Identifier
Values
[1,0] => [2,1] => [2,1] => 1 => 1
[1,0,1,0] => [3,1,2] => [2,3,1] => 01 => 0
[1,1,0,0] => [2,3,1] => [3,1,2] => 10 => 1
[1,0,1,0,1,0] => [4,1,2,3] => [2,3,4,1] => 001 => 0
[1,0,1,1,0,0] => [3,1,4,2] => [2,4,1,3] => 010 => 0
[1,1,0,0,1,0] => [2,4,1,3] => [3,1,4,2] => 101 => 1
[1,1,0,1,0,0] => [4,3,1,2] => [3,4,2,1] => 011 => 0
[1,1,1,0,0,0] => [2,3,4,1] => [4,1,2,3] => 100 => 1
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [2,3,4,5,1] => 0001 => 0
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [2,3,5,1,4] => 0010 => 0
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [2,4,1,5,3] => 0101 => 0
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [2,4,5,3,1] => 0011 => 0
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [2,5,1,3,4] => 0100 => 0
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [3,1,4,5,2] => 1001 => 1
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [3,1,5,2,4] => 1010 => 1
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [3,4,2,5,1] => 0101 => 0
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [3,4,5,2,1] => 0011 => 0
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [3,5,2,1,4] => 0110 => 0
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [4,1,2,5,3] => 1001 => 1
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [4,1,5,3,2] => 1011 => 1
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [4,5,2,3,1] => 0101 => 0
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => 1000 => 1
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => 00001 => 0
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [2,3,4,6,1,5] => 00010 => 0
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [2,3,5,1,6,4] => 00101 => 0
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [2,3,5,6,4,1] => 00011 => 0
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [2,3,6,1,4,5] => 00100 => 0
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [2,4,1,5,6,3] => 01001 => 0
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [2,4,1,6,3,5] => 01010 => 0
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [2,4,5,3,6,1] => 00101 => 0
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [2,4,5,6,3,1] => 00011 => 0
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [2,4,6,3,1,5] => 00110 => 0
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [2,5,1,3,6,4] => 01001 => 0
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [2,5,1,6,4,3] => 01011 => 0
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [2,5,6,3,4,1] => 00101 => 0
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [2,6,1,3,4,5] => 01000 => 0
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [3,1,4,5,6,2] => 10001 => 1
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [3,1,4,6,2,5] => 10010 => 1
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [3,1,5,2,6,4] => 10101 => 1
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [3,1,5,6,4,2] => 10011 => 1
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [3,1,6,2,4,5] => 10100 => 1
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => 01001 => 0
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [3,4,2,6,1,5] => 01010 => 0
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => 00101 => 0
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [3,4,5,6,1,2] => 00010 => 0
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [3,4,6,2,1,5] => 00110 => 0
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [3,5,2,1,6,4] => 01101 => 0
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [3,5,2,6,4,1] => 01011 => 0
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [3,5,6,2,4,1] => 00101 => 0
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [3,6,2,1,4,5] => 01100 => 0
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [4,1,2,5,6,3] => 10001 => 1
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [4,1,2,6,3,5] => 10010 => 1
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [4,1,5,3,6,2] => 10101 => 1
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [4,1,5,6,3,2] => 10011 => 1
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [4,1,6,3,2,5] => 10110 => 1
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [4,5,2,3,6,1] => 01001 => 0
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [4,5,2,6,3,1] => 01011 => 0
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => 00111 => 0
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [4,6,2,3,1,5] => 01010 => 0
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [5,1,2,3,6,4] => 10001 => 1
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [5,1,2,6,4,3] => 10011 => 1
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [5,1,6,3,4,2] => 10101 => 1
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [5,6,2,3,4,1] => 01001 => 0
