1100001
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => 0001111 => 1110000
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,6,5,8,4,1] => 0010111 => 1101000
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => 0011111 => 1100000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => 0110000 => 1001111
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => 0110011 => 1001100
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => 0110100 => 1001011
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => 0110101 => 1001010
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => 0110001 => 1001110
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => 0110011 => 1001100
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => 0110011 => 1001100
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => 0110101 => 1001010
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => 0110111 => 1001000
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => 0011000 => 1100111
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => 0011001 => 1100110
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => 0011010 => 1100101
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => 0011001 => 1100110
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => 0011011 => 1100100
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => 0010101 => 1101010
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => 0010001 => 1101110
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => 0010011 => 1101100
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => 0010011 => 1101100
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,4,3,5,8,7,6,1] => 0010111 => 1101000
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => 0011100 => 1100011
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => 0011101 => 1100010
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => 0010110 => 1101001
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => 0010101 => 1101010
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => 0010111 => 1101000
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,6,7,5,8,1] => 0010011 => 1101100
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,6,7,8,5,1] => 0011001 => 1100110
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => 0011011 => 1100100
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => 0010111 => 1101000
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => 0011111 => 1100000
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => 0101000 => 1010111
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,4,5,3,1,6,8,7] => 0101001 => 1010110
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,3,1,7,6,8] => 0101010 => 1010101
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,3,1,7,8,6] => 0101001 => 1010110
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => 0101011 => 1010100
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,3,6,1,8,7] => 0001101 => 1110010
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,4,5,3,6,7,1,8] => 0001010 => 1110101
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => 0001001 => 1110110
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,3,6,8,7,1] => 0001011 => 1110100
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,7,8,6,1] => 0001101 => 1110010
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,4,5,3,8,7,6,1] => 0001111 => 1110000
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,3,1,7,8] => 0100100 => 1011011
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,3,7,8,1] => 0000101 => 1111010
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,3,8,7,1] => 0000111 => 1111000
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => 0100010 => 1011101
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => 0000011 => 1111100
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,3,1] => 0100001 => 1011110
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,7,3,1] => 0100011 => 1011100
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,6,3,1] => 0100101 => 1011010
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,5,3,1,7,8] => 0101100 => 1010011
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => 0101101 => 1010010
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,5,3,7,8,1] => 0001101 => 1110010
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => 0001111 => 1110000
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => 0000111 => 1111000
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => 0100101 => 1011010
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => 0100111 => 1011000
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => 0101010 => 1010101
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,5,3,8,1] => 0001011 => 1110100
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,4,6,7,5,8,3,1] => 0100011 => 1011100
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => 0101001 => 1010110
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => 0101011 => 1010100
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,4,7,6,5,8,3,1] => 0100111 => 1011000
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,6,5,3,1] => 0101101 => 1010010
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => 0101111 => 1010000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => 0111000 => 1000111
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => 0111001 => 1000110
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => 0111010 => 1000101
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => 0111001 => 1000110
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => 0111011 => 1000100
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => 0011101 => 1100010
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => 0011010 => 1100101
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => 0011001 => 1100110
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => 0011011 => 1100100
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => 0011011 => 1100100
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,7,8,6,1] => 0011101 => 1100010
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => 0011111 => 1100000
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => 0001110 => 1110001
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,4,6,3,7,8,1] => 0001101 => 1110010
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => 0101010 => 1010101
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => 0001011 => 1110100
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,4,6,7,8,3,1] => 0101001 => 1010110
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,5,4,7,6,3,1,8] => 0101110 => 1010001
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,4,7,6,3,8,1] => 0001111 => 1110000
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,4,7,6,8,3,1] => 0101011 => 1010100
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,4,7,8,6,3,1] => 0101101 => 1010010
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,4,8,7,6,3,1] => 0101111 => 1010000
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,4,3,1,8,7] => 0110101 => 1001010
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,5,6,4,3,7,8,1] => 0010101 => 1101010
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,4,7,3,1,8] => 0100110 => 1011001
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,4,7,8,3,1] => 0100101 => 1011010
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,4,8,7,3,1] => 0100111 => 1011000
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,5,6,7,4,3,1,8] => 0110010 => 1001101
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,4,3,8,1] => 0010011 => 1101100
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => 0100011 => 1011100
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => 0110001 => 1001110
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,5,7,6,4,3,1,8] => 0110110 => 1001001
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,5,8,7,6,4,3,1] => 0110111 => 1001000
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => 0111101 => 1000010
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => 0011101 => 1100010
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => 0011111 => 1100000
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,5,4,7,8,3,1] => 0101101 => 1010010
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => 0101111 => 1010000
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => 0010111 => 1101000
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,6,5,7,8,4,3,1] => 0110101 => 1001010
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,5,4,3,1,8] => 0111010 => 1000101
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,6,7,5,4,8,3,1] => 0101011 => 1010100
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => 0110011 => 1001100
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,5,4,3,1] => 0111001 => 1000110
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => 0111011 => 1000100
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => 0111110 => 1000001
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => 0011111 => 1100000
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,6,5,4,8,3,1] => 0101111 => 1010000
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,6,8,5,4,3,1] => 0111011 => 1000100
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => 0111101 => 1000010
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => 0111111 => 1000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => 1100000 => 0011111
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => 1100001 => 0011110
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => 1100010 => 0011101
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => 1100001 => 0011110
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => 1100011 => 0011100
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => 1100001 => 0011110
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => 1100011 => 0011100
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => 1100110 => 0011001
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => 1100011 => 0011100
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => 1100101 => 0011010
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => 1100111 => 0011000
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => 1101000 => 0010111
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => 1101010 => 0010101
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => 1100100 => 0011011
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,5,6,7,4,8] => 1100010 => 0011101
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => 1100001 => 0011110
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => 1100011 => 0011100
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => 1100110 => 0011001
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => 1100011 => 0011100
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => 1100101 => 0011010
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => 1100111 => 0011000
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => 1101100 => 0010011
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => 1101101 => 0010010
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,2,1,6,5,7,4,8] => 1100110 => 0011001
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => 1100101 => 0011010
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => 1100111 => 0011000
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,6,7,5,4,8] => 1101010 => 0010101
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => 1100011 => 0011100
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,6,7,8,5,4] => 1101001 => 0010110
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => 1101011 => 0010100
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => 1101110 => 0010001
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => 1100111 => 0011000
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,7,6,8,5,4] => 1101011 => 0010100
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => 1101101 => 0010010
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 1101111 => 0010000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => 0110000 => 1001111
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => 0110001 => 1001110
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => 0110010 => 1001101
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => 0110001 => 1001110
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => 0110011 => 1001100
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => 0110100 => 1001011
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => 0110101 => 1001010
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => 0110010 => 1001101
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => 0110001 => 1001110
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => 0110011 => 1001100
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => 0110110 => 1001001
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => 0110011 => 1001100
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => 0110101 => 1001010
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => 0110111 => 1001000
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => 0101000 => 1010111
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => 0101011 => 1010100
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => 0100100 => 1011011
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => 0100010 => 1011101
