Identifier
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Images
[1,0] => [2,1] => [2,1] => 1 => 1
[1,0,1,0] => [3,1,2] => [3,2,1] => 11 => 11
[1,1,0,0] => [2,3,1] => [3,1,2] => 01 => 10
[1,0,1,0,1,0] => [4,1,2,3] => [4,3,2,1] => 111 => 111
[1,0,1,1,0,0] => [3,1,4,2] => [4,2,1,3] => 101 => 110
[1,1,0,0,1,0] => [2,4,1,3] => [4,3,1,2] => 011 => 101
[1,1,0,1,0,0] => [4,3,1,2] => [4,2,3,1] => 011 => 101
[1,1,1,0,0,0] => [2,3,4,1] => [4,1,2,3] => 001 => 100
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [5,4,3,2,1] => 1111 => 1111
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [5,3,2,1,4] => 1101 => 1110
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [5,4,2,1,3] => 1011 => 1101
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [5,3,4,2,1] => 1011 => 1101
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [5,2,1,3,4] => 1001 => 1100
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [5,4,3,1,2] => 0111 => 1011
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [5,3,1,2,4] => 0101 => 1010
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [5,4,2,3,1] => 0111 => 1011
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [4,2,5,3,1] => 0111 => 1011
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [5,2,3,1,4] => 0101 => 1010
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [5,4,1,2,3] => 0011 => 1001
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [5,3,4,1,2] => 0011 => 1001
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [5,2,3,4,1] => 0011 => 1001
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => 0001 => 1000
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => 11111 => 11111
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => 11101 => 11110
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => 11011 => 11101
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [6,4,5,3,2,1] => 11011 => 11101
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [6,3,2,1,4,5] => 11001 => 11100
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => 10111 => 11011
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [6,4,2,1,3,5] => 10101 => 11010
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [6,5,3,4,2,1] => 10111 => 11011
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [5,3,6,4,2,1] => 10111 => 11011
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [6,3,4,2,1,5] => 10101 => 11010
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [6,5,2,1,3,4] => 10011 => 11001
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [6,4,5,2,1,3] => 10011 => 11001
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [6,3,4,5,2,1] => 10011 => 11001
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [6,2,1,3,4,5] => 10001 => 11000
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [6,5,4,3,1,2] => 01111 => 10111
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [6,4,3,1,2,5] => 01101 => 10110
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [6,5,3,1,2,4] => 01011 => 10101
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [6,4,5,3,1,2] => 01011 => 10101
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [6,3,1,2,4,5] => 01001 => 10100
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [6,5,4,2,3,1] => 01111 => 10111
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [6,4,2,3,1,5] => 01101 => 10110
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,2,6,5,3,1] => 01111 => 10111
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [5,3,1,6,4,2] => 01111 => 10111
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [4,2,6,3,1,5] => 01101 => 10110
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [6,5,2,3,1,4] => 01011 => 10101
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [6,4,5,2,3,1] => 01011 => 10101
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [5,2,4,6,3,1] => 01011 => 10101
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [6,2,3,1,4,5] => 01001 => 10100
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [6,5,4,1,2,3] => 00111 => 10011
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [6,4,1,2,3,5] => 00101 => 10010
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [6,5,3,4,1,2] => 00111 => 10011
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [5,3,6,4,1,2] => 00111 => 10011
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [6,3,4,1,2,5] => 00101 => 10010
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [6,5,2,3,4,1] => 00111 => 10011
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [5,2,3,6,4,1] => 00111 => 10011
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [5,2,6,3,4,1] => 00111 => 10011
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [6,2,3,4,1,5] => 00101 => 10010
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [6,5,1,2,3,4] => 00011 => 10001
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [6,4,5,1,2,3] => 00011 => 10001
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [6,3,4,5,1,2] => 00011 => 10001
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [6,2,3,4,5,1] => 00011 => 10001
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => 00001 => 10000
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [7,6,5,4,3,2,1] => 111111 => 111111
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [7,5,4,3,2,1,6] => 111101 => 111110
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [7,6,4,3,2,1,5] => 111011 => 111101
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => [7,5,6,4,3,2,1] => 111011 => 111101
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [7,4,3,2,1,5,6] => 111001 => 111100
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [7,6,5,3,2,1,4] => 110111 => 111011
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [7,5,3,2,1,4,6] => 110101 => 111010
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => [7,6,4,5,3,2,1] => 110111 => 111011
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [6,4,7,5,3,2,1] => 110111 => 111011
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => [7,4,5,3,2,1,6] => 110101 => 111010
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [7,6,3,2,1,4,5] => 110011 => 111001
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => [7,5,6,3,2,1,4] => 110011 => 111001
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [7,4,5,6,3,2,1] => 110011 => 111001
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [7,3,2,1,4,5,6] => 110001 => 111000
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [7,6,5,4,2,1,3] => 101111 => 110111
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [7,5,4,2,1,3,6] => 101101 => 110110
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [7,6,4,2,1,3,5] => 101011 => 110101
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [7,5,6,4,2,1,3] => 101011 => 110101
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => 101001 => 110100
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => [7,6,5,3,4,2,1] => 101111 => 110111
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => [7,5,3,4,2,1,6] => 101101 => 110110
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [5,3,7,6,4,2,1] => 101111 => 110111
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [6,4,2,1,7,5,3] => 101111 => 110111
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [5,3,7,4,2,1,6] => 101101 => 110110
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [7,6,3,4,2,1,5] => 101011 => 110101
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => [7,5,6,3,4,2,1] => 101011 => 110101
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [6,3,5,7,4,2,1] => 101011 => 110101
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => [7,3,4,2,1,5,6] => 101001 => 110100
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [7,6,5,2,1,3,4] => 100111 => 110011
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => 100101 => 110010
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [7,6,4,5,2,1,3] => 100111 => 110011
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [6,4,7,5,2,1,3] => 100111 => 110011
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [7,4,5,2,1,3,6] => 100101 => 110010
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [7,6,3,4,5,2,1] => 100111 => 110011
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [6,3,4,7,5,2,1] => 100111 => 110011
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [6,3,7,4,5,2,1] => 100111 => 110011
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => [7,3,4,5,2,1,6] => 100101 => 110010
>>> Load all 759 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [7,6,2,1,3,4,5] => 100011 => 110001
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [7,5,6,2,1,3,4] => 100011 => 110001
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [7,4,5,6,2,1,3] => 100011 => 110001
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => [7,3,4,5,6,2,1] => 100011 => 110001
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [7,2,1,3,4,5,6] => 100001 => 110000
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [7,6,5,4,3,1,2] => 011111 => 101111
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [7,5,4,3,1,2,6] => 011101 => 101110
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [7,6,4,3,1,2,5] => 011011 => 101101
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [7,5,6,4,3,1,2] => 011011 => 101101
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [7,4,3,1,2,5,6] => 011001 => 101100
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [7,6,5,3,1,2,4] => 010111 => 101011
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [7,5,3,1,2,4,6] => 010101 => 101010
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [7,6,4,5,3,1,2] => 010111 => 101011
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [6,4,7,5,3,1,2] => 010111 => 101011
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => [7,4,5,3,1,2,6] => 010101 => 101010
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [7,6,3,1,2,4,5] => 010011 => 101001
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => [7,5,6,3,1,2,4] => 010011 => 101001
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [7,4,5,6,3,1,2] => 010011 => 101001