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => 10000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => 000001 => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [2,3,4,5,7,1,6] => 000010 => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [2,3,4,6,1,7,5] => 000101 => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => [2,3,4,6,7,5,1] => 000011 => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [2,3,4,7,1,5,6] => 000100 => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [2,3,5,1,6,7,4] => 001001 => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [2,3,5,1,7,4,6] => 001010 => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => [2,3,5,6,4,7,1] => 000101 => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [2,3,5,6,7,4,1] => 000011 => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => [2,3,5,7,4,1,6] => 000110 => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [2,3,6,1,4,7,5] => 001001 => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => [2,3,6,1,7,5,4] => 001011 => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [2,3,6,7,4,5,1] => 000101 => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [2,3,7,1,4,5,6] => 001000 => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [2,4,1,5,6,7,3] => 010001 => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [2,4,1,5,7,3,6] => 010010 => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [2,4,1,6,3,7,5] => 010101 => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [2,4,1,6,7,5,3] => 010011 => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [2,4,1,7,3,5,6] => 010100 => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => [2,4,5,3,6,7,1] => 001001 => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => [2,4,5,3,7,1,6] => 001010 => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [2,4,5,6,3,7,1] => 000101 => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [2,4,5,6,7,1,3] => 000010 => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [2,4,5,7,3,1,6] => 000110 => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [2,4,6,3,1,7,5] => 001101 => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => [2,4,6,3,7,5,1] => 001011 => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [2,4,6,7,3,5,1] => 000101 => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => [2,4,7,3,1,5,6] => 001100 => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [2,5,1,3,6,7,4] => 010001 => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [2,5,1,3,7,4,6] => 010010 => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [2,5,1,6,4,7,3] => 010101 => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [2,5,1,6,7,4,3] => 010011 => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [2,5,1,7,4,3,6] => 010110 => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [2,5,6,3,4,7,1] => 001001 => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [2,5,6,3,7,4,1] => 001011 => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [2,5,6,7,4,3,1] => 000111 => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => [2,5,7,3,4,1,6] => 001010 => 0
>>> Load all 790 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [2,6,1,3,4,7,5] => 010001 => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [2,6,1,3,7,5,4] => 010011 => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [2,6,1,7,4,5,3] => 010101 => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => [2,6,7,3,4,5,1] => 001001 => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [2,7,1,3,4,5,6] => 010000 => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [3,1,4,5,6,7,2] => 100001 => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [3,1,4,5,7,2,6] => 100010 => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [3,1,4,6,2,7,5] => 100101 => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [3,1,4,6,7,5,2] => 100011 => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [3,1,4,7,2,5,6] => 100100 => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [3,1,5,2,6,7,4] => 101001 => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [3,1,5,2,7,4,6] => 101010 => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [3,1,5,6,4,7,2] => 100101 => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [3,1,5,6,7,4,2] => 100011 => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => [3,1,5,7,4,2,6] => 100110 => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [3,1,6,2,4,7,5] => 101001 => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => [3,1,6,2,7,5,4] => 101011 => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [3,1,6,7,4,5,2] => 100101 => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [3,1,7,2,4,5,6] => 101000 => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => [3,4,2,5,6,7,1] => 010001 => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => [3,4,2,5,7,1,6] => 010010 => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [3,4,2,6,1,7,5] => 010101 => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => [3,4,2,6,7,5,1] => 010011 => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => [3,4,2,7,1,5,6] => 010100 => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => [3,4,5,2,6,7,1] => 001001 => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => [3,4,5,2,7,1,6] => 001010 => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [3,4,5,6,1,7,2] => 000101 => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [3,4,5,6,7,2,1] => 000011 => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [3,4,5,7,1,2,6] => 000100 => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [3,4,6,2,1,7,5] => 001101 => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [3,4,6,2,7,5,1] => 001011 => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [3,4,6,7,1,5,2] => 000101 => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => [3,4,7,2,1,5,6] => 001100 => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [3,5,2,1,6,7,4] => 011001 => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [3,5,2,1,7,4,6] => 011010 => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => [3,5,2,6,4,7,1] => 010101 => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [3,5,2,6,7,4,1] => 010011 => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => [3,5,2,7,4,1,6] => 010110 => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [3,5,6,2,4,7,1] => 001001 => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => [3,5,6,2,7,4,1] => 001011 => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [3,5,6,7,4,1,2] => 000110 => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [3,5,7,2,4,1,6] => 001010 => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [3,6,2,1,4,7,5] => 011001 => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [3,6,2,1,7,5,4] => 011011 => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [3,6,2,7,4,5,1] => 010101 => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [3,6,7,2,4,5,1] => 001001 => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [3,7,2,1,4,5,6] => 011000 => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [4,1,2,5,6,7,3] => 100001 => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [4,1,2,5,7,3,6] => 100010 => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [4,1,2,6,3,7,5] => 100101 => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => [4,1,2,6,7,5,3] => 100011 => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [4,1,2,7,3,5,6] => 100100 => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [4,1,5,3,6,7,2] => 101001 => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => [4,1,5,3,7,2,6] => 101010 => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [4,1,5,6,3,7,2] => 100101 => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [4,1,5,6,7,2,3] => 100010 => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => [4,1,5,7,3,2,6] => 100110 => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => [4,1,6,3,2,7,5] => 101101 => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => [4,1,6,3,7,5,2] => 101011 => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [4,1,6,7,3,5,2] => 100101 => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => [4,1,7,3,2,5,6] => 101100 => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => [4,5,2,3,6,7,1] => 010001 => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [4,5,2,3,7,1,6] => 010010 => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [4,5,2,6,3,7,1] => 010101 => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [4,5,2,6,7,1,3] => 010010 => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [4,5,2,7,3,1,6] => 010110 => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [4,5,6,3,2,7,1] => 001101 => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [4,5,6,3,7,1,2] => 001010 => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => [4,5,6,7,3,1,2] => 000110 => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [4,5,7,3,2,1,6] => 001110 => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => [4,6,2,3,1,7,5] => 010101 => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => [4,6,2,3,7,5,1] => 010011 => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [4,6,2,7,3,5,1] => 010101 => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [4,6,7,3,2,5,1] => 001101 => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => [4,7,2,3,1,5,6] => 010100 => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [5,1,2,3,6,7,4] => 100001 => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [5,1,2,3,7,4,6] => 100010 => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => [5,1,2,6,4,7,3] => 100101 => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => [5,1,2,6,7,4,3] => 100011 => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => [5,1,2,7,4,3,6] => 100110 => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => [5,1,6,3,4,7,2] => 101001 => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [5,1,6,3,7,4,2] => 101011 => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [5,1,6,7,4,3,2] => 100111 => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => [5,1,7,3,4,2,6] => 101010 => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [5,6,2,3,4,7,1] => 010001 => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [5,6,2,3,7,4,1] => 010011 => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [5,6,2,7,4,3,1] => 010111 => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => [5,6,7,3,4,2,1] => 001011 => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [5,7,2,3,4,1,6] => 010010 => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [6,1,2,3,4,7,5] => 100001 => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => [6,1,2,3,7,5,4] => 100011 => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => [6,1,2,7,4,5,3] => 100101 => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => [6,1,7,3,4,5,2] => 101001 => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => [6,7,2,3,4,5,1] => 010001 => 0