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => 0100001 => 1011110
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => 0100011 => 1011100
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => 0100011 => 1011100
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,7,8,6,1] => 0100101 => 1011010
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => 0100111 => 1011000
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,6,7,5,1,8] => 0101010 => 1010101
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => 0100111 => 1011000
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,7,8,6,5,1] => 0101101 => 1010010
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => 0101111 => 1010000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => 0111000 => 1000111
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => 0111001 => 1000110
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => 0111010 => 1000101
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => 0111001 => 1000110
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => 0111011 => 1000100
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => 0101101 => 1010010
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => 0101001 => 1010110
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => 0101011 => 1010100
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => 0101110 => 1010001
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => 0101011 => 1010100
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,7,8,6,1] => 0101101 => 1010010
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,5,6,4,1,8,7] => 0110101 => 1001010
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,5,6,4,7,8,1] => 0100101 => 1011010
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,5,6,7,4,1,8] => 0110010 => 1001101
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => 0100011 => 1011100
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => 0110001 => 1001110
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,5,7,6,4,1,8] => 0110110 => 1001001
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,5,7,6,4,8,1] => 0100111 => 1011000
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,5,7,6,8,4,1] => 0110011 => 1001100
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,5,7,8,6,4,1] => 0110101 => 1001010
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => 0111101 => 1000010
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => 0101110 => 1010001
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => 0101111 => 1010000
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,6,5,7,4,1,8] => 0110110 => 1001001
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => 0100111 => 1011000
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,6,5,8,7,4,1] => 0110111 => 1001000
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => 0111010 => 1000101
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => 0101011 => 1010100
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => 0111011 => 1000100
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => 0111110 => 1000001
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => 0101111 => 1010000
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,7,8,6,5,4,1] => 0111101 => 1000010
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => 0111111 => 1000000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => 1010000 => 0101111
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,4,2,1,5,6,8,7] => 1010001 => 0101110
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,4,2,1,5,8,7,6] => 1010011 => 0101100
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => 1010101 => 0101010
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => 1010001 => 0101110
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => 1010011 => 0101100
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => 1010011 => 0101100
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => 1010101 => 0101010
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => 1010111 => 0101000
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => 0011000 => 1100111
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,2,5,1,7,6,8] => 0011010 => 1100101
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,2,5,1,7,8,6] => 0011001 => 1100110
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => 0011011 => 1100100
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,2,5,6,1,7,8] => 0010100 => 1101011
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,2,5,6,1,8,7] => 0010101 => 1101010
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,2,5,6,7,1,8] => 0010010 => 1101101
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => 0010001 => 1101110
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,2,5,6,8,7,1] => 0010011 => 1101100
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,2,5,7,6,1,8] => 0010110 => 1101001
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,2,5,7,6,8,1] => 0010011 => 1101100
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => 0010101 => 1101010
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,2,5,8,7,6,1] => 0010111 => 1101000
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,2,6,5,1,8,7] => 0011101 => 1100010
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,2,6,5,7,1,8] => 0010110 => 1101001
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,2,6,5,7,8,1] => 0010101 => 1101010
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,4,2,6,5,8,7,1] => 0010111 => 1101000
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,2,6,7,5,1,8] => 0011010 => 1100101
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => 0010011 => 1101100
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,4,2,7,6,5,1,8] => 0011110 => 1100001
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,4,2,7,6,5,8,1] => 0010111 => 1101000
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,4,2,7,8,6,5,1] => 0011101 => 1100010
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => 0011111 => 1100000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => 1001000 => 0110111
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,2,1,6,8,7] => 1001001 => 0110110
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,5,2,1,7,6,8] => 1001010 => 0110101
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,5,2,1,7,8,6] => 1001001 => 0110110
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => 1001011 => 0110100
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => 0001100 => 1110011
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,2,6,1,8,7] => 0001101 => 1110010
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => 0001010 => 1110101
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => 0001001 => 1110110
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,5,2,7,6,1,8] => 0001110 => 1110001
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => 0001011 => 1110100
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,2,7,8,6,1] => 0001101 => 1110010
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => 1000100 => 0111011
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,2,1,8,7] => 1000101 => 0111010
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => 0000110 => 1111001
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => 0000101 => 1111010
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => 0000111 => 1111000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => 1000010 => 0111101
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => 0000011 => 1111100
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => 1000001 => 0111110
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,7,2,1] => 1000011 => 0111100
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,5,7,6,2,8,1] => 0000111 => 1111000
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => 1000011 => 0111100
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => 1000101 => 0111010
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => 1000111 => 0111000
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,5,2,1,8,7] => 1001101 => 0110010
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,5,2,7,1,8] => 0001110 => 1110001
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,5,2,7,8,1] => 0001101 => 1110010
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => 0000111 => 1111000
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,5,7,8,2,1] => 1000101 => 0111010
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,5,2,8,1] => 0001011 => 1110100
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,4,6,7,5,8,2,1] => 1000011 => 0111100
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => 1001001 => 0110110
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => 1001110 => 0110001
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,6,5,2,8,1] => 0001111 => 1110000
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,4,7,6,5,8,2,1] => 1000111 => 0111000
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,7,6,5,2,1] => 1001111 => 0110000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => 1011000 => 0100111
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,4,2,1,6,8,7] => 1011001 => 0100110
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,4,2,1,7,6,8] => 1011010 => 0100101
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,4,2,1,7,8,6] => 1011001 => 0100110
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => 1011011 => 0100100
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,5,4,2,6,1,7,8] => 0011100 => 1100011
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,4,2,6,1,8,7] => 0011101 => 1100010
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,4,2,6,7,1,8] => 0011010 => 1100101
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,4,2,6,7,8,1] => 0011001 => 1100110
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => 0011110 => 1100001
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,4,2,7,6,8,1] => 0011011 => 1100100
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,4,2,7,8,6,1] => 0011101 => 1100010
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => 0001110 => 1110001
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,4,6,2,7,8,1] => 0001101 => 1110010
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,5,4,6,2,8,7,1] => 0001111 => 1110000
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,4,6,7,2,8,1] => 0001011 => 1110100
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,4,6,7,8,2,1] => 1001001 => 0110110
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,5,4,7,6,2,1,8] => 1001110 => 0110001
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,4,7,6,2,8,1] => 0001111 => 1110000
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => 1001011 => 0110100
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,4,7,8,6,2,1] => 1001101 => 0110010
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,4,2,1,8,7] => 1010101 => 0101010
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,4,2,7,1,8] => 0010110 => 1101001
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,4,2,7,8,1] => 0010101 => 1101010
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,5,6,4,2,8,7,1] => 0010111 => 1101000
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,4,7,2,1,8] => 1000110 => 0111001
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => 0000111 => 1111000
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,4,7,8,2,1] => 1000101 => 0111010
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,4,2,1,8] => 1010010 => 0101101
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => 0010011 => 1101100
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,4,8,2,1] => 1000011 => 0111100
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => 1010001 => 0101110
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => 1010011 => 0101100
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => 1010110 => 0101001
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,6,4,2,8,1] => 0010111 => 1101000
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,6,4,8,2,1] => 1000111 => 0111000
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,5,7,6,8,4,2,1] => 1010011 => 0101100
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => 1010101 => 0101010
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => 1010111 => 0101000
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,5,4,2,1,7,8] => 1011100 => 0100011
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => 1011101 => 0100010
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,6,5,4,2,7,1,8] => 0011110 => 1100001
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,5,4,2,7,8,1] => 0011101 => 1100010
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,6,5,4,2,8,7,1] => 0011111 => 1100000
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,6,5,4,7,2,1,8] => 1001110 => 0110001
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => 0001111 => 1110000
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,5,4,7,8,2,1] => 1001101 => 0110010
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,5,4,8,7,2,1] => 1001111 => 0110000
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,6,7,5,8,4,2,1] => 1010011 => 0101100
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => 1011011 => 0100100
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => 1001111 => 0110000
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,6,5,8,4,2,1] => 1010111 => 0101000
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,6,8,5,4,2,1] => 1011011 => 0100100