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [7,3,1,2,4,5,6] => 010001 => 101000
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => [7,6,5,4,2,3,1] => 011111 => 101111
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => [7,5,4,2,3,1,6] => 011101 => 101110
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [7,6,4,2,3,1,5] => 011011 => 101101
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => [7,5,6,4,2,3,1] => 011011 => 101101
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => [7,4,2,3,1,5,6] => 011001 => 101100
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => [4,2,7,6,5,3,1] => 011111 => 101111
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => [4,2,7,5,3,1,6] => 011101 => 101110
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [5,3,1,7,6,4,2] => 011111 => 101111
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [6,4,2,7,5,3,1] => 011111 => 101111
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [5,3,1,7,4,2,6] => 011101 => 101110
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [4,2,7,6,3,1,5] => 011011 => 101101
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [4,2,7,5,6,3,1] => 011011 => 101101
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [6,3,1,5,7,4,2] => 011011 => 101101
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => [4,2,7,3,1,5,6] => 011001 => 101100
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [7,6,5,2,3,1,4] => 010111 => 101011
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [7,5,2,3,1,4,6] => 010101 => 101010
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => [7,6,4,5,2,3,1] => 010111 => 101011
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [6,4,7,5,2,3,1] => 010111 => 101011
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => [7,4,5,2,3,1,6] => 010101 => 101010
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [5,2,4,7,6,3,1] => 010111 => 101011
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => [7,5,2,4,6,3,1] => 010111 => 101011
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [6,3,1,7,4,5,2] => 010111 => 101011
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [5,2,4,7,3,1,6] => 010101 => 101010
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [7,6,2,3,1,4,5] => 010011 => 101001
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [7,5,6,2,3,1,4] => 010011 => 101001
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [7,4,5,6,2,3,1] => 010011 => 101001
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [6,2,4,5,7,3,1] => 010011 => 101001
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [7,2,3,1,4,5,6] => 010001 => 101000
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [7,6,5,4,1,2,3] => 001111 => 100111
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [7,5,4,1,2,3,6] => 001101 => 100110
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [7,6,4,1,2,3,5] => 001011 => 100101
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => [7,5,6,4,1,2,3] => 001011 => 100101
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [7,4,1,2,3,5,6] => 001001 => 100100
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [7,6,5,3,4,1,2] => 001111 => 100111
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => [7,5,3,4,1,2,6] => 001101 => 100110
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [5,3,7,6,4,1,2] => 001111 => 100111
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [6,4,1,2,7,5,3] => 001111 => 100111
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => [5,3,7,4,1,2,6] => 001101 => 100110
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => [7,6,3,4,1,2,5] => 001011 => 100101
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => [7,5,6,3,4,1,2] => 001011 => 100101
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [6,3,5,7,4,1,2] => 001011 => 100101
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => [7,3,4,1,2,5,6] => 001001 => 100100
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => [7,6,5,2,3,4,1] => 001111 => 100111
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [7,5,2,3,4,1,6] => 001101 => 100110
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [5,2,3,7,6,4,1] => 001111 => 100111
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [6,4,1,7,5,2,3] => 001111 => 100111
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [5,2,3,7,4,1,6] => 001101 => 100110
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [5,2,7,6,3,4,1] => 001111 => 100111
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [6,3,4,1,7,5,2] => 001111 => 100111
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => [7,4,1,6,3,5,2] => 001111 => 100111
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [5,2,7,3,4,1,6] => 001101 => 100110
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => [7,6,2,3,4,1,5] => 001011 => 100101
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => [7,5,6,2,3,4,1] => 001011 => 100101
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [6,2,3,5,7,4,1] => 001011 => 100101
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [6,2,5,7,3,4,1] => 001011 => 100101
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => [7,2,3,4,1,5,6] => 001001 => 100100
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [7,6,5,1,2,3,4] => 000111 => 100011
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [7,5,1,2,3,4,6] => 000101 => 100010
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => [7,6,4,5,1,2,3] => 000111 => 100011
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => [6,4,7,5,1,2,3] => 000111 => 100011
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => [7,4,5,1,2,3,6] => 000101 => 100010
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => [7,6,3,4,5,1,2] => 000111 => 100011
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [6,3,4,7,5,1,2] => 000111 => 100011
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [6,3,7,4,5,1,2] => 000111 => 100011
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => [7,3,4,5,1,2,6] => 000101 => 100010
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [7,6,2,3,4,5,1] => 000111 => 100011
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [6,2,3,4,7,5,1] => 000111 => 100011
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [6,2,3,7,4,5,1] => 000111 => 100011
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => [6,2,7,3,4,5,1] => 000111 => 100011
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [7,2,3,4,5,1,6] => 000101 => 100010
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [7,6,1,2,3,4,5] => 000011 => 100001
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => [7,5,6,1,2,3,4] => 000011 => 100001
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => [7,4,5,6,1,2,3] => 000011 => 100001
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => [7,3,4,5,6,1,2] => 000011 => 100001
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => [7,2,3,4,5,6,1] => 000011 => 100001
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => 000001 => 100000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => [8,7,6,5,4,3,2,1] => 1111111 => 1111111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [8,6,5,4,3,2,1,7] => 1111101 => 1111110
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => [8,7,5,4,3,2,1,6] => 1111011 => 1111101
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,1,2,3,4,7,5,6] => [8,6,7,5,4,3,2,1] => 1111011 => 1111101
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [8,5,4,3,2,1,6,7] => 1111001 => 1111100
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => [8,7,6,4,3,2,1,5] => 1110111 => 1111011
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [8,6,4,3,2,1,5,7] => 1110101 => 1111010
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,1,2,3,6,4,5,7] => [8,7,5,6,4,3,2,1] => 1110111 => 1111011
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,1,2,3,7,4,5,6] => [7,5,8,6,4,3,2,1] => 1110111 => 1111011
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,1,2,3,6,4,8,5] => [8,5,6,4,3,2,1,7] => 1110101 => 1111010
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [8,7,4,3,2,1,5,6] => 1110011 => 1111001
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,1,2,3,8,7,4,6] => [8,6,7,4,3,2,1,5] => 1110011 => 1111001
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,1,2,3,6,7,4,5] => [8,5,6,7,4,3,2,1] => 1110011 => 1111001
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [8,4,3,2,1,5,6,7] => 1110001 => 1111000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => [8,7,6,5,3,2,1,4] => 1101111 => 1110111
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => [8,6,5,3,2,1,4,7] => 1101101 => 1110110
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [8,7,5,3,2,1,4,6] => 1101011 => 1110101
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [4,1,2,8,3,7,5,6] => [8,6,7,5,3,2,1,4] => 1101011 => 1110101
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,5,3,2,1,4,6,7] => 1101001 => 1110100
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,1,2,5,3,4,6,7] => [8,7,6,4,5,3,2,1] => 1101111 => 1110111
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,1,2,5,3,4,8,6] => [8,6,4,5,3,2,1,7] => 1101101 => 1110110
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,1,2,6,3,4,5,7] => [6,4,8,7,5,3,2,1] => 1101111 => 1110111
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,1,2,8,3,4,5,6] => [7,5,3,2,1,8,6,4] => 1101111 => 1110111
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [7,1,2,6,3,4,8,5] => [6,4,8,5,3,2,1,7] => 1101101 => 1110110
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,1,2,5,3,8,4,7] => [8,7,4,5,3,2,1,6] => 1101011 => 1110101
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [8,1,2,5,3,7,4,6] => [8,6,7,4,5,3,2,1] => 1101011 => 1110101
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [8,1,2,6,3,7,4,5] => [7,4,6,8,5,3,2,1] => 1101011 => 1110101
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [6,1,2,5,3,7,8,4] => [8,4,5,3,2,1,6,7] => 1101001 => 1110100
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => [8,7,6,3,2,1,4,5] => 1100111 => 1110011
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,6,3,2,1,4,5,7] => 1100101 => 1110010