[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] => 100000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => 0000001 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [2,3,4,5,6,8,1,7] => 0000010 => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => [2,3,4,5,7,1,8,6] => 0000101 => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,1,2,3,4,7,5,6] => [2,3,4,5,7,8,6,1] => 0000011 => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [2,3,4,5,8,1,6,7] => 0000100 => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => [2,3,4,6,1,7,8,5] => 0001001 => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [2,3,4,6,1,8,5,7] => 0001010 => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,1,2,3,6,4,5,7] => [2,3,4,6,7,5,8,1] => 0000101 => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,1,2,3,7,4,5,6] => [2,3,4,6,7,8,5,1] => 0000011 => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,1,2,3,6,4,8,5] => [2,3,4,6,8,5,1,7] => 0000110 => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [2,3,4,7,1,5,8,6] => 0001001 => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,1,2,3,8,7,4,6] => [2,3,4,7,1,8,6,5] => 0001011 => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,1,2,3,6,7,4,5] => [2,3,4,7,8,5,6,1] => 0000101 => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [2,3,4,8,1,5,6,7] => 0001000 => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => [2,3,5,1,6,7,8,4] => 0010001 => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => [2,3,5,1,6,8,4,7] => 0010010 => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [2,3,5,1,7,4,8,6] => 0010101 => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [2,3,5,1,8,4,6,7] => 0010100 => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,1,2,5,3,4,6,7] => [2,3,5,6,4,7,8,1] => 0001001 => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,1,2,6,3,4,5,7] => [2,3,5,6,7,4,8,1] => 0000101 => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,1,2,8,3,4,5,6] => [2,3,5,6,7,8,1,4] => 0000010 => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [8,1,2,5,3,7,4,6] => [2,3,5,7,4,8,6,1] => 0001011 => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [8,1,2,6,3,7,4,5] => [2,3,5,7,8,4,6,1] => 0000101 => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => [2,3,6,1,4,7,8,5] => 0010001 => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [2,3,6,1,4,8,5,7] => 0010010 => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [4,1,2,8,6,3,5,7] => [2,3,6,1,7,5,8,4] => 0010101 => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [4,1,2,8,7,3,5,6] => [2,3,6,1,7,8,5,4] => 0010011 => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,1,2,7,6,3,8,5] => [2,3,6,1,8,5,4,7] => 0010110 => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,1,2,5,6,3,4,7] => [2,3,6,7,4,5,8,1] => 0001001 => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [8,1,2,5,7,3,4,6] => [2,3,6,7,4,8,5,1] => 0001011 => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [8,1,2,7,6,3,4,5] => [2,3,6,7,8,5,4,1] => 0000111 => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [7,1,2,5,6,3,8,4] => [2,3,6,8,4,5,1,7] => 0001010 => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [2,3,7,1,4,5,8,6] => 0010001 => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,8,7,3,6] => [2,3,7,1,4,8,6,5] => 0010011 => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,1,2,8,6,7,3,5] => [2,3,7,1,8,5,6,4] => 0010101 => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => [2,3,7,8,4,5,6,1] => 0001001 => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [2,3,8,1,4,5,6,7] => 0010000 => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [2,4,1,5,6,7,8,3] => 0100001 => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => [2,4,1,5,6,8,3,7] => 0100010 => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,6,2,4,8,5,7] => [2,4,1,5,7,3,8,6] => 0100101 => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [2,4,1,5,8,3,6,7] => 0100100 => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [2,4,1,6,3,7,8,5] => 0101001 => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [2,4,1,6,3,8,5,7] => 0101010 => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,8,2,6,4,5,7] => [2,4,1,6,7,5,8,3] => 0100101 => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [3,1,8,2,7,4,5,6] => [2,4,1,6,7,8,5,3] => 0100011 => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,1,7,2,6,4,8,5] => [2,4,1,6,8,5,3,7] => 0100110 => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [2,4,1,7,3,5,8,6] => 0101001 => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,5,2,8,7,4,6] => [2,4,1,7,3,8,6,5] => 0101011 => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [2,4,1,8,3,5,6,7] => 0101000 => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,1,4,2,3,5,6,7] => [2,4,5,3,6,7,8,1] => 0010001 => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,1,4,2,3,5,8,6] => [2,4,5,3,6,8,1,7] => 0010010 => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,1,4,2,3,8,5,7] => [2,4,5,3,7,1,8,6] => 0010101 => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [8,1,4,2,3,7,5,6] => [2,4,5,3,7,8,6,1] => 