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => 1011101 => 0100010
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => 1011111 => 0100000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => 1110000 => 0001111
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => 1110001 => 0001110
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => 1110010 => 0001101
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => 1110001 => 0001110
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => 1110011 => 0001100
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => 1110100 => 0001011
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 1110101 => 0001010
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => 1110010 => 0001101
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => 1110001 => 0001110
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => 1110011 => 0001100
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => 1110110 => 0001001
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => 1110011 => 0001100
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => 1110101 => 0001010
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 1110111 => 0001000
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => 0111000 => 1000111
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => 0111001 => 1000110
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => 0111011 => 1000100
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => 0110100 => 1001011
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => 0110101 => 1001010
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => 0110010 => 1001101
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => 0110001 => 1001110
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => 0110011 => 1001100
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => 0110110 => 1001001
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => 0110011 => 1001100
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,3,2,5,7,8,6,1] => 0110101 => 1001010
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => 0110111 => 1001000
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => 0111100 => 1000011
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => 0111101 => 1000010
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => 0110110 => 1001001
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => 0110101 => 1001010
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => 0110111 => 1001000
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,3,2,6,7,5,1,8] => 0111010 => 1000101
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,6,7,5,8,1] => 0110011 => 1001100
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,6,8,7,5,1] => 0111011 => 1000100
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => 0110111 => 1001000
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,7,8,6,5,1] => 0111101 => 1000010
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => 0111111 => 1000000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => 1011000 => 0100111
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,3,5,2,1,6,8,7] => 1011001 => 0100110
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,3,5,2,1,8,7,6] => 1011011 => 0100100
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => 0011100 => 1100011
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => 0011101 => 1100010
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => 0011001 => 1100110
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,3,5,2,7,6,1,8] => 0011110 => 1100001
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => 0011011 => 1100100
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,3,5,2,8,7,6,1] => 0011111 => 1100000
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => 1010101 => 0101010
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,3,5,6,2,7,1,8] => 0010110 => 1101001
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => 0010101 => 1101010
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,3,5,6,7,2,8,1] => 0010011 => 1101100
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => 1010001 => 0101110
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,3,5,6,8,7,2,1] => 1010011 => 0101100
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,3,5,7,6,2,1,8] => 1010110 => 0101001
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,3,5,7,6,8,2,1] => 1010011 => 0101100
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,7,8,6,2,1] => 1010101 => 0101010
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,3,6,5,2,1,7,8] => 1011100 => 0100011
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => 1011101 => 0100010
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => 0011111 => 1100000
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,3,6,5,7,2,1,8] => 1010110 => 0101001
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => 0010111 => 1101000
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => 1010101 => 0101010
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => 1010111 => 0101000
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,3,6,7,5,2,8,1] => 0011011 => 1100100
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => 1011001 => 0100110
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,7,6,5,2,1,8] => 1011110 => 0100001
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,7,6,5,2,8,1] => 0011111 => 1100000
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,7,6,5,8,2,1] => 1010111 => 0101000
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,7,8,6,5,2,1] => 1011101 => 0100010
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,3,8,7,6,5,2,1] => 1011111 => 0100000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => 1101000 => 0010111
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,5,3,2,1,6,8,7] => 1101001 => 0010110
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,5,3,2,1,7,6,8] => 1101010 => 0010101
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,3,2,1,8,7,6] => 1101011 => 0010100
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,5,3,2,6,1,7,8] => 0101100 => 1010011
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,3,2,6,1,8,7] => 0101101 => 1010010
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,3,2,6,7,8,1] => 0101001 => 1010110
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,5,3,2,6,8,7,1] => 0101011 => 1010100
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,3,2,7,6,1,8] => 0101110 => 1010001
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,3,2,8,7,6,1] => 0101111 => 1010000
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => 1001101 => 0110010
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => 0001110 => 1110001
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,3,6,2,8,7,1] => 0001111 => 1110000
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,3,6,7,2,8,1] => 0001011 => 1110100
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,6,8,7,2,1] => 1001011 => 0110100
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,5,3,7,6,2,1,8] => 1001110 => 0110001
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,5,3,7,6,2,8,1] => 0001111 => 1110000
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,3,7,6,8,2,1] => 1001011 => 0110100
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,3,7,8,6,2,1] => 1001101 => 0110010
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,3,2,1,7,8] => 1100100 => 0011011
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => 1100101 => 0011010
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => 0100101 => 1011010
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,3,2,8,7,1] => 0100111 => 1011000
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => 0000111 => 1111000
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,5,6,3,7,8,2,1] => 1000101 => 0111010
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,3,8,7,2,1] => 1000111 => 0111000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,3,2,1,8] => 1100010 => 0011101
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => 0100011 => 1011100
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => 1000011 => 0111100
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => 1100001 => 0011110
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => 1100011 => 0011100
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,6,3,2,1,8] => 1100110 => 0011001
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,6,8,3,2,1] => 1100011 => 0011100
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,5,7,8,6,3,2,1] => 1100101 => 0011010
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => 1100111 => 0011000
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,5,3,2,1,8,7] => 1101101 => 0010010
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,5,3,2,8,7,1] => 0101111 => 1010000
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => 0001111 => 1110000
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,5,7,3,2,1,8] => 1100110 => 0011001
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => 0100111 => 1011000
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => 1100101 => 0011010
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,5,8,7,3,2,1] => 1100111 => 0011000
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,6,7,5,3,2,1,8] => 1101010 => 0010101
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => 0101011 => 1010100
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => 1100011 => 0011100
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,5,3,2,1] => 1101001 => 0010110
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => 1101011 => 0010100
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => 1101110 => 0010001
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => 0101111 => 1010000
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,6,5,3,8,2,1] => 1001111 => 0110000
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => 1100111 => 0011000
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,6,8,5,3,2,1] => 1101011 => 0010100
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,6,5,3,2,1] => 1101101 => 0010010
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => 1101111 => 0010000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => 1111000 => 0000111
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => 1111001 => 0000110
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => 1111010 => 0000101
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => 1111001 => 0000110
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 1111011 => 0000100
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => 0111100 => 1000011
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => 0111101 => 1000010
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => 0111010 => 1000101
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => 0111001 => 1000110
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => 0111011 => 1000100
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => 0111110 => 1000001
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => 0111011 => 1000100
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => 0111101 => 1000010
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => 0111111 => 1000000
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,4,3,6,2,1,7,8] => 1011100 => 0100011
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,4,3,6,2,1,8,7] => 1011101 => 0100010
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => 0011110 => 1100001
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,4,3,6,2,7,8,1] => 0011101 => 1100010
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,4,3,6,2,8,7,1] => 0011111 => 1100000
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,4,3,6,7,2,1,8] => 1011010 => 0100101
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,4,3,6,7,2,8,1] => 0011011 => 1100100
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,2,1] => 1011001 => 0100110
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,4,3,6,8,7,2,1] => 1011011 => 0100100
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,4,3,7,6,2,1,8] => 1011110 => 0100001
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,4,3,7,6,2,8,1] => 0011111 => 1100000
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,3,7,8,6,2,1] => 1011101 => 0100010
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,4,3,8,7,6,2,1] => 1011111 => 0100000
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => 1101100 => 0010011
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => 1101101 => 0010010
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,4,6,3,2,7,1,8] => 0101110 => 1010001
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,4,6,3,2,7,8,1] => 0101101 => 1010010
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,4,6,3,2,8,7,1] => 0101111 => 1010000
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => 1001110 => 0110001
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => 0001111 => 1110000
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => 1101010 => 0010101
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => 1001011 => 0110100
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => 1101001 => 0010110
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,4,7,6,3,2,1,8] => 1101110 => 0010001
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,4,7,6,3,8,2,1] => 1001111 => 0110000
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,4,7,6,8,3,2,1] => 1101011 => 0010100