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [4,1,2,8,6,3,5,7] => [8,7,5,6,3,2,1,4] => 1100111 => 1110011
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [4,1,2,8,7,3,5,6] => [7,5,8,6,3,2,1,4] => 1100111 => 1110011
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,1,2,7,6,3,8,5] => [8,5,6,3,2,1,4,7] => 1100101 => 1110010
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,1,2,5,6,3,4,7] => [8,7,4,5,6,3,2,1] => 1100111 => 1110011
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [8,1,2,5,7,3,4,6] => [7,4,5,8,6,3,2,1] => 1100111 => 1110011
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [8,1,2,7,6,3,4,5] => [7,4,8,5,6,3,2,1] => 1100111 => 1110011
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [7,1,2,5,6,3,8,4] => [8,4,5,6,3,2,1,7] => 1100101 => 1110010
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [8,7,3,2,1,4,5,6] => 1100011 => 1110001
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,8,7,3,6] => [8,6,7,3,2,1,4,5] => 1100011 => 1110001
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,1,2,8,6,7,3,5] => [8,5,6,7,3,2,1,4] => 1100011 => 1110001
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => [8,4,5,6,7,3,2,1] => 1100011 => 1110001
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [8,3,2,1,4,5,6,7] => 1100001 => 1110000
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [8,7,6,5,4,2,1,3] => 1011111 => 1101111
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => [8,6,5,4,2,1,3,7] => 1011101 => 1101110
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [3,1,8,2,4,7,5,6] => [8,6,7,5,4,2,1,3] => 1011011 => 1101101
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [8,5,4,2,1,3,6,7] => 1011001 => 1101100
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [8,7,6,4,2,1,3,5] => 1010111 => 1101011
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,6,4,2,1,3,5,7] => 1010101 => 1101010
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,8,2,6,4,5,7] => [8,7,5,6,4,2,1,3] => 1010111 => 1101011
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [3,1,8,2,7,4,5,6] => [7,5,8,6,4,2,1,3] => 1010111 => 1101011
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,1,7,2,6,4,8,5] => [8,5,6,4,2,1,3,7] => 1010101 => 1101010
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [8,7,4,2,1,3,5,6] => 1010011 => 1101001
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,5,2,8,7,4,6] => [8,6,7,4,2,1,3,5] => 1010011 => 1101001
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,4,2,1,3,5,6,7] => 1010001 => 1101000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,1,4,2,3,5,6,7] => [8,7,6,5,3,4,2,1] => 1011111 => 1101111
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,1,4,2,3,5,8,6] => [8,6,5,3,4,2,1,7] => 1011101 => 1101110
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,1,4,2,3,8,5,7] => [8,7,5,3,4,2,1,6] => 1011011 => 1101101
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [8,1,4,2,3,7,5,6] => [8,6,7,5,3,4,2,1] => 1011011 => 1101101
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,1,5,2,3,4,6,7] => [5,3,8,7,6,4,2,1] => 1011111 => 1101111
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7] => [6,4,2,1,8,7,5,3] => 1011111 => 1101111
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,1,7,2,3,4,5,6] => [7,5,3,8,6,4,2,1] => 1011111 => 1101111
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,1,7,2,3,4,8,5] => [6,4,2,1,8,5,3,7] => 1011101 => 1101110
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,1,5,2,3,8,4,7] => [5,3,8,7,4,2,1,6] => 1011011 => 1101101
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,1,8,2,3,7,4,5] => [7,4,2,1,6,8,5,3] => 1011011 => 1101101
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,1,5,2,3,7,8,4] => [5,3,8,4,2,1,6,7] => 1011001 => 1101100
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [5,1,4,2,8,3,6,7] => [8,7,6,3,4,2,1,5] => 1010111 => 1101011
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,1,4,2,7,3,8,6] => [8,6,3,4,2,1,5,7] => 1010101 => 1101010
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,1,4,2,6,3,5,7] => [8,7,5,6,3,4,2,1] => 1010111 => 1101011
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [8,1,4,2,7,3,5,6] => [7,5,8,6,3,4,2,1] => 1010111 => 1101011
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [7,1,4,2,6,3,8,5] => [8,5,6,3,4,2,1,7] => 1010101 => 1101010
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [8,1,5,2,7,3,4,6] => [8,6,3,5,7,4,2,1] => 1010111 => 1101011
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [7,1,8,2,6,3,4,5] => [7,4,2,1,8,5,6,3] => 1010111 => 1101011
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [7,1,5,2,6,3,8,4] => [6,3,5,8,4,2,1,7] => 1010101 => 1101010
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,4,2,6,8,3,7] => [8,7,3,4,2,1,5,6] => 1010011 => 1101001
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [8,1,4,2,6,7,3,5] => [8,5,6,7,3,4,2,1] => 1010011 => 1101001
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [8,1,5,2,6,7,3,4] => [7,3,5,6,8,4,2,1] => 1010011 => 1101001
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [5,1,4,2,6,7,8,3] => [8,3,4,2,1,5,6,7] => 1010001 => 1101000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,8,2,5,6,7] => [8,7,6,5,2,1,3,4] => 1001111 => 1100111
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => [8,6,5,2,1,3,4,7] => 1001101 => 1100110
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,7,5,2,1,3,4,6] => 1001011 => 1100101
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,5,2,1,3,4,6,7] => 1001001 => 1100100
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,8,5,2,4,6,7] => [8,7,6,4,5,2,1,3] => 1001111 => 1100111
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,7,5,2,4,8,6] => [8,6,4,5,2,1,3,7] => 1001101 => 1100110
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,8,6,2,4,5,7] => [6,4,8,7,5,2,1,3] => 1001111 => 1100111
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,7,8,2,4,5,6] => [7,5,2,1,3,8,6,4] => 1001111 => 1100111
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,8,5,2,7,4,6] => [8,6,7,4,5,2,1,3] => 1001011 => 1100101
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,1,4,5,2,3,6,7] => [8,7,6,3,4,5,2,1] => 1001111 => 1100111
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,1,4,8,2,3,5,6] => [7,5,2,1,8,6,3,4] => 1001111 => 1100111
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,1,6,5,2,3,4,7] => [6,3,8,7,4,5,2,1] => 1001111 => 1100111
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,1,8,5,2,3,4,6] => [7,4,5,2,1,8,6,3] => 1001111 => 1100111
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [7,1,8,6,2,3,4,5] => [8,5,2,1,7,4,6,3] => 1001111 => 1100111
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [7,1,6,5,2,3,8,4] => [6,3,8,4,5,2,1,7] => 1001101 => 1100110
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,1,4,5,2,8,3,7] => [8,7,3,4,5,2,1,6] => 1001011 => 1100101
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [8,1,4,5,2,7,3,6] => [8,6,7,3,4,5,2,1] => 1001011 => 1100101
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [8,1,6,5,2,7,3,4] => [7,3,6,8,4,5,2,1] => 1001011 => 1100101
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [6,1,4,5,2,7,8,3] => [8,3,4,5,2,1,6,7] => 1001001 => 1100100
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => [8,7,6,2,1,3,4,5] => 1000111 => 1100011
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,1,4,8,6,2,5,7] => [8,7,5,6,2,1,3,4] => 1000111 => 1100011
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,1,4,8,7,2,5,6] => [7,5,8,6,2,1,3,4] => 1000111 => 1100011
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,1,4,7,6,2,8,5] => [8,5,6,2,1,3,4,7] => 1000101 => 1100010
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,8,5,6,2,4,7] => [8,7,4,5,6,2,1,3] => 1000111 => 1100011
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,8,5,7,2,4,6] => [7,4,5,8,6,2,1,3] => 1000111 => 1100011
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,1,8,7,6,2,4,5] => [7,4,8,5,6,2,1,3] => 1000111 => 1100011
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,1,7,5,6,2,8,4] => [8,4,5,6,2,1,3,7] => 1000101 => 1100010
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,1,4,5,6,2,3,7] => [8,7,3,4,5,6,2,1] => 1000111 => 1100011
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [8,1,4,5,7,2,3,6] => [7,3,4,5,8,6,2,1] => 1000111 => 1100011
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [8,1,4,7,6,2,3,5] => [7,3,4,8,5,6,2,1] => 1000111 => 1100011
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [8,1,7,5,6,2,3,4] => [7,3,8,4,5,6,2,1] => 1000111 => 1100011
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [7,1,4,5,6,2,8,3] => [8,3,4,5,6,2,1,7] => 1000101 => 1100010
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [8,7,2,1,3,4,5,6] => 1000011 => 1100001
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,1,4,5,8,7,2,6] => [8,6,7,2,1,3,4,5] => 1000011 => 1100001
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,1,4,8,6,7,2,5] => [8,5,6,7,2,1,3,4] => 1000011 => 1100001
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,8,5,6,7,2,4] => [8,4,5,6,7,2,1,3] => 1000011 => 1100001
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [8,1,4,5,6,7,2,3] => [8,3,4,5,6,7,2,1] => 1000011 => 1100001
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [8,2,1,3,4,5,6,7] => 1000001 => 1100000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => [8,7,6,5,4,3,1,2] => 0111111 => 1011111
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => [8,6,5,4,3,1,2,7] => 0111101 => 1011110
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,6,1,3,4,8,5,7] => [8,7,5,4,3,1,2,6] => 0111011 => 1011101
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,8,1,3,4,7,5,6] => [8,6,7,5,4,3,1,2] => 0111011 => 1011101
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7] => [8,7,6,4,3,1,2,5] => 0110111 => 1011011
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [8,6,4,3,1,2,5,7] => 0110101 => 1011010
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,8,1,3,6,4,5,7] => [8,7,5,6,4,3,1,2] => 0110111 => 1011011
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => [8,7,6,5,3,1,2,4] => 0101111 => 1010111
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [8,7,5,3,1,2,4,6] => 0101011 => 1010101
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,8,3,7,5,6] => [8,6,7,5,3,1,2,4] => 0101011 => 1010101
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,5,3,1,2,4,6,7] => 0101001 => 1010100
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,8,1,5,3,4,6,7] => [8,7,6,4,5,3,1,2] => 0101111 => 1010111
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,7,1,5,3,4,8,6] => [8,6,4,5,3,1,2,7] => 0101101 => 1010110
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,8,1,6,3,4,5,7] => [6,4,8,7,5,3,1,2] => 0101111 => 1010111
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,7,1,8,3,4,5,6] => [7,5,3,1,2,8,6,4] => 0101111 => 1010111
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,7,1,6,3,4,8,5] => [6,4,8,5,3,1,2,7] => 0101101 => 1010110
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,8,1,5,3,7,4,6] => [8,6,7,4,5,3,1,2] => 0101011 => 1010101
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,8,1,6,3,7,4,5] => [7,4,6,8,5,3,1,2] => 0101011 => 1010101
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => [8,7,6,3,1,2,4,5] => 0100111 => 1010011
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1,8,6,3,5,7] => [8,7,5,6,3,1,2,4] => 0100111 => 1010011
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,8,7,3,5,6] => [7,5,8,6,3,1,2,4] => 0100111 => 1010011
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,4,1,7,6,3,8,5] => [8,5,6,3,1,2,4,7] => 0100101 => 1010010
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,8,1,7,6,3,4,5] => [7,4,8,5,6,3,1,2] => 0100111 => 1010011
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,8,7,3,6] => [8,6,7,3,1,2,4,5] => 0100011 => 1010001
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,3,1,2,4,5,6,7] => 0100001 => 1010000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => [8,7,6,5,4,2,3,1] => 0111111 => 1011111
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,3,1,2,4,5,8,6] => [8,6,5,4,2,3,1,7] => 0111101 => 1011110
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [8,3,1,2,4,7,5,6] => [8,6,7,5,4,2,3,1] => 0111011 => 1011101
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [5,3,1,2,8,4,6,7] => [8,7,6,4,2,3,1,5] => 0110111 => 1011011
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,3,1,2,7,4,8,6] => [8,6,4,2,3,1,5,7] => 0110101 => 1011010
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,3,1,2,6,4,5,7] => [8,7,5,6,4,2,3,1] => 0110111 => 1011011
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [7,3,1,2,6,4,8,5] => [8,5,6,4,2,3,1,7] => 0110101 => 1011010
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,1,2,8,7,4,6] => [8,6,7,4,2,3,1,5] => 0110011 => 1011001
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [8,3,1,2,6,7,4,5] => [8,5,6,7,4,2,3,1] => 0110011 => 1011001
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,3,1,2,6,7,8,4] => [8,4,2,3,1,5,6,7] => 0110001 => 1011000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => [4,2,8,7,6,5,3,1] => 0111111 => 1011111
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,1,2,3,8,5,7] => [4,2,8,7,5,3,1,6] => 0111011 => 1011101
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [8,4,1,2,3,7,5,6] => [4,2,8,6,7,5,3,1] => 0111011 => 1011101
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,8,1,2,3,4,6,7] => [5,3,1,8,7,6,4,2] => 0111111 => 1011111
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [5,3,1,8,6,4,2,7] => 0111101 => 1011110
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [6,4,2,8,7,5,3,1] => 0111111 => 1011111
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6] => [8,6,4,2,7,5,3,1] => 0111111 => 1011111
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,6,1,2,3,4,8,5] => [6,4,2,8,5,3,1,7] => 0111101 => 1011110
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [5,6,1,2,3,8,4,7] => [5,3,1,8,7,4,2,6] => 0111011 => 1011101
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,8,1,2,3,7,4,6] => [5,3,1,8,6,7,4,2] => 0111011 => 1011101
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,6,1,2,3,7,4,5] => [7,4,2,6,8,5,3,1] => 0111011 => 1011101
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,1,2,3,7,8,4] => [5,3,1,8,4,2,6,7] => 0111001 => 1011100
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,2,8,3,6,7] => [4,2,8,7,6,3,1,5] => 0110111 => 1011011
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,4,1,2,7,3,8,6] => [4,2,8,6,3,1,5,7] => 0110101 => 1011010
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,4,1,2,7,3,5,6] => [4,2,7,5,8,6,3,1] => 0110111 => 1011011
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7,4,1,2,6,3,8,5] => [4,2,8,5,6,3,1,7] => 0110101 => 1011010
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,8,1,2,7,3,4,6] => [8,6,3,1,5,7,4,2] => 0110111 => 1011011
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,1,2,6,3,4,5] => [7,4,2,8,5,6,3,1] => 0110111 => 1011011
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,7,1,2,6,3,8,4] => [6,3,1,5,8,4,2,7] => 0110101 => 1011010
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [5,4,1,2,6,8,3,7] => [4,2,8,7,3,1,5,6] => 0110011 => 1011001
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,4,1,2,8,7,3,6] => [4,2,8,6,7,3,1,5] => 0110011 => 1011001
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8,4,1,2,6,7,3,5] => [4,2,8,5,6,7,3,1] => 0110011 => 1011001
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,8,1,2,6,7,3,4] => [7,3,1,5,6,8,4,2] => 0110011 => 1011001
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,4,1,2,6,7,8,3] => [4,2,8,3,1,5,6,7] => 0110001 => 1011000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,3,1,8,2,5,6,7] => [8,7,6,5,2,3,1,4] => 0101111 => 1010111
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,3,1,7,2,5,8,6] => [8,6,5,2,3,1,4,7] => 0101101 => 1010110
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,3,1,6,2,8,5,7] => [8,7,5,2,3,1,4,6] => 0101011 => 1010101
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3,1,8,2,7,5,6] => [8,6,7,5,2,3,1,4] => 0101011 => 1010101
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,3,1,5,2,4,6,7] => [8,7,6,4,5,2,3,1] => 0101111 => 1010111
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,3,1,5,2,4,8,6] => [8,6,4,5,2,3,1,7] => 0101101 => 1010110
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,3,1,6,2,4,5,7] => [6,4,8,7,5,2,3,1] => 0101111 => 1010111
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,3,1,8,2,4,5,6] => [7,5,2,3,1,8,6,4] => 0101111 => 1010111
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7,3,1,6,2,4,8,5] => [6,4,8,5,2,3,1,7] => 0101101 => 1010110
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,1,5,2,8,4,7] => [8,7,4,5,2,3,1,6] => 0101011 => 1010101
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8,3,1,5,2,7,4,6] => [8,6,7,4,5,2,3,1] => 0101011 => 1010101
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8,3,1,6,2,7,4,5] => [7,4,6,8,5,2,3,1] => 0101011 => 1010101
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [6,3,1,5,2,7,8,4] => [8,4,5,2,3,1,6,7] => 0101001 => 1010100
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,4,1,6,2,3,5,7] => [8,7,5,2,4,6,3,1] => 0101111 => 1010111
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,4,1,8,2,3,5,6] => [8,6,3,1,7,5,2,4] => 0101111 => 1010111
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7,4,1,6,2,3,8,5] => [8,5,2,4,6,3,1,7] => 0101101 => 1010110
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,8,1,5,2,3,4,7] => [6,3,1,8,7,4,5,2] => 0101111 => 1010111
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8,7,1,5,2,3,4,6] => [7,4,5,2,8,6,3,1] => 0101111 => 1010111
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8,7,1,6,2,3,4,5] => [8,5,2,7,4,6,3,1] => 0101111 => 1010111
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [6,7,1,5,2,3,8,4] => [6,3,1,8,4,5,2,7] => 0101101 => 1010110
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,4,1,5,2,8,3,7] => [5,2,4,8,7,3,1,6] => 0101011 => 1010101
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8,4,1,5,2,7,3,6] => [5,2,4,8,6,7,3,1] => 0101011 => 1010101
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8,4,1,6,2,7,3,5] => [8,5,2,4,6,7,3,1] => 0101011 => 1010101
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [6,8,1,5,2,7,3,4] => [7,3,1,6,8,4,5,2] => 0101011 => 1010101
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [6,4,1,5,2,7,8,3] => [5,2,4,8,3,1,6,7] => 0101001 => 1010100
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [4,3,1,5,8,2,6,7] => [8,7,6,2,3,1,4,5] => 0100111 => 1010011
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [4,3,1,8,6,2,5,7] => [8,7,5,6,2,3,1,4] => 0100111 => 1010011
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [4,3,1,8,7,2,5,6] => [7,5,8,6,2,3,1,4] => 0100111 => 1010011
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,3,1,7,6,2,8,5] => [8,5,6,2,3,1,4,7] => 0100101 => 1010010
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,3,1,5,6,2,4,7] => [8,7,4,5,6,2,3,1] => 0100111 => 1010011
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8,3,1,5,7,2,4,6] => [7,4,5,8,6,2,3,1] => 0100111 => 1010011
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8,3,1,7,6,2,4,5] => [7,4,8,5,6,2,3,1] => 0100111 => 1010011
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7,3,1,5,6,2,8,4] => [8,4,5,6,2,3,1,7] => 0100101 => 1010010
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,1,5,6,2,3,7] => [6,2,4,5,8,7,3,1] => 0100111 => 1010011
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8,4,1,5,7,2,3,6] => [8,6,2,4,5,7,3,1] => 0100111 => 1010011
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8,4,1,7,6,2,3,5] => [8,5,6,2,4,7,3,1] => 0100111 => 1010011
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [7,3,1,8,4,5,6,2] => 0100111 => 1010011
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7,4,1,5,6,2,8,3] => [6,2,4,5,8,3,1,7] => 0100101 => 1010010
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [4,3,1,5,6,8,2,7] => [8,7,2,3,1,4,5,6] => 0100011 => 1010001
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [4,3,1,5,8,7,2,6] => [8,6,7,2,3,1,4,5] => 0100011 => 1010001