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,4,7,8,6,3,2,1] => 1101101 => 0010010
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,4,3,2,1,7,8] => 1110100 => 0001011
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => 1110101 => 0001010
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,6,4,3,2,7,1,8] => 0110110 => 1001001
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => 1010110 => 0101001
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,4,3,8,7,2,1] => 1010111 => 0101000
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,4,7,3,2,1,8] => 1100110 => 0011001
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => 1100101 => 0011010
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,4,8,7,3,2,1] => 1100111 => 0011000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => 1110010 => 0001101
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,4,3,2,8,1] => 0110011 => 1001100
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,4,3,8,2,1] => 1010011 => 0101100
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => 1100011 => 0011100
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => 1110001 => 0001110
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => 1110011 => 0001100
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => 1110110 => 0001001
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,6,4,3,2,8,1] => 0110111 => 1001000
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,6,4,3,8,2,1] => 1010111 => 0101000
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,6,4,8,3,2,1] => 1100111 => 0011000
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => 1110011 => 0001100
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => 1110101 => 0001010
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => 1110111 => 0001000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => 1111100 => 0000011
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => 1111101 => 0000010
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => 0111110 => 1000001
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => 0111101 => 1000010
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => 0111111 => 1000000
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => 1011110 => 0100001
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => 0011111 => 1100000
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => 1011101 => 0100010
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => 1011111 => 0100000
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => 1101110 => 0010001
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => 0101111 => 1010000
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => 1001111 => 0110000
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => 1101101 => 0010010
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,5,4,8,7,3,2,1] => 1101111 => 0010000
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => 1110110 => 0001001
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => 0110111 => 1001000
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => 1010111 => 0101000
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => 1100111 => 0011000
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => 1110101 => 0001010
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => 1110111 => 0001000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => 1111010 => 0000101
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => 0111011 => 1000100
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,5,4,3,8,2,1] => 1011011 => 0100100
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => 1101011 => 0010100
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => 1110011 => 0001100
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => 1111001 => 0000110
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => 1111011 => 0000100
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => 1111110 => 0000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => 0111111 => 1000000
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => 1011111 => 0100000
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => 1101111 => 0010000
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => 1110111 => 0001000
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => 1111011 => 0000100
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => 1111101 => 0000010
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => 1111111 => 0000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => 11111110 => 00000001
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => 01111111 => 10000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => 111111110 => 000000001
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,6,5,4,3,2,1,9] => 11111010 => 00000101
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,7,6,5,4,3,2] => 01111101 => 10000010
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 100000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110 => 0000000001
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,7,6,5,4,3,2,1,10] => 111111010 => 000000101
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,6,8,5,4,3,2,1,9] => 11110110 => 00001001
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,7,5,4,3,2,1,9] => 11110110 => 00001001
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,7,9,6,5,4,3,2] => 01111011 => 10000100
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,8,6,5,4,3,2] => 01111011 => 10000100
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,8,7,6,5,4,3,2] => 011111101 => 100000010
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 1000000000
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1,12] => 11111111110 => 00000000001
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [8,7,9,6,5,4,3,2,1,10] => 111110110 => 000001001
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [7,6,5,8,4,3,2,1,9] => 11101110 => 00010001
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,7,8,5,4,3,2,1,9] => 11110010 => 00001101
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,7,8,9,6,5,4,3,2] => 01111001 => 10000110
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,8,10,7,6,5,4,3,2] => 011111011 => 100000100
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,6,9,8,7,5,4,3,2] => 01110111 => 10001000
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,8,10,9,7,6,5,4,3,2] => 011111011 => 100000100
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [9,8,10,7,6,5,4,3,2,1,11] => 1111110110 => 0000001001
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [8,7,6,9,5,4,3,2,1,10] => 111101110 => 000010001
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,9,6,5,4,3,2,1,10] => 111110010 => 000001101
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [6,7,5,8,4,3,2,1,9] => 11100110 => 00011001
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [6,5,8,7,4,3,2,1,9] => 11101110 => 00010001
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,8,7,6,5,3,2,1,9] => 11011110 => 00100001
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,6,9,8,5,4,3,2] => 01110111 => 10001000
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,8,9,10,7,6,5,4,3,2] => 011111001 => 100000110
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,7,10,9,8,6,5,4,3,2] => 011110111 => 100001000
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,9,11,10,8,7,6,5,4,3,2] => 0111111011 => 1000000100
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,9,8,7,6,4,3,2,1,10] => 111011110 => 000100001
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [7,6,5,4,3,8,2,1,9] => 10111110 => 01000001
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [6,5,7,8,4,3,2,1,9] => 11101010 => 00010101
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,6,8,9,5,4,3,2] => 01110101 => 10001010
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,4,9,8,7,6,5,3,2] => 01011111 => 10100000
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,8,11,10,9,7,6,5,4,3,2] => 0111110111 => 1000001000
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [8,7,6,5,4,9,3,2,1,10] => 110111110 => 001000001
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [7,6,8,9,5,4,3,2,1,10] => 111101010 => 000010101
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,6,5,4,3,2,8,1,9] => 01111110 => 10000001
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => 01111110 => 10000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => 11111101 => 00000010
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,9,5,4,3,2] => 01110001 => 10001110
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => 10111111 => 01000000
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => 00111111 => 11000000
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,5,10,9,8,7,6,4,3,2] => 011011111 => 100100000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [8,7,6,5,4,3,9,2,1,10] => 101111110 => 010000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => 11111100 => 00000011
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => 01111110 => 10000001
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [6,7,5,4,3,2,1,9,8] => 11110101 => 00001010
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,7,8,9,10,6,5,4,3,2] => 011110001 => 100001110
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,8,9,7,6,5,4,3] => 10111101 => 01000010
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => 00111111 => 11000000
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,4,10,9,8,7,6,5,3,2] => 010111111 => 101000000
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,6,11,10,9,8,7,5,4,3,2] => 0111011111 => 1000100000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,7,6,5,4,3,2,9,1,10] => 011111110 => 100000001
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => 111111101 => 000000010
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9] => 11110100 => 00001011
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,7,8,6,5,4,3,2,9] => 01111010 => 10000101
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 010000000
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,10,9,8,7,6,5,4,2] => 001111111 => 110000000
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,5,11,10,9,8,7,6,4,3,2] => 0110111111 => 1001000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => 111111100 => 000000011
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => 011111110 => 100000001
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [6,5,4,3,7,8,2,1,9] => 10111010 => 01000101
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,5,7,8,9,4,3,2] => 01101001 => 10010110
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => 001111111 => 110000000
[] => [] => =>
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => 00000001 => 11111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => 00000011 => 11111100
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => 00000011 => 11111100
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,8,9,7,1] => 00000101 => 11111010
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => 00000111 => 11111000
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,1] => 00000101 => 11111010
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,5,7,8,6,9,1] => 00000011 => 11111100
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,7,8,9,6,1] => 00001001 => 11110110
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,5,7,9,8,6,1] => 00001011 => 11110100
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,5,8,7,6,9,1] => 00000111 => 11111000
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,5,8,7,9,6,1] => 00001011 => 11110100
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,8,9,7,6,1] => 00001101 => 11110010
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,1] => 00001001 => 11110110
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,4,6,7,5,8,9,1] => 00000101 => 11111010
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,7,8,9,6,5,1] => 00011001 => 11100110
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,5,6,4,7,8,9,1] => 00001001 => 11110110
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,9,4,1] => 00100001 => 11011110
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,6,5,7,8,9,4,1] => 00101001 => 11010110
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,9,5,4,1] => 00110001 => 11001110
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => 00111111 => 11000000
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => 00100001 => 11011110
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,3,1] => 01000001 => 10111110
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,9,4,3,1] => 01100001 => 10011110
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => 00111111 => 11000000
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,8,7,9,6,5,4,3,1] => 01111011 => 10000100
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,8,9,7,6,5,4,3,1] => 01111101 => 10000010
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => 01111111 => 10000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => 01000001 => 10111110
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,9,8,1] => 01010111 => 10101000
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,9,8,7,6,5,4,1] => 01111111 => 10000000
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,1] => 00100001 => 11011110
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,2,9,1] => 00000011 => 11111100
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,2,1] => 10000001 => 01111110