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,3,1,8,6,7,2,5] => [8,5,6,7,2,3,1,4] => 0100011 => 1010001
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8,3,1,5,6,7,2,4] => [8,4,5,6,7,2,3,1] => 0100011 => 1010001
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8,4,1,5,6,7,2,3] => [7,2,4,5,6,8,3,1] => 0100011 => 1010001
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [8,2,3,1,4,5,6,7] => 0100001 => 1010000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => [8,7,6,5,4,1,2,3] => 0011111 => 1001111
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,3,7,1,4,5,8,6] => [8,6,5,4,1,2,3,7] => 0011101 => 1001110
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7] => [8,7,5,4,1,2,3,6] => 0011011 => 1001101
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => [8,5,4,1,2,3,6,7] => 0011001 => 1001100
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => [8,7,6,4,1,2,3,5] => 0010111 => 1001011
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,3,8,1,7,4,5,6] => [7,5,8,6,4,1,2,3] => 0010111 => 1001011
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,3,7,1,6,4,8,5] => [8,5,6,4,1,2,3,7] => 0010101 => 1001010
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [8,7,4,1,2,3,5,6] => 0010011 => 1001001
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,3,8,1,6,7,4,5] => [8,5,6,7,4,1,2,3] => 0010011 => 1001001
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,4,1,2,3,5,6,7] => 0010001 => 1001000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,8,4,1,3,5,6,7] => [8,7,6,5,3,4,1,2] => 0011111 => 1001111
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,7,4,1,3,5,8,6] => [8,6,5,3,4,1,2,7] => 0011101 => 1001110
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,6,4,1,3,8,5,7] => [8,7,5,3,4,1,2,6] => 0011011 => 1001101
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,6,4,1,3,7,8,5] => [8,5,3,4,1,2,6,7] => 0011001 => 1001100
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,8,5,1,3,4,6,7] => [5,3,8,7,6,4,1,2] => 0011111 => 1001111
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,8,1,3,4,5,7] => [6,4,1,2,8,7,5,3] => 0011111 => 1001111
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,8,7,1,3,4,5,6] => [7,5,3,8,6,4,1,2] => 0011111 => 1001111
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => [6,4,1,2,8,5,3,7] => 0011101 => 1001110
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,6,5,1,3,8,4,7] => [5,3,8,7,4,1,2,6] => 0011011 => 1001101
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,8,5,1,3,7,4,6] => [5,3,8,6,7,4,1,2] => 0011011 => 1001101
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,6,8,1,3,7,4,5] => [7,4,1,2,6,8,5,3] => 0011011 => 1001101
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,6,5,1,3,7,8,4] => [5,3,8,4,1,2,6,7] => 0011001 => 1001100
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,5,4,1,8,3,6,7] => [8,7,6,3,4,1,2,5] => 0010111 => 1001011
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,5,4,1,7,3,8,6] => [8,6,3,4,1,2,5,7] => 0010101 => 1001010
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,8,4,1,6,3,5,7] => [8,7,5,6,3,4,1,2] => 0010111 => 1001011
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,8,4,1,7,3,5,6] => [7,5,8,6,3,4,1,2] => 0010111 => 1001011
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,7,4,1,6,3,8,5] => [8,5,6,3,4,1,2,7] => 0010101 => 1001010
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,8,5,1,6,3,4,7] => [6,3,5,8,7,4,1,2] => 0010111 => 1001011
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,8,5,1,7,3,4,6] => [8,6,3,5,7,4,1,2] => 0010111 => 1001011
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,7,8,1,6,3,4,5] => [7,4,1,2,8,5,6,3] => 0010111 => 1001011
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,7,5,1,6,3,8,4] => [6,3,5,8,4,1,2,7] => 0010101 => 1001010
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,5,4,1,6,8,3,7] => [8,7,3,4,1,2,5,6] => 0010011 => 1001001
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,5,4,1,8,7,3,6] => [8,6,7,3,4,1,2,5] => 0010011 => 1001001
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,8,4,1,6,7,3,5] => [8,5,6,7,3,4,1,2] => 0010011 => 1001001
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,8,5,1,6,7,3,4] => [7,3,5,6,8,4,1,2] => 0010011 => 1001001
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,5,4,1,6,7,8,3] => [8,3,4,1,2,5,6,7] => 0010001 => 1001000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,3,4,1,2,5,6,7] => [8,7,6,5,2,3,4,1] => 0011111 => 1001111
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,3,4,1,2,5,8,6] => [8,6,5,2,3,4,1,7] => 0011101 => 1001110
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [8,3,4,1,2,7,5,6] => [8,6,7,5,2,3,4,1] => 0011011 => 1001101
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,3,4,1,2,7,8,5] => [8,5,2,3,4,1,6,7] => 0011001 => 1001100
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,3,7,1,2,4,5,6] => [7,5,2,3,8,6,4,1] => 0011111 => 1001111
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,3,7,1,2,4,8,5] => [6,4,1,8,5,2,3,7] => 0011101 => 1001110
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,5,1,2,8,4,7] => [5,2,3,8,7,4,1,6] => 0011011 => 1001101
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8,3,5,1,2,7,4,6] => [5,2,3,8,6,7,4,1] => 0011011 => 1001101
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,3,8,1,2,7,4,5] => [7,4,1,6,8,5,2,3] => 0011011 => 1001101
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [6,3,5,1,2,7,8,4] => [5,2,3,8,4,1,6,7] => 0011001 => 1001100
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,8,4,1,2,3,5,7] => [6,3,4,1,8,7,5,2] => 0011111 => 1001111
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,4,1,2,3,5,6] => [7,5,2,8,6,3,4,1] => 0011111 => 1001111
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,1,2,3,8,5] => [6,3,4,1,8,5,2,7] => 0011101 => 1001110
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,8,5,1,2,3,4,7] => [8,7,4,1,6,3,5,2] => 0011111 => 1001111
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8,7,5,1,2,3,4,6] => [8,6,3,5,2,7,4,1] => 0011111 => 1001111
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,7,8,1,2,3,4,5] => [8,5,2,7,4,1,6,3] => 0011111 => 1001111
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,1,2,3,8,4] => [8,4,1,6,3,5,2,7] => 0011101 => 1001110
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,5,4,1,2,8,3,7] => [5,2,8,7,3,4,1,6] => 0011011 => 1001101
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,4,1,2,7,3,6] => [5,2,8,6,7,3,4,1] => 0011011 => 1001101
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,8,4,1,2,7,3,5] => [7,3,4,1,6,8,5,2] => 0011011 => 1001101
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [6,8,5,1,2,7,3,4] => [8,4,1,6,7,3,5,2] => 0011011 => 1001101
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [6,5,4,1,2,7,8,3] => [5,2,8,3,4,1,6,7] => 0011001 => 1001100
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,3,4,1,8,2,6,7] => [8,7,6,2,3,4,1,5] => 0010111 => 1001011
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,3,4,1,7,2,8,6] => [8,6,2,3,4,1,5,7] => 0010101 => 1001010
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,3,4,1,6,2,5,7] => [8,7,5,6,2,3,4,1] => 0010111 => 1001011
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8,3,4,1,7,2,5,6] => [7,5,8,6,2,3,4,1] => 0010111 => 1001011
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7,3,4,1,6,2,8,5] => [8,5,6,2,3,4,1,7] => 0010101 => 1001010
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8,3,5,1,7,2,4,6] => [8,6,2,3,5,7,4,1] => 0010111 => 1001011
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,3,8,1,6,2,4,5] => [7,4,1,8,5,6,2,3] => 0010111 => 1001011
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,3,5,1,6,2,8,4] => [6,2,3,5,8,4,1,7] => 0010101 => 1001010
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,5,4,1,6,2,3,7] => [6,2,5,8,7,3,4,1] => 0010111 => 1001011
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8,5,4,1,7,2,3,6] => [8,6,2,5,7,3,4,1] => 0010111 => 1001011
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,8,4,1,6,2,3,5] => [7,3,4,1,8,5,6,2] => 0010111 => 1001011
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,8,5,1,6,2,3,4] => [8,4,1,7,3,5,6,2] => 0010111 => 1001011
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,5,4,1,6,2,8,3] => [6,2,5,8,3,4,1,7] => 0010101 => 1001010
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [5,3,4,1,6,8,2,7] => [8,7,2,3,4,1,5,6] => 0010011 => 1001001
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,3,4,1,8,7,2,6] => [8,6,7,2,3,4,1,5] => 0010011 => 1001001
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => [8,5,6,7,2,3,4,1] => 0010011 => 1001001
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8,3,5,1,6,7,2,4] => [7,2,3,5,6,8,4,1] => 0010011 => 1001001
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8,5,4,1,6,7,2,3] => [7,2,5,6,8,3,4,1] => 0010011 => 1001001
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [5,3,4,1,6,7,8,2] => [8,2,3,4,1,5,6,7] => 0010001 => 1001000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => [8,7,6,5,1,2,3,4] => 0001111 => 1000111
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,4,7,1,5,8,6] => [8,6,5,1,2,3,4,7] => 0001101 => 1000110
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => [8,7,5,1,2,3,4,6] => 0001011 => 1000101
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,4,8,1,7,5,6] => [8,6,7,5,1,2,3,4] => 0001011 => 1000101
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,5,1,2,3,4,6,7] => 0001001 => 1000100
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,8,5,1,4,6,7] => [8,7,6,4,5,1,2,3] => 0001111 => 1000111
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,7,5,1,4,8,6] => [8,6,4,5,1,2,3,7] => 0001101 => 1000110
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,8,6,1,4,5,7] => [6,4,8,7,5,1,2,3] => 0001111 => 1000111
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,7,8,1,4,5,6] => [7,5,1,2,3,8,6,4] => 0001111 => 1000111
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,7,6,1,4,8,5] => [6,4,8,5,1,2,3,7] => 0001101 => 1000110
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,6,5,1,8,4,7] => [8,7,4,5,1,2,3,6] => 0001011 => 1000101