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,9,4,2,1] => 10100001 => 01011110
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,7,9,8,4,2,1] => 10100011 => 01011100
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [3,8,7,6,5,4,9,2,1] => 10011111 => 01100000
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,9,8,7,6,5,4,2,1] => 10111111 => 01000000
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => 01100001 => 10011110
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,9,5,2,1] => 10110001 => 01001110
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,6,3,7,8,9,2,1] => 10001001 => 01110110
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,7,3,9,8,2,1] => 10000111 => 01111000
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => 11000001 => 00111110
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,7,9,8,3,2,1] => 11000011 => 00111100
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,8,7,6,5,9,3,2,1] => 11001111 => 00110000
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,9,8,7,6,5,3,2,1] => 11011111 => 00100000
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => 01110001 => 10001110
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,4,3,2,9,8,7,6,1] => 01111111 => 10000000
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,8,3,9,2,1] => 10010011 => 01101100
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => 11010001 => 00101110
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,9,8,3,2,1] => 11010111 => 00101000
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,6,4,7,3,8,2,9,1] => 00001111 => 11110000
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => 11100001 => 00011110
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,9,8,4,3,2,1] => 11100011 => 00011100
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [5,7,9,8,6,4,3,2,1] => 11101011 => 00010100
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,8,7,6,9,4,3,2,1] => 11100111 => 00011000
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,9,8,7,6,4,3,2,1] => 11101111 => 00010000
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,1] => 01111001 => 10000110
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [6,5,4,9,8,7,3,2,1] => 11011111 => 00100000
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,5,7,8,9,4,3,2,1] => 11101001 => 00010110
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [6,5,8,9,7,4,3,2,1] => 11101101 => 00010010
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [6,7,5,9,8,4,3,2,1] => 11100111 => 00011000
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => 11110001 => 00001110
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,7,9,8,5,4,3,2,1] => 11110011 => 00001100
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [6,8,7,5,4,3,2,9,1] => 01110111 => 10001000
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [6,8,7,9,5,4,3,2,1] => 11110011 => 00001100
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [6,9,8,7,5,4,3,2,1] => 11110111 => 00001000
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,1] => 01111101 => 10000010
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,6,5,4,3,2,9,8,1] => 01111111 => 10000000
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,6,8,5,4,3,2,9,1] => 01110111 => 10001000
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [7,6,8,5,9,4,3,2,1] => 11100111 => 00011000
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,6,8,9,5,4,3,2,1] => 11110101 => 00001010
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,6,9,8,5,4,3,2,1] => 11110111 => 00001000
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,8,6,5,4,3,2,9,1] => 01111011 => 10000100
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,6,5,4,3,2,1] => 11111001 => 00000110
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,8,6,5,4,3,2,1] => 11111011 => 00000100
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => 01111111 => 10000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1] => 10111111 => 01000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,7,6,5,4,9,3,2,1] => 11011111 => 00100000
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,7,6,5,9,4,3,2,1] => 11101111 => 00010000
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,7,6,9,5,4,3,2,1] => 11110111 => 00001000
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,7,9,6,5,4,3,2,1] => 11111011 => 00000100
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,7,6,5,4,3,2,1] => 11111101 => 00000010
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => 11111111 => 00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => 00000000 => 11111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => 00000001 => 11111110
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => 00000001 => 11111110
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => 00000001 => 11111110
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => 00000001 => 11111110
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => 00000001 => 11111110
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => 00000001 => 11111110
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => 00000001 => 11111110
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => 000000001 => 111111110
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => 00000011 => 11111100
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => 000000001 => 111111110
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => 00000011 => 11111100
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => 000000001 => 111111110
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,6,8,9,5] => 00000101 => 11111010
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => 000000001 => 111111110
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,5,7,8,9,4] => 00001001 => 11110110
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => 000000001 => 111111110
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => 00010001 => 11101110
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => 000000001 => 111111110
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => 00100001 => 11011110
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => 000000001 => 111111110
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => 000000001 => 111111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => 000000001 => 111111110
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000 => 1111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => 0000000001 => 1111111110
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => 000000011 => 111111100
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => 0000000001 => 1111111110
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,8,9,7,6] => 00000101 => 11111010
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => 00000111 => 11111000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => 010000001 => 101111110
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => 0000000001 => 1111111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000001 => 1111111110
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => 0000000011 => 1111111100
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => 000000111 => 111111000
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,7,4,8,9,3] => 00000101 => 11111010
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,10,1] => 011000001 => 100111110
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,11,1] => 0100000001 => 1011111110
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,12,2] => 00000000001 => 11111111110
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => 00001111 => 11110000
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => 000001111 => 111110000
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,8,3,9,2] => 00000011 => 11111100
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,2,7,8,9,10,1] => 000010001 => 111101110
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,10,1] => 011100001 => 100011110
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,3,2] => 01000001 => 10111110
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => 00011111 => 11100000
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,9,4,3,2] => 01100001 => 10011110
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => 000011111 => 111100000
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,10,1] => 011110001 => 100001110
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,10,3,2] => 010000001 => 101111110
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,9,2,10,1] => 000000011 => 111111100
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,9,10,4,3,2] => 011000001 => 100111110
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => 00000010 => 11111101
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => 00000100 => 11111011
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => 00000101 => 11111010
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => 00001000 => 11110111
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => 00001010 => 11110101
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,9,8,7] => 00001011 => 11110100
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => 00010000 => 11101111
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => 00010101 => 11101010
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,9,8,7,6] => 00010111 => 11101000
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,3,6,5,4,9,8,7] => 00011011 => 11100100
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => 00100000 => 11011111
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => 00101010 => 11010101
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,9,8,7,6,5] => 00101111 => 11010000
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => 01000000 => 10111111
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => 01000001 => 10111110
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,8,7] => 01000011 => 10111100
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => 01010000 => 10101111
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => 01010101 => 10101010
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,9,8,7,6,5,4] => 01011111 => 10100000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => 01100000 => 10011111
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2,9,8,7,6] => 01110111 => 10001000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,6,5,4,3,2,9,8] => 01111101 => 10000010
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => 10000000 => 01111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => 10000001 => 01111110
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => 10000010 => 01111101
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => 10100000 => 01011111
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => 10101010 => 01010101
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,9,8,7] => 10101011 => 01010100
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,9,8,7,6,5] => 10101111 => 01010000
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => 10111110 => 01000001
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => 11000000 => 00111111
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9] => 11010000 => 00101111
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6,9,8] => 11010101 => 00101010
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,6,5,4,7,8,9] => 11011000 => 00100111
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4,9,8,7] => 11011011 => 00100100
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => 11011111 => 00100000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => 11100000 => 00011111
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,3,2,1,6,5,7,8,9] => 11101000 => 00010111
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,8,7,9] => 11101010 => 00010101
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,3,2,1,7,6,5,8,9] => 11101100 => 00010011
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2,1,7,6,5,9,8] => 11101101 => 00010010
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,8,7,6,5,9] => 11101110 => 00010001
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => 11101111 => 00010000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => 11110000 => 00001111
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,4,3,2,1,7,6,8,9] => 11110100 => 00001011
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,4,3,2,1,8,7,6,9] => 11110110 => 00001001
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => 11110111 => 00001000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => 11111000 => 00000111
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,5,4,3,2,1,8,7,9] => 11111010 => 00000101
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => 11111011 => 00000100
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => 000000010 => 111111101
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => 000000100 => 111111011
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => 000000101 => 111111010
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => 000001000 => 111110111
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => 000010000 => 111101111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => 000100000 => 111011111
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => 000101010 => 111010101
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => 000111111 => 111000000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => 001000000 => 110111111