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,8,5,1,7,4,6] => [8,6,7,4,5,1,2,3] => 0001011 => 1000101
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,8,6,1,7,4,5] => [7,4,6,8,5,1,2,3] => 0001011 => 1000101
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,6,5,1,7,8,4] => [8,4,5,1,2,3,6,7] => 0001001 => 1000100
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,8,4,5,1,3,6,7] => [8,7,6,3,4,5,1,2] => 0001111 => 1000111
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,4,5,1,3,8,6] => [8,6,3,4,5,1,2,7] => 0001101 => 1000110
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,8,4,6,1,3,5,7] => [6,3,4,8,7,5,1,2] => 0001111 => 1000111
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,7,4,8,1,3,5,6] => [7,5,1,2,8,6,3,4] => 0001111 => 1000111
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,7,4,6,1,3,8,5] => [6,3,4,8,5,1,2,7] => 0001101 => 1000110
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,8,6,5,1,3,4,7] => [6,3,8,7,4,5,1,2] => 0001111 => 1000111
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,8,5,1,3,4,6] => [7,4,5,1,2,8,6,3] => 0001111 => 1000111
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7,8,6,1,3,4,5] => [8,5,1,2,7,4,6,3] => 0001111 => 1000111
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,7,6,5,1,3,8,4] => [6,3,8,4,5,1,2,7] => 0001101 => 1000110
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,6,4,5,1,8,3,7] => [8,7,3,4,5,1,2,6] => 0001011 => 1000101
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,6,7,3,4,5,1,2] => 0001011 => 1000101
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,6,1,7,3,5] => [7,3,4,6,8,5,1,2] => 0001011 => 1000101
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,6,5,1,7,3,4] => [7,3,6,8,4,5,1,2] => 0001011 => 1000101
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,6,4,5,1,7,8,3] => [8,3,4,5,1,2,6,7] => 0001001 => 1000100
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [8,3,4,5,1,2,6,7] => [8,7,6,2,3,4,5,1] => 0001111 => 1000111
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,3,4,8,1,2,5,6] => [7,5,1,8,6,2,3,4] => 0001111 => 1000111
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7,3,4,6,1,2,8,5] => [6,2,3,4,8,5,1,7] => 0001101 => 1000110
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,3,6,5,1,2,4,7] => [6,2,3,8,7,4,5,1] => 0001111 => 1000111
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,3,8,5,1,2,4,6] => [7,4,5,1,8,6,2,3] => 0001111 => 1000111
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,8,6,1,2,4,5] => [8,5,1,7,4,6,2,3] => 0001111 => 1000111
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,6,5,1,2,8,4] => [6,2,3,8,4,5,1,7] => 0001101 => 1000110
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,6,4,5,1,2,3,7] => [6,2,8,7,3,4,5,1] => 0001111 => 1000111
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,8,4,5,1,2,3,6] => [7,3,4,5,1,8,6,2] => 0001111 => 1000111
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,8,4,6,1,2,3,5] => [8,5,1,7,3,4,6,2] => 0001111 => 1000111
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,6,5,1,2,3,4] => [8,4,5,1,7,3,6,2] => 0001111 => 1000111
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,6,4,5,1,2,8,3] => [6,2,8,3,4,5,1,7] => 0001101 => 1000110
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,4,5,1,8,2,7] => [8,7,2,3,4,5,1,6] => 0001011 => 1000101
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8,3,4,5,1,7,2,6] => [8,6,7,2,3,4,5,1] => 0001011 => 1000101
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8,3,4,6,1,7,2,5] => [7,2,3,4,6,8,5,1] => 0001011 => 1000101
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8,3,6,5,1,7,2,4] => [7,2,3,6,8,4,5,1] => 0001011 => 1000101
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8,6,4,5,1,7,2,3] => [7,2,6,8,3,4,5,1] => 0001011 => 1000101
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [6,3,4,5,1,7,8,2] => [8,2,3,4,5,1,6,7] => 0001001 => 1000100
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7] => [8,7,6,1,2,3,4,5] => 0000111 => 1000011
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [8,6,1,2,3,4,5,7] => 0000101 => 1000010
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,3,4,8,6,1,5,7] => [8,7,5,6,1,2,3,4] => 0000111 => 1000011
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,4,8,7,1,5,6] => [7,5,8,6,1,2,3,4] => 0000111 => 1000011
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,4,7,6,1,8,5] => [8,5,6,1,2,3,4,7] => 0000101 => 1000010
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,3,8,5,6,1,4,7] => [8,7,4,5,6,1,2,3] => 0000111 => 1000011
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,8,5,7,1,4,6] => [7,4,5,8,6,1,2,3] => 0000111 => 1000011
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,8,7,6,1,4,5] => [7,4,8,5,6,1,2,3] => 0000111 => 1000011
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,7,5,6,1,8,4] => [8,4,5,6,1,2,3,7] => 0000101 => 1000010
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,8,4,5,6,1,3,7] => [8,7,3,4,5,6,1,2] => 0000111 => 1000011
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,8,4,5,7,1,3,6] => [7,3,4,5,8,6,1,2] => 0000111 => 1000011
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,4,7,6,1,3,5] => [7,3,4,8,5,6,1,2] => 0000111 => 1000011
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [7,3,8,4,5,6,1,2] => 0000111 => 1000011
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,7,4,5,6,1,8,3] => [8,3,4,5,6,1,2,7] => 0000101 => 1000010
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [8,7,2,3,4,5,6,1] => 0000111 => 1000011
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8,3,4,5,7,1,2,6] => [7,2,3,4,5,8,6,1] => 0000111 => 1000011
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8,3,4,7,6,1,2,5] => [7,2,3,4,8,5,6,1] => 0000111 => 1000011
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8,3,7,5,6,1,2,4] => [7,2,3,8,4,5,6,1] => 0000111 => 1000011
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,7,4,5,6,1,2,3] => [7,2,8,3,4,5,6,1] => 0000111 => 1000011
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,3,4,5,6,1,8,2] => [8,2,3,4,5,6,1,7] => 0000101 => 1000010
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => [8,7,1,2,3,4,5,6] => 0000011 => 1000001
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,4,5,8,7,1,6] => [8,6,7,1,2,3,4,5] => 0000011 => 1000001
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,8,6,7,1,5] => [8,5,6,7,1,2,3,4] => 0000011 => 1000001
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,8,5,6,7,1,4] => [8,4,5,6,7,1,2,3] => 0000011 => 1000001
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,4,5,6,7,1,3] => [8,3,4,5,6,7,1,2] => 0000011 => 1000001
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8,3,4,5,6,7,1,2] => [8,2,3,4,5,6,7,1] => 0000011 => 1000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => 0000001 => 1000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,1,2,3,4,5,6,7,8] => [9,8,7,6,5,4,3,2,1] => 11111111 => 11111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7] => [9,7,6,5,4,3,2,1,8] => 11111101 => 11111110
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => [9,8,6,5,4,3,2,1,7] => 11111011 => 11111101
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,1,2,3,4,5,8,6,7] => [9,7,8,6,5,4,3,2,1] => 11111011 => 11111101
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6] => [9,6,5,4,3,2,1,7,8] => 11111001 => 11111100
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,1,2,3,4,9,5,7,8] => [9,8,7,5,4,3,2,1,6] => 11110111 => 11111011
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,1,2,3,4,8,5,6,7] => [8,6,9,7,5,4,3,2,1] => 11110111 => 11111011
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [8,1,2,3,4,7,5,9,6] => [9,6,7,5,4,3,2,1,8] => 11110101 => 11111010
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,1,2,3,4,7,9,5,8] => [9,8,5,4,3,2,1,6,7] => 11110011 => 11111001
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,1,2,3,4,9,8,5,7] => [9,7,8,5,4,3,2,1,6] => 11110011 => 11111001
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [9,1,2,3,4,7,8,5,6] => [9,6,7,8,5,4,3,2,1] => 11110011 => 11111001
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => [9,5,4,3,2,1,6,7,8] => 11110001 => 11111000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [5,1,2,3,9,4,6,7,8] => [9,8,7,6,4,3,2,1,5] => 11101111 => 11110111
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [9,1,2,3,6,4,5,7,8] => [9,8,7,5,6,4,3,2,1] => 11101111 => 11110111
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,1,2,3,9,4,5,6,7] => [8,6,4,3,2,1,9,7,5] => 11101111 => 11110111
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,1,2,3,9,8,4,6,7] => [8,6,9,7,4,3,2,1,5] => 11100111 => 11110011
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [9,1,2,3,6,8,4,5,7] => [8,5,6,9,7,4,3,2,1] => 11100111 => 11110011
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,1,2,3,6,9,8,4,7] => [9,7,8,4,3,2,1,5,6] => 11100011 => 11110001
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [9,1,2,5,3,4,6,7,8] => [9,8,7,6,4,5,3,2,1] => 11011111 => 11101111
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,1,2,8,3,4,5,6,7] => [8,6,4,9,7,5,3,2,1] => 11011111 => 11101111
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,9,3,6,7,8] => [9,8,7,6,3,2,1,4,5] => 11001111 => 11100111
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [4,1,2,8,9,3,5,6,7] => [8,6,3,2,1,4,9,7,5] => 11001111 => 11100111
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [8,1,2,5,9,3,4,6,7] => [8,6,3,2,1,9,7,4,5] => 11001111 => 11100111
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,9,8,3,6,7] => [8,6,9,7,3,2,1,4,5] => 11000111 => 11100011
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,9,2,4,5,6,7,8] => [9,8,7,6,5,4,2,1,3] => 10111111 => 11011111
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,1,4,2,3,5,6,7,8] => [9,8,7,6,5,3,4,2,1] => 10111111 => 11011111
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,8,2,3,4,5,6,7] => [9,7,5,3,8,6,4,2,1] => 10111111 => 11011111
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,4,9,2,5,6,7,8] => [9,8,7,6,5,2,1,3,4] => 10011111 => 11001111
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,9,8,2,4,5,6,7] => [8,6,4,9,7,5,2,1,3] => 10011111 => 11001111
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9,1,4,8,2,3,5,6,7] => [8,6,3,4,9,7,5,2,1] => 10011111 => 11001111
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,4,8,9,2,5,6,7] => [8,6,2,1,3,4,9,7,5] => 10001111 => 11000111
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,1,4,5,6,2,8,9,3] => [9,3,4,5,6,2,1,7,8] => 10001001 => 11000100
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [9,1,8,5,6,7,2,3,4] => [8,3,9,4,5,6,7,2,1] => 10000111 => 11000011
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [8,1,4,5,6,7,2,9,3] => [9,3,4,5,6,7,2,1,8] => 10000101 => 11000010
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,4,9,6,7,8,2,5] => [9,5,6,7,8,2,1,3,4] => 10000011 => 11000001
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,9,5,6,7,8,2,4] => [9,4,5,6,7,8,2,1,3] => 10000011 => 11000001
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [9,1,4,5,6,7,8,2,3] => [9,3,4,5,6,7,8,2,1] => 10000011 => 11000001
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [9,2,1,3,4,5,6,7,8] => 10000001 => 11000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,9,1,3,4,5,6,7,8] => [9,8,7,6,5,4,3,1,2] => 01111111 => 10111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,8,1,3,4,5,6,9,7] => [9,7,6,5,4,3,1,2,8] => 01111101 => 10111110
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,9,1,3,4,5,8,6,7] => [9,7,8,6,5,4,3,1,2] => 01111011 => 10111101
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,9,3,5,6,7,8] => [9,8,7,6,5,3,1,2,4] => 01011111 => 10101111
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [9,7,5,3,1,2,4,6,8] => 01010101 => 10101010
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,3,1,2,4,5,6,7,8] => 01000001 => 10100000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,3,1,2,4,5,6,7,8] => [9,8,7,6,5,4,2,3,1] => 01111111 => 10111111
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,4,1,2,3,5,6,7,8] => [4,2,9,8,7,6,5,3,1] => 01111111 => 10111111
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [5,9,1,2,3,4,6,7,8] => [5,3,1,9,8,7,6,4,2] => 01111111 => 10111111
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,9,1,2,3,4,5,6,7] => [9,7,5,3,1,8,6,4,2] => 01111111 => 10111111
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,3,1,9,2,5,6,7,8] => [9,8,7,6,5,2,3,1,4] => 01011111 => 10101111
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,3,1,6,2,8,5,9,7] => [9,7,5,2,3,1,4,6,8] => 01010101 => 10101010
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [9,3,1,5,2,4,6,7,8] => [9,8,7,6,4,5,2,3,1] => 01011111 => 10101111
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9,3,1,8,2,4,5,6,7] => [8,6,4,9,7,5,2,3,1] => 01011111 => 10101111
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [9,3,1,5,2,8,4,6,7] => [8,6,9,7,4,5,2,3,1] => 01010111 => 10101011
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,3,1,5,2,7,4,9,6] => [9,6,7,4,5,2,3,1,8] => 01010101 => 10101010
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,3,1,5,8,7,2,9,6] => [9,6,7,2,3,1,4,5,8] => 01000101 => 10100010
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,3,1,5,6,7,8,9,2] => [9,2,3,1,4,5,6,7,8] => 01000001 => 10100000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,9,1,4,5,6,7,8] => [9,8,7,6,5,4,1,2,3] => 00111111 => 10011111
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [9,8,4,1,2,3,5,6,7] => 00100011 => 10010001
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,4,1,2,3,5,6,7,8] => 00100001 => 10010000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,9,4,1,3,5,6,7,8] => [9,8,7,6,5,3,4,1,2] => 00111111 => 10011111
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,9,8,1,3,4,5,6,7] => [9,7,5,3,8,6,4,1,2] => 00111111 => 10011111
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,5,4,1,6,7,8,9,3] => [9,3,4,1,2,5,6,7,8] => 00100001 => 10010000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [9,3,4,1,2,5,6,7,8] => [9,8,7,6,5,2,3,4,1] => 00111111 => 10011111
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,3,8,1,2,4,5,6,7] => [9,7,5,2,3,8,6,4,1] => 00111111 => 10011111
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,7,8,1,2,3,4,5,6] => [9,6,3,8,5,2,7,4,1] => 00111111 => 10011111
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [5,3,4,1,6,7,8,9,2] => [9,2,3,4,1,5,6,7,8] => 00100001 => 10010000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,9,1,5,6,7,8] => [9,8,7,6,5,1,2,3,4] => 00011111 => 10001111
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [2,3,9,5,1,4,6,7,8] => [9,8,7,6,4,5,1,2,3] => 00011111 => 10001111
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [2,3,9,8,1,4,5,6,7] => [8,6,4,9,7,5,1,2,3] => 00011111 => 10001111
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [6,3,4,5,1,7,9,2,8] => [9,8,2,3,4,5,1,6,7] => 00010011 => 10001001
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [6,3,4,5,1,7,8,9,2] => [9,2,3,4,5,1,6,7,8] => 00010001 => 10001000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,9,1,6,7,8] => [9,8,7,6,1,2,3,4,5] => 00001111 => 10000111
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,6,1,2,3,4,5,7,8] => 00001001 => 10000100
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [2,3,4,9,6,1,5,7,8] => [9,8,7,5,6,1,2,3,4] => 00001111 => 10000111
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [2,3,9,5,6,1,4,7,8] => [9,8,7,4,5,6,1,2,3] => 00001111 => 10000111
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [2,3,8,5,6,1,4,9,7] => [9,7,4,5,6,1,2,3,8] => 00001101 => 10000110
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [9,7,4,5,6,1,2,3,8] => [7,2,9,8,3,4,5,6,1] => 00001111 => 10000111
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,3,4,5,6,1,9,2,8] => [9,8,2,3,4,5,6,1,7] => 00001011 => 10000101
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [7,3,4,5,6,1,8,9,2] => [9,2,3,4,5,6,1,7,8] => 00001001 => 10000100
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,9,1,7,8] => [9,8,7,1,2,3,4,5,6] => 00000111 => 10000011
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,8,1,9,7] => [9,7,1,2,3,4,5,6,8] => 00000101 => 10000010
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [2,3,4,5,9,7,1,6,8] => [9,8,6,7,1,2,3,4,5] => 00000111 => 10000011
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [2,3,4,9,6,7,1,5,8] => [9,8,5,6,7,1,2,3,4] => 00000111 => 10000011
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [2,3,9,5,6,7,1,4,8] => [9,8,4,5,6,7,1,2,3] => 00000111 => 10000011
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [2,9,4,5,6,7,1,3,8] => [9,8,3,4,5,6,7,1,2] => 00000111 => 10000011
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,8,4,5,6,7,1,9,3] => [9,3,4,5,6,7,1,2,8] => 00000101 => 10000010
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,1,2,8] => [9,8,2,3,4,5,6,7,1] => 00000111 => 10000011
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,3,4,5,6,7,1,9,2] => [9,2,3,4,5,6,7,1,8] => 00000101 => 10000010
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => [9,8,1,2,3,4,5,6,7] => 00000011 => 10000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,9,8,1,7] => [9,7,8,1,2,3,4,5,6] => 00000011 => 10000001
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,3,4,5,9,7,8,1,6] => [9,6,7,8,1,2,3,4,5] => 00000011 => 10000001
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [2,3,4,9,6,7,8,1,5] => [9,5,6,7,8,1,2,3,4] => 00000011 => 10000001
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,9,4,5,6,7,8,1,3] => [9,3,4,5,6,7,8,1,2] => 00000011 => 10000001
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9,3,4,5,6,7,8,1,2] => [9,2,3,4,5,6,7,8,1] => 00000011 => 10000001
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => 00000001 => 10000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,10,1,9] => [10,9,1,2,3,4,5,6,7,8] => 000000011 => 100000001
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [10,2,1,3,4,5,6,7,8,9] => 100000001 => 110000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,9,11,1,10] => [11,10,1,2,3,4,5,6,7,8,9] => 0000000011 => 1000000001
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,1,2,9] => [10,9,2,3,4,5,6,7,8,1] => 000000111 => 100000011
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [10,1,4,5,6,7,8,9,2,3] => [10,3,4,5,6,7,8,9,2,1] => 100000011 => 110000001
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => [11,2,1,3,4,5,6,7,8,9,10] => 1000000001 => 1100000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,9,10,12,1,11] => [12,11,1,2,3,4,5,6,7,8,9,10] => 00000000011 => 10000000001
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [11,3,4,5,6,7,8,9,1,2,10] => [11,10,2,3,4,5,6,7,8,9,1] => 0000000111 => 1000000011
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [2,10,4,5,6,7,8,1,3,9] => [10,9,3,4,5,6,7,8,1,2] => 000000111 => 100000011
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,10,2,9] => [10,9,2,3,4,5,6,7,1,8] => 000001011 => 100000101
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,10,5,6,7,8,9,2,4] => [10,4,5,6,7,8,9,2,1,3] => 100000011 => 110000001
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9,1,4,5,6,7,8,2,10,3] => [10,3,4,5,6,7,8,2,1,9] => 100000101 => 110000010
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [11,1,4,5,6,7,8,9,10,2,3] => [11,3,4,5,6,7,8,9,10,2,1] => 1000000011 => 1100000001
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => [12,2,1,3,4,5,6,7,8,9,10,11] => 10000000001 => 11000000000
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,1,11,2,10] => [11,10,2,3,4,5,6,7,8,1,9] => 0000001011 => 1000000101
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [2,3,4,5,6,10,8,1,7,9] => [10,9,7,8,1,2,3,4,5,6] => 000000111 => 100000011
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,3,1,2,4,5,6,7,8,9] => 010000001 => 101000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,7,10,1,8,9] => [10,9,8,1,2,3,4,5,6,7] => 000000111 => 100000011
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,8,10,1,11,9] => [11,9,1,2,3,4,5,6,7,8,10] => 0000000101 => 1000000010