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => 001010101 => 110101010
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3,10,9,8,7] => 001110111 => 110001000
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => 010000000 => 101111111
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => 010101010 => 101010101
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,9,8] => 010101011 => 101010100
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,10,9,8,7,6,5,4] => 010111111 => 101000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => 100000000 => 011111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => 100000001 => 011111110
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => 101000000 => 010111111
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 101010101 => 010101010
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5,10,9,8] => 101011011 => 010100100
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 101110111 => 010001000
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => 101111101 => 010000010
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => 110000000 => 001111111
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9,10] => 110100000 => 001011111
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,9,8,10] => 110101010 => 001010101
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7,10,9] => 110110101 => 001001010
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,6,5,4,10,9,8,7] => 110110111 => 001001000
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => 110111111 => 001000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => 111000000 => 000111111
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => 111010101 => 000101010
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => 111010111 => 000101000
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5,10,9,8] => 111011011 => 000100100
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,8,7,6,5,9,10] => 111011100 => 000100011
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 111011101 => 000100010
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 111011111 => 000100000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => 111100000 => 000011111
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,9,8,10] => 111101010 => 000010101
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,3,2,1,9,8,7,6,10] => 111101110 => 000010001
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => 111101111 => 000010000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => 111110000 => 000001111
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,5,4,3,2,1,9,8,7,10] => 111110110 => 000001001
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 111110111 => 000001000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => 111111000 => 000000111
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,6,5,4,3,2,1,9,8,10] => 111111010 => 000000101
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => 111111011 => 000000100
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => 111111111 => 000000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => 01000000 => 10111111
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => 00100000 => 11011111
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => 00010000 => 11101111
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => 00001000 => 11110111
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => 00000100 => 11111011
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => 00000010 => 11111101
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => 010000000 => 101111111
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => 01100000 => 10011111
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => 001000000 => 110111111
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8,9] => 00110000 => 11001111
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => 000100000 => 111011111
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,4,6,5,1,7,8,9] => 00011000 => 11100111
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => 000010000 => 111101111
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,5,7,6,1,8,9] => 00001100 => 11110011
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => 000001000 => 111110111
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => 00000110 => 11111001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => 000000100 => 111111011
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => 000000010 => 111111101
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,8,10,9,4,3,2,1] => 111000011 => 000111100
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,7,8,9,10,4,3,2,1] => 111010001 => 000101110
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,8,9,11,10,4,3,2,1] => 1110000011 => 0001111100
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,7,8,10,9,3,2,1] => 110000011 => 001111100
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,9,10,3,2,1] => 110100001 => 001011110
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,7,8,9,10,11,4,3,2,1] => 1110100001 => 0001011110
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000 => 0111111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => 10000001 => 01111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => 000000011 => 111111100
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,10,9,7,6,5,4,3,2,1] => 111111011 => 000000100
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,8,10,7,6,5,4,3,2,1] => 111111011 => 000000100
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [9,11,10,8,7,6,5,4,3,2,1] => 1111111011 => 0000000100
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [7,8,10,9,6,5,4,3,2,1] => 111110011 => 000001100
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [8,7,9,10,6,5,4,3,2,1] => 111110101 => 000001010
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [10,9,11,8,7,6,5,4,3,2,1] => 1111111011 => 0000000100
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,7,9,10,8] => 100000001 => 011111110
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,6,8,9,7] => 01000001 => 10111110
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,6,8,9,7] => 01000001 => 10111110
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => 01000001 => 10111110
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,2,1,9] => 10000010 => 01111101
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,7,2,1,8,9] => 10000100 => 01111011
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,6,2,1,7,8,9] => 10001000 => 01110111
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8,9] => 10010000 => 01101111
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9] => 10100000 => 01011111
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => 011111111 => 100000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => 011111111 => 100000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => 0111111111 => 1000000000
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,9,7,6,5,4,3,2,10,1] => 011111011 => 100000100
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,5,4,3,2,7,1,8,9] => 01111100 => 10000011
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,4,3,2,6,1,7,8,9] => 01111000 => 10000111
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8,9] => 01110000 => 10001111
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => 01100000 => 10011111
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => 111111101 => 000000010
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [7,10,9,8,6,5,4,3,2,1] => 111110111 => 000001000
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,10,9,8,7,5,4,3,2,1] => 111101111 => 000010000
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,10,9,8,7,6,4,3,2,1] => 111011111 => 000100000
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,10,9,8,7,6,5,3,2,1] => 110111111 => 001000000
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,10,9,8,7,6,5,4,2,1] => 101111111 => 010000000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,7,2,1,9,8] => 10000101 => 01111010
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,9,4,3] => 10100001 => 01011110
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,8,3,1,9] => 01000010 => 10111101
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,10,3,1] => 010000001 => 101111110
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => 1111111101 => 0000000010
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => 01011111 => 10100000
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,2,1,9,8,7,6,5] => 10101111 => 01010000
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,5,3,2,1,9,8,7,6] => 11010111 => 00101000
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [5,6,4,3,2,1,9,8,7] => 11101011 => 00010100
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => 00010000 => 11101111
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8,9] => 00010000 => 11101111
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6,9,10] => 000000100 => 111111011
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,9,6,10] => 000000010 => 111111101
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6,7,9,8] => 00010001 => 11101110
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8,9] => 10010000 => 01101111
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,3,7,8,9,10,1] => 000010001 => 111101110
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,4,7,8,9,10,1] => 000010001 => 111101110
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,10,1] => 000010001 => 111101110
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,9,10,5,4,3,2] => 011100001 => 100011110
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,9,3,2] => 01010001 => 10101110
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => 01000010 => 10111101
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => 00000011 => 11111100
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => 00000101 => 11111010
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => 10000001 => 01111110
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => 00001011 => 11110100
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => 000000111 => 111111000
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,9,8,7,6] => 00010111 => 11101000
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,6,9,10,8,7,1] => 000001101 => 111110010
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,1,8,9,7,6,5] => 00101101 => 11010010
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,8,9,10,7,6,1] => 000011001 => 111100110
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,1,7,8,9,6,5,4] => 01011001 => 10100110
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,7,8,9,10,6,5,1] => 000110001 => 111001110
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,9,5,4,3] => 10110001 => 01001110
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,9,10,5,4,1] => 001100001 => 110011110
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,9,10,4,3,1] => 011000001 => 100111110
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => 110000001 => 001111110
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,4,9,8,7,6,5,3] => 10011111 => 01100000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,7,6,5,4,2,1,9,8] => 10111101 => 01000010
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,2,1,6,9,8,7,5,4] => 11010111 => 00101000
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [4,6,5,3,2,1,9,8,7] => 11011011 => 00100100
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,2,1,8,9,7,6,5] => 11101101 => 00010010
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,5,4,3,2,1,8,9,7] => 11111001 => 00000110
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,8,7,6,5,4,3,10,2,1] => 101111111 => 010000000
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,3,2,1,8,9,7,6] => 11110101 => 00001010
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,8,7,6,5,4,10,3,2,1] => 110111111 => 001000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,8,7,6,5,10,4,3,2,1] => 111011111 => 000100000
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,1,8,9,7,6,5,4] => 11011101 => 00100010
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,8,7,6,10,5,4,3,2,1] => 111101111 => 000010000
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [9,8,7,10,6,5,4,3,2,1] => 111110111 => 000001000
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,3,5,7,8,9,6] => 00100001 => 11011110
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,10,1] => 000001001 => 111110110
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,9] => 00001010 => 11110101
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,6,8,9] => 00010100 => 11101011
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,5,7,8,9] => 00101000 => 11010111
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8,9] => 01010000 => 10101111
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,8,7,1,9] => 00101110 => 11010001
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => 01010101 => 10101010
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9] => 011010101 => 100101010
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,1] => 001010111 => 110101000
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => 010101010 => 101010101
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,7,9,10,8,1] => 000000101 => 111111010
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,8,9,10,7,1] => 000001001 => 111110110