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [11,3,1,2,4,5,6,7,8,9,10] => 0100000001 => 1010000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,1,2,3,4,5,6,7,8] => [10,8,6,4,2,9,7,5,3,1] => 011111111 => 101111111
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [10,3,1,5,2,7,4,9,6,8] => [10,8,9,6,7,4,5,2,3,1] => 010101011 => 101010101
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,3,1,5,6,7,8,9,10,2] => [10,2,3,1,4,5,6,7,8,9] => 010000001 => 101000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,9,10,1,3,4,5,6,7,8] => [10,8,6,4,1,2,9,7,5,3] => 001111111 => 100111111
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,3,10,1,2,4,5,6,7,8] => [10,8,6,4,1,9,7,5,2,3] => 001111111 => 100111111
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,9,8,1,2,3,4,5,6,7] => [9,6,3,8,5,2,10,7,4,1] => 001111111 => 100111111
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [5,3,4,1,6,7,8,9,10,2] => [10,2,3,4,1,5,6,7,8,9] => 001000001 => 100100000
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [9,5,1,7,3,10,6,2,8,4] => 000111111 => 100011111
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [6,3,4,5,1,7,8,9,10,2] => [10,2,3,4,5,1,6,7,8,9] => 000100001 => 100010000
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0] => [8,3,4,9,10,1,2,5,6,7] => [10,7,2,3,4,9,6,1,8,5] => 000011111 => 100001111
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [7,3,4,5,6,1,8,9,10,2] => [10,2,3,4,5,6,1,7,8,9] => 000010001 => 100001000
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [8,3,4,5,6,7,1,9,10,2] => [10,2,3,4,5,6,7,1,8,9] => 000001001 => 100000100
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9,3,4,5,6,7,8,1,10,2] => [10,2,3,4,5,6,7,8,1,9] => 000000101 => 100000010
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,7,10,9,1,8] => [10,8,9,1,2,3,4,5,6,7] => 000000011 => 100000001
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [2,3,4,5,6,10,8,9,1,7] => [10,7,8,9,1,2,3,4,5,6] => 000000011 => 100000001
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [2,3,4,5,10,7,8,9,1,6] => [10,6,7,8,9,1,2,3,4,5] => 000000011 => 100000001
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,10,4,5,6,7,8,9,1,3] => [10,3,4,5,6,7,8,9,1,2] => 000000011 => 100000001
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10,3,4,5,6,7,8,9,1,2] => [10,2,3,4,5,6,7,8,9,1] => 000000011 => 100000001
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => 000000001 => 100000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [10,9,8,7,6,5,4,3,2,1] => 111111111 => 111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => [10,8,7,6,5,4,3,2,1,9] => 111111101 => 111111110
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,1,2,3,4,5,6,9,7,8] => [10,8,9,7,6,5,4,3,2,1] => 111111011 => 111111101
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [10,1,2,3,4,5,9,6,7,8] => [9,7,10,8,6,5,4,3,2,1] => 111110111 => 111111011
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,1,2,3,4,10,5,6,7,8] => [9,7,5,4,3,2,1,10,8,6] => 111101111 => 111110111
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,3,9,4,5,6,7,8] => [9,7,5,10,8,6,4,3,2,1] => 111011111 => 111101111
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,9,3,4,5,6,7,8] => [10,8,6,4,9,7,5,3,2,1] => 110111111 => 111011111
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,10,2,3,4,5,6,7,8] => [10,8,6,4,2,1,9,7,5,3] => 101111111 => 110111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [11,10,9,8,7,6,5,4,3,2,1] => 1111111111 => 1111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,1,2,3,4,5,6,7,8,11,9] => [11,9,8,7,6,5,4,3,2,1,10] => 1111111101 => 1111111110
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,1,2,3,4,5,6,9,10,7] => [10,7,6,5,4,3,2,1,8,9] => 111111001 => 111111100
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [11,1,2,3,4,5,6,7,10,8,9] => [11,9,10,8,7,6,5,4,3,2,1] => 1111111011 => 1111111101
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,1,2,3,4,5,10,9,6,8] => [10,8,9,6,5,4,3,2,1,7] => 111110011 => 111111001
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,1,2,3,4,10,9,5,7,8] => [9,7,10,8,5,4,3,2,1,6] => 111100111 => 111110011
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,1,2,3,9,10,4,6,7,8] => [9,7,4,3,2,1,5,10,8,6] => 111001111 => 111100111
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,2,10,9,3,5,6,7,8] => [9,7,5,10,8,6,3,2,1,4] => 110011111 => 111001111
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,1,2,3,10,4,5,6,7,8,9] => [11,9,7,5,10,8,6,4,3,2,1] => 1110111111 => 1111011111
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,10,9,2,4,5,6,7,8] => [10,8,6,4,9,7,5,2,1,3] => 100111111 => 110011111
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,11,3,4,5,6,7,8,9] => [11,9,7,5,3,2,1,10,8,6,4] => 1101111111 => 1110111111
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,1,10,2,3,4,5,6,7,8,9] => [11,9,7,5,3,10,8,6,4,2,1] => 1011111111 => 1101111111
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,10,1,2,3,4,5,6,7,8,9] => [10,8,6,4,2,11,9,7,5,3,1] => 0111111111 => 1011111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [11,1,2,3,4,5,6,7,8,9,12,10] => [12,10,9,8,7,6,5,4,3,2,1,11] => 11111111101 => 11111111110
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,12,1,2,3,4,5,6,7,8,9,10] => [11,9,7,5,3,1,12,10,8,6,4,2] => 01111111111 => 10111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,1,2,3,4,5,6,10,7,9] => [10,9,7,6,5,4,3,2,1,8] => 111111011 => 111111101
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,1,2,3,4,5,9,6,10,8] => [10,8,6,5,4,3,2,1,7,9] => 111110101 => 111111010
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,10,4,6,7,8,9] => [10,9,8,7,6,4,3,2,1,5] => 111011111 => 111101111
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,9,6,10,8] => [10,8,6,4,3,2,1,5,7,9] => 111010101 => 111101010
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,10,3,5,6,7,8,9] => [10,9,8,7,6,5,3,2,1,4] => 110111111 => 111011111
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,10,2,4,5,6,7,8,9] => [10,9,8,7,6,5,4,2,1,3] => 101111111 => 110111111
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,9,2,4,5,6,7,10,8] => [10,8,7,6,5,4,2,1,3,9] => 101111101 => 110111110
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,10,4,6,7,8,9] => [10,9,8,7,6,4,2,1,3,5] => 101011111 => 110101111
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,8,6,4,2,1,3,5,7,9] => 101010101 => 110101010
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,10,1,3,4,5,6,7,8,9] => [10,9,8,7,6,5,4,3,1,2] => 011111111 => 101111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,9,1,3,4,5,6,7,10,8] => [10,8,7,6,5,4,3,1,2,9] => 011111101 => 101111110
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,9,7,5,3,1,2,4,6,8] => 010101011 => 101010101
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,10,1,4,5,6,7,8,9] => [10,9,8,7,6,5,4,1,2,3] => 001111111 => 100111111
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,4,1,2,3,5,6,7,8,9] => 001000001 => 100100000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,10,1,5,6,7,8,9] => [10,9,8,7,6,5,1,2,3,4] => 000111111 => 100011111
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,10,1,6,7,8,9] => [10,9,8,7,6,1,2,3,4,5] => 000011111 => 100001111
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,6,1,2,3,4,5,7,8,9] => 000010001 => 100001000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,6,10,1,7,8,9] => [10,9,8,7,1,2,3,4,5,6] => 000001111 => 100000111
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,7,1,2,3,4,5,6,8,9] => 000001001 => 100000100
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,11,1,3,4,5,6,7,8,9,10] => [11,10,9,8,7,6,5,4,3,1,2] => 0111111111 => 1011111111
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [11,4,1,2,3,5,6,7,8,9,10] => 0010000001 => 1001000000
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [11,6,1,2,3,4,5,7,8,9,10] => 0000100001 => 1000010000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => [11,7,1,2,3,4,5,6,8,9,10] => 0000010001 => 1000001000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10] => 0000000001 => 1000000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,3,1,2,4,5,6,7,8,9] => [10,9,8,7,6,5,4,2,3,1] => 011111111 => 101111111
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,10,1,2,3,4,6,7,8,9] => [5,3,1,10,9,8,7,6,4,2] => 011111111 => 101111111
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,10,1,2,3,4,5,6,7,9] => [10,9,7,5,3,1,8,6,4,2] => 011111111 => 101111111
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [10,3,4,5,6,7,8,9,1,11,2] => [11,2,3,4,5,6,7,8,9,1,10] => 0000000101 => 1000000010
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2,11,4,5,6,7,8,9,10,1,3] => [11,3,4,5,6,7,8,9,10,1,2] => 0000000011 => 1000000001
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2,12,4,5,6,7,8,9,10,11,1,3] => [12,3,4,5,6,7,8,9,10,11,1,2] => 00000000011 => 10000000001
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [2,3,4,5,10,7,1,6,8,9] => [10,9,8,6,7,1,2,3,4,5] => 000001111 => 100000111
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [2,3,4,10,6,1,5,7,8,9] => [10,9,8,7,5,6,1,2,3,4] => 000011111 => 100001111
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,10,5,1,4,6,7,8,9] => [10,9,8,7,6,4,5,1,2,3] => 000111111 => 100011111
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,10,4,1,3,5,6,7,8,9] => [10,9,8,7,6,5,3,4,1,2] => 001111111 => 100111111
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [11,3,4,5,6,7,8,9,10,1,2] => [11,2,3,4,5,6,7,8,9,10,1] => 0000000011 => 1000000001
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [2,3,4,5,6,7,11,9,10,1,8] => [11,8,9,10,1,2,3,4,5,6,7] => 0000000011 => 1000000001
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,12,1] => [12,1,2,3,4,5,6,7,8,9,10,11] => 00000000001 => 10000000000
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,11,8,12,10] => [12,10,8,6,4,2,1,3,5,7,9,11] => 10101010101 => 11010101010
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
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.
Map
rotate back-to-front
Description
The rotation of a binary word, last letter first.
This is the word obtained by moving the last letter to the beginnig.