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,9,10,5,1] => 000100001 => 111011110
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,9,10,4,1] => 001000001 => 110111110
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => 100000001 => 011111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,9,11,10,1] => 0000000011 => 1111111100
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,7,8,10,11,9,1] => 0000000101 => 1111111010
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,5,6,9,8,10,7,1] => 000001011 => 111110100
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,7,9,10,11,8,1] => 0000001001 => 1111110110
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,5,7,8,9,10,11,6,1] => 0000100001 => 1111011110
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,9,10,11,5,1] => 0001000001 => 1110111110
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,10,11,3,1] => 0100000001 => 1011111110
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => 1000000001 => 0111111110
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [8,7,10,9,6,5,4,3,2,1] => 111110111 => 000001000
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [7,6,5,10,9,8,4,3,2,1] => 111011111 => 000100000
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,10,9,8,7,2,1] => 101111111 => 010000000
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,5,7,9,10,8,6,4,2] => 001010101 => 110101010
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,7,5,8,4,9,3,10,2] => 000001111 => 111110000
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,6,4,7,3,8,2,9,1,10] => 000011110 => 111100001
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => 1111111111 => 0000000000
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,11,10,9,8,7,6,5,4,3] => 1011111111 => 0100000000
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,11,10,9,8,7,6,5,4,3,1] => 0111111111 => 1000000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10,11] => 0100000000 => 1011111111
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => 00011111 => 11100000
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => 00001111 => 11110000
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => 00000111 => 11111000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => 00000011 => 11111100
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,9,4] => 11000001 => 00111110
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,9,5] => 11100001 => 00011110
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,8,7,6,5,4,3,2,1,11,10] => 1111111101 => 0000000010
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => 111000001 => 000111110
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9] => 11101000 => 00010111
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8,9] => 11010000 => 00101111
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => 00100000 => 11011111
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => 100000001 => 011111110
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => 01000001 => 10111110
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => 111111001 => 000000110
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => 0000000010 => 1111111101
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,1,8,9,10,7] => 000010001 => 111101110
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => 00000010 => 11111101
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,7,9,8,4] => 00000011 => 11111100
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,6,8,9,7,10] => 000000010 => 111111101
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,7,2,9,8] => 00000101 => 11111010
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8,9] => 00110000 => 11001111
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => 111100001 => 000011110
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => 111110001 => 000001110
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => 0000000010 => 1111111101
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => 00000010 => 11111101
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,7,6,5,4,3,2,10,9,1] => 011111111 => 100000000
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,2,10,9,8,7,6,5,4,1] => 011111111 => 100000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,5,7,6,8,1,9] => 00000110 => 11111001
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,5,8,7,6,1,9] => 00001110 => 11110001
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,9,4] => 10000001 => 01111110
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,4,6,8,9,7,5] => 00000101 => 11111010
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8,9,10] => 100100000 => 011011111
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9,10] => 101000000 => 010111111
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => 000000101 => 111111010
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => 00001001 => 11110110
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9,10] => 111010000 => 000101111
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [5,6,4,3,2,7,1,8,9] => 01101100 => 10010011
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9,10] => 111101000 => 000010111
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9,10,11] => 1111010000 => 0000101111
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => 0101010101 => 1010101010
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7,10,9] => 101010101 => 010101010
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1,10,11] => 1111111100 => 0000000011
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => 001000000 => 110111111
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => 000000010 => 111111101
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,3,7,8,9,10] => 000010000 => 111101111
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,9,5] => 00100001 => 11011110
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,6,8,10,9,7] => 000000011 => 111111100
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,7,8,4,9,10] => 000000100 => 111111011
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,7,6,5,4,3,9,8,2] => 00111111 => 11000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,7,10,9,8,5] => 000000111 => 111111000
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,8,7,9] => 01101010 => 10010101
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,5,4,6,1,8,7,9] => 01011010 => 10100101
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7,10,9] => 011010101 => 100101010
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7,10,9] => 010110101 => 101001010
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,7,6,8,1,10,9] => 010101101 => 101010010
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,10,1] => 010101011 => 101010100
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,9,8,1,10] => 010101110 => 101010001
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,2,1,7,8,9,6] => 11110001 => 00001110
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,6,8,7,9,2] => 00000011 => 11111100
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,2,8,7,6,5,4,1,9] => 01111110 => 10000001
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => 000000011 => 111111100
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,8,3,9] => 10000010 => 01111101
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,10,1] => 011111101 => 100000010
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,10,1] => 011111001 => 100000110
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,8,10,7] => 101010011 => 010101100
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,7,6,9,8,10,5] => 101001011 => 010110100
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,9,8,10,3] => 100101011 => 011010100
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => 010101001 => 101010110
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9,10] => 011000000 => 100111111
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,5] => 10100001 => 01011110
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9,10] => 011000000 => 100111111
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => 00000100 => 11111011
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,5,7,9,8,6,4,2] => 00101011 => 11010100
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,7,9,8,1,10] => 000000110 => 111111001
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,9,8,5] => 00000011 => 11111100
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,9,8,3] => 00010111 => 11101000
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,10,9,2] => 001010111 => 110101000
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,4,5,7,8,9,10,6] => 100000001 => 011111110
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7,10,9] => 001110101 => 110001010
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7,10,9] => 100110101 => 011001010
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,6,5,7,4,8,3,10,9] => 100011101 => 011100010
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,2,6,5,7,4,8,1,10,9] => 010011101 => 101100010
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,6,5,7,2,8,1,10,9] => 001011101 => 110100010
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,4,6,3,7,2,8,1,10,9] => 000111101 => 111000010
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,7,6,8,5,10,9] => 101001101 => 010110010
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,7,6,8,5,10,9] => 011001101 => 100110010
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,7,6,8,1,10,9] => 001101101 => 110010010
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,7,6,8,3,10,9] => 100101101 => 011010010
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,8,7,9,6,10,5] => 101000111 => 010111000
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,2,4,1,8,7,9,6,10,5] => 011000111 => 100111000
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,8,7,9,6,10,1] => 001100111 => 110011000
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,5,4,8,7,9,6,10,3] => 100100111 => 011011000
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,5,4,8,7,9,6,10,1] => 010100111 => 101011000
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,8,7,9,2,10,1] => 001010111 => 110101000
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,4,6,3,8,7,9,2,10,1] => 000110111 => 111001000
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,7,6,8,5,9,2,10,1] => 001001111 => 110110000
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,7,6,8,3,9,2,10,1] => 000101111 => 111010000
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,8,7,9,4,10,3] => 100010111 => 011101000
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,8,7,9,4,10,1] => 010010111 => 101101000
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,7,4,8,3,9,2,10,1] => 000011111 => 111100000
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,7,6,8,5,9,4,10,3] => 100001111 => 011110000
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,7,6,8,5,9,4,10,1] => 010001111 => 101110000
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,6,5,9,8,10,7] => 011010011 => 100101100
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,3,5,2,6,1,9,8,10,7] => 001110011 => 110001100
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3,9,8,10,7] => 100110011 => 011001100
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,5,4,6,1,9,8,10,7] => 010110011 => 101001100
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,6,5,7,4,9,8,10,3] => 100011011 => 011100100
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,6,5,7,4,9,8,10,1] => 010011011 => 101100100
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,6,5,7,2,9,8,10,1] => 001011011 => 110100100
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,4,6,3,7,2,9,8,10,1] => 000111011 => 111000100
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,4,1,7,6,9,8,10,5] => 011001011 => 100110100
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,9,8,10,1] => 001101011 => 110010100
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 10101010101 => 01010101010
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7,10,9,12,11] => 01101010101 => 10010101010
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7,10,9,12,11] => 00111010101 => 11000101010
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7,10,9,12,11] => 10011010101 => 01100101010
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,6,5,7,4,8,3,10,9,12,11] => 10001110101 => 01110001010
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,6,5,7,4,8,1,10,9,12,11] => 01001110101 => 10110001010
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,3,6,5,7,2,8,1,10,9,12,11] => 00101110101 => 11010001010
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,4,6,3,7,2,8,1,10,9,12,11] => 00011110101 => 11100001010
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,7,6,8,5,10,9,12,11] => 10100110101 => 01011001010
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,4,7,6,8,3,10,9,12,11] => 10010110101 => 01101001010
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,8,7,9,6,10,5,12,11] => 10100011101 => 01011100010
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,8,7,9,6,10,5,12,11] => 01100011101 => 10011100010
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,8,7,9,6,10,3,12,11] => 10010011101 => 01101100010
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,4,6,3,8,7,9,2,10,1,12,11] => 00011011101 => 11100100010
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,4,7,6,8,3,9,2,10,1,12,11] => 00010111101 => 11101000010
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,6,5,8,7,9,4,10,3,12,11] => 10001011101 => 01110100010
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [6,5,7,4,8,3,9,2,10,1,12,11] => 00001111101 => 11110000010
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,7,6,8,5,9,4,10,3,12,11] => 10000111101 => 01111000010
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,2,7,6,8,5,9,4,10,1,12,11] => 01000111101 => 10111000010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,6,5,9,8,10,7,12,11] => 10101001101 => 01010110010
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,9,8,10,7,12,11] => 10011001101 => 01100110010
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,6,5,7,4,9,8,10,3,12,11] => 10001101101 => 01110010010
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,3,6,5,7,2,9,8,10,1,12,11] => 00101101101 => 11010010010
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,7,6,9,8,10,5,12,11] => 10100101101 => 01011010010
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,7,6,9,8,10,3,12,11] => 10010101101 => 01101010010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,6,5,10,9,11,8,12,7] => 10101000111 => 01010111000
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1,10,9,11,8,12,7] => 00111000111 => 11000111000
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,5,4,6,3,10,9,11,8,12,7] => 10011000111 => 01100111000
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,10,9,11,8,12,3] => 10001100111 => 01110011000
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,10,9,11,8,12,1] => 01001100111 => 10110011000
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,10,9,11,8,12,1] => 00101100111 => 11010011000
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,10,9,11,8,12,1] => 00011100111 => 11100011000
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,7,6,10,9,11,8,12,5] => 10100100111 => 01011011000
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,7,6,10,9,11,8,12,1] => 00110100111 => 11001011000
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,5,4,7,6,10,9,11,8,12,3] => 10010100111 => 01101011000
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,5,4,7,6,10,9,11,8,12,1] => 01010100111 => 10101011000
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,8,7,10,9,11,4,12,3] => 10001010111 => 01110101000
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,8,7,10,9,11,4,12,1] => 01001010111 => 10110101000
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,5,7,4,8,3,10,9,11,2,12,1] => 00001110111 => 11110001000
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,7,6,8,5,10,9,11,4,12,3] => 10000110111 => 01111001000
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,7,6,8,5,10,9,11,4,12,1] => 01000110111 => 10111001000
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,6,5,9,8,10,7,11,4,12,3] => 10001001111 => 01110110000
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,6,5,9,8,10,7,11,4,12,1] => 01001001111 => 10110110000
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,7,4,9,8,10,3,11,2,12,1] => 00001101111 => 11110010000
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,7,6,9,8,10,5,11,4,12,3] => 10000101111 => 01111010000
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,7,6,9,8,10,5,11,4,12,1] => 01000101111 => 10111010000
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,8,7,10,9,11,2,12,1] => 00101010111 => 11010101000
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,7,6,8,5,10,9,11,2,12,1] => 00100110111 => 11011001000
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,4,6,3,8,7,10,9,11,2,12,1] => 00011010111 => 11100101000
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,4,7,6,8,3,10,9,11,2,12,1] => 00010110111 => 11101001000
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,8,7,9,4,10,3,11,2,12,1] => 00001011111 => 11110100000
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,6,8,5,9,4,10,3,11,2,12,1] => 00000111111 => 11111000000
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,6,5,9,8,10,7,11,2,12,1] => 00101001111 => 11010110000
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,7,6,9,8,10,5,11,2,12,1] => 00100101111 => 11011010000
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,9,8,10,7,11,2,12,1] => 00011001111 => 11100110000
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,7,6,9,8,10,3,11,2,12,1] => 00010101111 => 11101010000
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,8,7,10,9,11,6,12,5] => 10100010111 => 01011101000
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,8,7,10,9,11,6,12,1] => 00110010111 => 11001101000
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,5,4,8,7,10,9,11,6,12,3] => 10010010111 => 01101101000
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,5,4,8,7,10,9,11,6,12,1] => 01010010111 => 10101101000
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,8,7,9,6,10,5,11,4,12,3] => 10000011111 => 01111100000
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,8,7,9,6,10,5,11,4,12,1] => 01000011111 => 10111100000
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,8,7,9,6,10,5,11,2,12,1] => 00100011111 => 11011100000
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,8,7,9,6,10,3,11,2,12,1] => 00010011111 => 11101100000
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,4,3,9,8,10,7,11,6,12,5] => 10100001111 => 01011110000
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,4,1,9,8,10,7,11,6,12,5] => 01100001111 => 10011110000
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,5,2,9,8,10,7,11,6,12,1] => 00110001111 => 11001110000
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,5,4,9,8,10,7,11,6,12,3] => 10010001111 => 01101110000
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,5,4,9,8,10,7,11,6,12,1] => 01010001111 => 10101110000
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,8,7,11,10,12,9] => 10101010011 => 01010101100
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3,8,7,11,10,12,9] => 10011010011 => 01100101100
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3,11,10,12,9] => 10001110011 => 01110001100
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1,11,10,12,9] => 01001110011 => 10110001100
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5,11,10,12,9] => 10100110011 => 01011001100
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5,11,10,12,9] => 01100110011 => 10011001100
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1,11,10,12,9] => 00110110011 => 11001001100
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3,11,10,12,9] => 10010110011 => 01101001100
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,8,7,9,6,11,10,12,5] => 10100011011 => 01011100100
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,8,7,9,6,11,10,12,1] => 00110011011 => 11001100100
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,8,7,9,6,11,10,12,3] => 10010011011 => 01101100100
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,8,7,9,6,11,10,12,1] => 01010011011 => 10101100100
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,6,5,8,7,9,2,11,10,12,1] => 00101011011 => 11010100100
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,4,6,3,8,7,9,2,11,10,12,1] => 00011011011 => 11100100100
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,7,6,8,5,9,2,11,10,12,1] => 00100111011 => 11011000100
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,4,7,6,8,3,9,2,11,10,12,1] => 00010111011 => 11101000100
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,6,5,8,7,9,4,11,10,12,3] => 10001011011 => 01110100100
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,6,5,8,7,9,4,11,10,12,1] => 01001011011 => 10110100100
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,5,7,4,8,3,9,2,11,10,12,1] => 00001111011 => 11110000100
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,7,6,8,5,9,4,11,10,12,3] => 10000111011 => 01111000100
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,7,6,8,5,9,4,11,10,12,1] => 01000111011 => 10111000100
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,8,11,10,12,7] => 10101001011 => 01010110100
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,6,3,9,8,11,10,12,7] => 10011001011 => 01100110100
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,6,5,7,4,9,8,11,10,12,3] => 10001101011 => 01110010100
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,6,5,7,4,9,8,11,10,12,1] => 01001101011 => 10110010100
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,3,6,5,7,2,9,8,11,10,12,1] => 00101101011 => 11010010100
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [5,4,6,3,7,2,9,8,11,10,12,1] => 00011101011 => 11100010100
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,7,6,9,8,11,10,12,5] => 10100101011 => 01011010100
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,9,8,11,10,12,1] => 00110101011 => 11001010100
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,9,8,11,10,12,3] => 10010101011 => 01101010100
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,11,10,12,1] => 01010101011 => 10101010100
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8,10] => 000001010 => 111110101
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,10,9,2,1] => 101010111 => 010101000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => 11111111101 => 00000000010
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,11,10,9,8,7,6,5,4,3] => 0011111111 => 1100000000
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,10,9] => 001010101 => 110101010
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,11,10] => 0000000101 => 1111111010
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,1,7,8,9,6] => 00010001 => 11101110
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,7,8,10,9,1] => 010000011 => 101111100
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,5,4,3,2,1,9,10,8] => 111111001 => 000000110
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,3,2,1,8,9,10,7] => 111110001 => 000001110
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,7,8,9,10,6] => 111100001 => 000011110
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,9,10,5] => 111000001 => 000111110
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,9,10,4] => 110000001 => 001111110
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,6,9,8,7,2] => 00000111 => 11111000
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9] => 100110101 => 011001010
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9] => 101001101 => 010110010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => 101010011 => 010101100
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0] => [2,6,5,8,9,7,10,4,3,1] => 011010011 => 100101100
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,3,11,10,9,8,7,6,5,4,2] => 0011111111 => 1100000000
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7,9] => 00101010 => 11010101
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,10,9,8,1] => 011011111 => 100100000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,7,1,9,10,8] => 000001001 => 111110110
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,5,8,9,10,7] => 001010001 => 110101110
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,8,10,9,5] => 000000011 => 111111100
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,5,7,8,10,9,6] => 000000011 => 111111100
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,4,6,3,7,2,8,1,9] => 00011110 => 11100001
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,5,7,4,8,3,9,2] => 00001111 => 11110000
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,7,4,8,3,9,2] => 00000111 => 11111000
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,10,5] => 101000001 => 010111110
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,5,8,9,10,7] => 101010001 => 010101110
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,1,7,8,9,10,6,5,4,3] => 101110001 => 010001110
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,6,5,9,10,8,7] => 101010101 => 010101010
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7,9] => 00101010 => 11010101
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,9,8,10] => 000101010 => 111010101
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,9,8] => 00010101 => 11101010
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,9,8] => 00010101 => 11101010
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,9,8,10] => 000101010 => 111010101
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,4,6,5,8,7,9] => 01001010 => 10110101
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,5,3,6,2,7,1,8,9] => 00011100 => 11100011
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,4,5,7,9,10,8,6] => 000000101 => 111111010
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,3,5,6,8,9,7,4] => 00000101 => 11111010
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,10,9,8,7,6,5,3] => 000111111 => 111000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7,10,9] => 000010101 => 111101010
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,10,9] => 001010101 => 110101010
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,5,9,8,7,6,4,2] => 00101111 => 11010000
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,5,10,9,8,7,6,4,2] => 001011111 => 110100000
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,3,5,7,10,9,8,6,4,2] => 001010111 => 110101000
Map
to 312-avoiding permutation
Description
Map
descent tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
searching the database
Sorry, this map was not found in the database.