0010011 => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,1,5,2,3,4,6,7] => [2,4,5,6,3,7,8,1] => 0001001 => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,1,5,2,3,4,8,6] => [2,4,5,6,3,8,1,7] => 0001010 => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7] => [2,4,5,6,7,1,8,3] => 0000101 => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,1,7,2,3,4,5,6] => [2,4,5,6,7,8,3,1] => 0000011 => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,1,7,2,3,4,8,5] => [2,4,5,6,8,1,3,7] => 0000100 => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,1,5,2,3,8,4,7] => [2,4,5,7,3,1,8,6] => 0001101 => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [8,1,5,2,3,7,4,6] => [2,4,5,7,3,8,6,1] => 0001011 => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,1,8,2,3,7,4,5] => [2,4,5,7,8,1,6,3] => 0000101 => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,1,5,2,3,7,8,4] => [2,4,5,8,3,1,6,7] => 0001100 => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [5,1,4,2,8,3,6,7] => [2,4,6,3,1,7,8,5] => 0011001 => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,1,4,2,7,3,8,6] => [2,4,6,3,1,8,5,7] => 0011010 => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,1,4,2,6,3,5,7] => [2,4,6,3,7,5,8,1] => 0010101 => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [8,1,4,2,7,3,5,6] => [2,4,6,3,7,8,5,1] => 0010011 => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [7,1,4,2,6,3,8,5] => [2,4,6,3,8,5,1,7] => 0010110 => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,1,5,2,6,3,4,7] => [2,4,6,7,3,5,8,1] => 0001001 => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [8,1,5,2,7,3,4,6] => [2,4,6,7,3,8,5,1] => 0001011 => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [7,1,8,2,6,3,4,5] => [2,4,6,7,8,5,1,3] => 0000110 => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [7,1,5,2,6,3,8,4] => [2,4,6,8,3,5,1,7] => 0001010 => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,4,2,6,8,3,7] => [2,4,7,3,1,5,8,6] => 0011001 => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,1,4,2,8,7,3,6] => [2,4,7,3,1,8,6,5] => 0011011 => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [8,1,4,2,6,7,3,5] => [2,4,7,3,8,5,6,1] => 0010101 => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [8,1,5,2,6,7,3,4] => [2,4,7,8,3,5,6,1] => 0001001 => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [5,1,4,2,6,7,8,3] => [2,4,8,3,1,5,6,7] => 0011000 => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,8,2,5,6,7] => [2,5,1,3,6,7,8,4] => 0100001 => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => [2,5,1,3,6,8,4,7] => 0100010 => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [2,5,1,3,7,4,8,6] => 0100101 => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,4,8,2,7,5,6] => [2,5,1,3,7,8,6,4] => 0100011 => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [2,5,1,3,8,4,6,7] => 0100100 => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,7,5,2,4,8,6] => [2,5,1,6,4,8,3,7] => 0101010 => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,8,6,2,4,5,7] => [2,5,1,6,7,4,8,3] => 0100101 => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,7,8,2,4,5,6] => [2,5,1,6,7,8,3,4] => 0100010 => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,6,5,2,8,4,7] => [2,5,1,7,4,3,8,6] => 0101101 => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,8,5,2,7,4,6] => [2,5,1,7,4,8,6,3] => 0101011 => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,1,4,5,2,3,6,7] => [2,5,6,3,4,7,8,1] => 0010001 => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,1,4,5,2,3,8,6] => [2,5,6,3,4,8,1,7] => 0010010 => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,1,4,6,2,3,5,7] => [2,5,6,3,7,4,8,1] => 0010101 => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,1,4,8,2,3,5,6] => [2,5,6,3,7,8,1,4] => 0010010 => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [7,1,4,6,2,3,8,5] => [2,5,6,3,8,4,1,7] => 0010110 => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,1,6,5,2,3,4,7] => [2,5,6,7,4,3,8,1] => 0001101 => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,1,8,5,2,3,4,6] => [2,5,6,7,4,8,1,3] => 0001010 => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [7,1,8,6,2,3,4,5] => [2,5,6,7,8,4,1,3] => 0000110 => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [7,1,6,5,2,3,8,4] => [2,5,6,8,4,3,1,7] => 0001110 => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [8,1,4,5,2,7,3,6] => [2,5,7,3,4,8,6,1] => 0010011 => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [8,1,4,6,2,7,3,5] => [2,5,7,3,8,4,6,1] => 0010101 => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [8,1,6,5,2,7,3,4] => [2,5,7,8,4,3,6,1] => 0001101 => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [6,1,4,5,2,7,8,3] => [2,5,8,3,4,1,6,7] => 0010100 => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => [2,6,1,3,4,7,8,5] => 0100001 => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,1,4,5,7,2,8,6] => [2,6,1,3,4,8,5,7] => 0100010 => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,1,4,8,7,2,5,6] => [2,6,1,3,7,8,5,4] => 0100011 => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,1,4,7,6,2,8,5] => [2,6,1,3,8,5,4,7] => 0100110 => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,8,5,7,2,4,6] => [2,6,1,7,4,8,5,3] => 0101011 => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,1,7,5,6,2,8,4] => [2,6,1,8,4,5,3,7] => 0101010 => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [8,1,4,5,7,2,3,6] => [2,6,7,3,4,8,5,1] => 0010011 => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [8,1,4,7,6,2,3,5] => [2,6,7,3,8,5,4,1] => 0010111 => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [8,1,7,5,6,2,3,4] => [2,6,7,8,4,5,3,1] => 0001011 => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [7,1,4,5,6,2,8,3] => [2,6,8,3,4,5,1,7] => 0010010 => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [2,7,1,3,4,5,8,6] => 0100001 => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,1,4,5,8,7,2,6] => [2,7,1,3,4,8,6,5] => 0100011 => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,1,4,8,6,7,2,5] => [2,7,1,3,8,5,6,4] => 0100101 => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,8,5,6,7,2,4] => [2,7,1,8,4,5,6,3] => 0101001 => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [8,1,4,5,6,7,2,3] => [2,7,8,3,4,5,6,1] => 0010001 => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [2,8,1,3,4,5,6,7] => 0100000 => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => [3,1,4,5,6,7,8,2] => 1000001 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => [3,1,4,5,6,8,2,7] => 1000010 => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,6,1,3,4,8,5,7] => [3,1,4,5,7,2,8,6] => 1000101 => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,8,1,3,4,7,5,6] => [3,1,4,5,7,8,6,2] => 1000011 => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,6,1,3,4,7,8,5] => [3,1,4,5,8,2,6,7] => 1000100 => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7] => [3,1,4,6,2,7,8,5] => 1001001 => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [3,1,4,6,2,8,5,7] => 1001010 => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,8,1,3,6,4,5,7] => [3,1,4,6,7,5,8,2] => 1000101 => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,8,1,3,7,4,5,6] => [3,1,4,6,7,8,5,2] => 1000011 => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,5,1,3,6,8,4,7] => [3,1,4,7,2,5,8,6] => 1001001 => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,1,3,6,7,8,4] => [3,1,4,8,2,5,6,7] => 1001000 => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => [3,1,5,2,6,7,8,4] => 1010001 => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,7,3,5,8,6] => [3,1,5,2,6,8,4,7] => 1010010 => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [3,1,5,2,7,4,8,6] => 1010101 => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,8,3,7,5,6] => [3,1,5,2,7,8,6,4] => 1010011 => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [3,1,5,2,8,4,6,7] => 1010100 => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,8,1,5,3,4,6,7] => [3,1,5,6,4,7,8,2] => 1001001 => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,8,1,6,3,4,5,7] => [3,1,5,6,7,4,8,2] => 1000101 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,7,1,8,3,4,5,6] => [3,1,5,6,7,8,2,4] => 1000010 => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,8,1,5,3,7,4,6] => [3,1,5,7,4,8,6,2] => 1001011 => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,8,1,6,3,7,4,5] => [3,1,5,7,8,4,6,2] => 1000101 => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,6,1,5,3,7,8,4] => [3,1,5,8,4,2,6,7] => 1001100 => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => [3,1,6,2,4,7,8,5] => 1010001 => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,5,7,3,8,6] => [3,1,6,2,4,8,5,7] => 1010010 => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1,8,6,3,5,7] => [3,1,6,2,7,5,8,4] => 1010101 => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,8,1,5,7,3,4,6] => [3,1,6,7,4,8,5,2] => 1001011 => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1,5,6,8,3,7] => [3,1,7,2,4,5,8,6] => 1010001 => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1,8,6,7,3,5] => [3,1,7,2,8,5,6,4] => 1010101 => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [3,1,8,2,4,5,6,7] => 1010000 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => [3,4,2,5,6,7,8,1] => 0100001 => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,3,1,2,4,5,8,6] => [3,4,2,5,6,8,1,7] => 0100010 => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [8,3,1,2,4,7,5,6] => [3,4,2,5,7,8,6,1] => 0100011 => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,3,1,2,6,4,5,7] => [3,4,2,6,7,5,8,1] => 0100101 => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,3,1,2,6,7,8,4] => [3,4,2,8,1,5,6,7] => 0101000 => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => [3,4,5,2,6,7,8,1] => 0010001 => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [8,4,1,2,3,7,5,6] => [3,4,5,2,7,8,6,1] => 0010011 => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,8,1,2,3,4,6,7] => [3,4,5,6,1,7,8,2] => 0001001 => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [3,4,5,6,1,8,2,7] => 0001010 => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [3,4,5,6,7,2,8,1] => 0000101 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6] => [3,4,5,6,7,8,2,1] => 0000011 => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,6,1,2,3,4,8,5] => [3,4,5,6,8,2,1,7] => 0000110 => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [5,6,1,2,3,8,4,7] => [3,4,5,7,1,2,8,6] => 0001001 => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,8,1,2,3,7,4,6] => [3,4,5,7,1,8,6,2] => 0001011 => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,6,1,2,3,7,4,5] => [3,4,5,7,8,2,6,1] => 0000101 => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,1,2,3,7,8,4] => [3,4,5,8,1,2,6,7] => 0001000 => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,2,8,3,6,7] => [3,4,6,2,1,7,8,5] => 0011001 => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,4,1,2,7,3,8,6] => [3,4,6,2,1,8,5,7] => 0011010 => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,4,1,2,7,3,5,6] => [3,4,6,2,7,8,5,1] => 0010011 => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7,4,1,2,6,3,8,5] => [3,4,6,2,8,5,1,7] => 0010110 => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [5,8,1,2,6,3,4,7] => [3,4,6,7,1,5,8,2] => 0001001 => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,8,1,2,7,3,4,6] => [3,4,6,7,1,8,5,2] => 0001011 => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,1,2,6,3,4,5] => [3,4,6,7,8,5,2,1] => 0000111 => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,7,1,2,6,3,8,4] => [3,4,6,8,1,5,2,7] => 0001010 => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [5,4,1,2,6,8,3,7] => [3,4,7,2,1,5,8,6] => 0011001 => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,4,1,2,8,7,3,6] => [3,4,7,2,1,8,6,5] => 0011011 => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8,4,1,2,6,7,3,5] => [3,4,7,2,8,5,6,1] => 0010101 => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,8,1,2,6,7,3,4] => [3,4,7,8,1,5,6,2] => 0001001 => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,4,1,2,6,7,8,3] => [3,4,8,2,1,5,6,7] => 0011000 => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,3,1,8,2,5,6,7] => [3,5,2,1,6,7,8,4] => 0110001 => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,3,1,7,2,5,8,6] => [3,5,2,1,6,8,4,7] => 0110010 => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3,1,8,2,7,5,6] => [3,5,2,1,7,8,6,4] => 0110011 => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,3,1,5,2,4,6,7] => [3,5,2,6,4,7,8,1] => 0101001 => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,3,1,5,2,4,8,6] => [3,5,2,6,4,8,1,7] => 0101010 => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,3,1,6,2,4,5,7] => [3,5,2,6,7,4,8,1] => 0100101 => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,3,1,8,2,4,5,6] => [3,5,2,6,7,8,1,4] => 0100010 => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7,3,1,6,2,4,8,5] => [3,5,2,6,8,4,1,7] => 0100110 => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,1,5,2,8,4,7] => [3,5,2,7,4,1,8,6] => 0101101 => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8,3,1,5,2,7,4,6] => [3,5,2,7,4,8,6,1] => 0101011 => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8,3,1,6,2,7,4,5] => [3,5,2,7,8,4,6,1] => 0100101 => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [6,3,1,5,2,7,8,4] => [3,5,2,8,4,1,6,7] => 0101100 => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,4,1,5,2,3,6,7] => [3,5,6,2,4,7,8,1] => 0010001 => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,4,1,5,2,3,8,6] => [3,5,6,2,4,8,1,7] => 0010010 => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,4,1,6,2,3,5,7] => [3,5,6,2,7,4,8,1] => 0010101 => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,4,1,8,2,3,5,6] => [3,5,6,2,7,8,1,4] => 0010010 => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7,4,1,6,2,3,8,5] => [3,5,6,2,8,4,1,7] => 0010110 => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,8,1,5,2,3,4,7] => [3,5,6,7,4,1,8,2] => 0001101 => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8,7,1,5,2,3,4,6] => [3,5,6,7,4,8,2,1] => 0001011 => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8,7,1,6,2,3,4,5] => [3,5,6,7,8,4,2,1] => 0000111 => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [6,7,1,5,2,3,8,4] => [3,5,6,8,4,1,2,7] => 0001100 => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,4,1,5,2,8,3,7] => [3,5,7,2,4,1,8,6] => 0010101 => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8,4,1,5,2,7,3,6] => [3,5,7,2,4,8,6,1] => 0010011 => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8,4,1,6,2,7,3,5] => [3,5,7,2,8,4,6,1] => 0010101 => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [6,8,1,5,2,7,3,4] => [3,5,7,8,4,1,6,2] => 0001101 => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [6,4,1,5,2,7,8,3] => [3,5,8,2,4,1,6,7] => 0010100 => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [4,3,1,5,8,2,6,7] => [3,6,2,1,4,7,8,5] => 0110001 => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [4,3,1,5,7,2,8,6] => [3,6,2,1,4,8,5,7] => 0110010 => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [4,3,1,8,6,2,5,7] => [3,6,2,1,7,5,8,4] => 0110101 => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [4,3,1,8,7,2,5,6] => [3,6,2,1,7,8,5,4] => 0110011 => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,3,1,7,6,2,8,5] => [3,6,2,1,8,5,4,7] => 0110110 => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8,3,1,5,7,2,4,6] => [3,6,2,7,4,8,5,1] => 0101011 => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8,3,1,7,6,2,4,5] => [3,6,2,7,8,5,4,1] => 0100111 => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7,3,1,5,6,2,8,4] => [3,6,2,8,4,5,1,7] => 0101010 => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,1,5,6,2,3,7] => [3,6,7,2,4,5,8,1] => 0010001 => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8,4,1,5,7,2,3,6] => [3,6,7,2,4,8,5,1] => 0010011 => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8,4,1,7,6,2,3,5] => [3,6,7,2,8,5,4,1] => 0010111 => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [3,6,7,8,4,5,1,2] => 0001010 => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7,4,1,5,6,2,8,3] => [3,6,8,2,4,5,1,7] => 0010010 => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [4,3,1,5,6,8,2,7] => [3,7,2,1,4,5,8,6] => 0110001 => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [4,3,1,5,8,7,2,6] => [3,7,2,1,4,8,6,5] => 0110011 => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,3,1,8,6,7,2,5] => [3,7,2,1,8,5,6,4] => 0110101 => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8,3,1,5,6,7,2,4] => [3,7,2,8,4,5,6,1] => 0101001 => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8,4,1,5,6,7,2,3] => [3,7,8,2,4,5,6,1] => 0010001 => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [3,8,2,1,4,5,6,7] => 0110000 => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => [4,1,2,5,6,7,8,3] => 1000001 => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,3,7,1,4,5,8,6] => [4,1,2,5,6,8,3,7] => 1000010 => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7] => [4,1,2,5,7,3,8,6] => 1000101 => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => [4,1,2,5,8,3,6,7] => 1000100 => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => [4,1,2,6,3,7,8,5] => 1001001 => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [4,1,2,6,3,8,5,7] => 1001010 => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,3,8,1,7,4,5,6] => [4,1,2,6,7,8,5,3] => 1000011 => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,3,7,1,6,4,8,5] => [4,1,2,6,8,5,3,7] => 1000110 => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [4,1,2,7,3,5,8,6] => 1001001 => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,3,5,1,8,7,4,6] => [4,1,2,7,3,8,6,5] => 1001011 => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,3,8,1,6,7,4,5] => [4,1,2,7,8,5,6,3] => 1000101 => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [4,1,2,8,3,5,6,7] => 1001000 => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,8,4,1,3,5,6,7] => [4,1,5,3,6,7,8,2] => 1010001 => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,7,4,1,3,5,8,6] => [4,1,5,3,6,8,2,7] => 1010010 => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,6,4,1,3,8,5,7] => [4,1,5,3,7,2,8,6] => 1010101 => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,7,5,1,3,4,8,6] => [4,1,5,6,3,8,2,7] => 1001010 => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,8,1,3,4,5,7] => [4,1,5,6,7,2,8,3] => 1000101 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,8,7,1,3,4,5,6] => [4,1,5,6,7,8,3,2] => 1000011 => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => [4,1,5,6,8,2,3,7] => 1000100 => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,6,5,1,3,8,4,7] => [4,1,5,7,3,2,8,6] => 1001101 => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,8,5,1,3,7,4,6] => [4,1,5,7,3,8,6,2] => 1001011 => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,6,8,1,3,7,4,5] => [4,1,5,7,8,2,6,3] => 1000101 => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,6,5,1,3,7,8,4] => [4,1,5,8,3,2,6,7] => 1001100 => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,5,4,1,8,3,6,7] => [4,1,6,3,2,7,8,5] => 1011001 => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,8,4,1,6,3,5,7] => [4,1,6,3,7,5,8,2] => 1010101 => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,8,4,1,7,3,5,6] => [4,1,6,3,7,8,5,2] => 1010011 => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,7,4,1,6,3,8,5] => [4,1,6,3,8,5,2,7] => 1010110 => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,8,5,1,7,3,4,6] => [4,1,6,7,3,8,5,2] => 1001011 => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,7,8,1,6,3,4,5] => [4,1,6,7,8,5,2,3] => 1000110 => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,7,5,1,6,3,8,4] => [4,1,6,8,3,5,2,7] => 1001010 => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,5,4,1,6,8,3,7] => [4,1,7,3,2,5,8,6] => 1011001 => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,5,4,1,8,7,3,6] => [4,1,7,3,2,8,6,5] => 1011011 => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,8,4,1,6,7,3,5] => [4,1,7,3,8,5,6,2] => 1010101 => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,8,5,1,6,7,3,4] => [4,1,7,8,3,5,6,2] => 1001001 => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,5,4,1,6,7,8,3] => [4,1,8,3,2,5,6,7] => 1011000 => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,3,4,1,2,5,6,7] => [4,5,2,3,6,7,8,1] => 0100001 => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,3,4,1,2,8,5,7] => [4,5,2,3,7,1,8,6] => 0100101 => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,3,4,1,2,7,8,5] => [4,5,2,3,8,1,6,7] => 0100100 => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,3,5,1,2,4,6,7] => [4,5,2,6,3,7,8,1] => 0101001 => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,3,5,1,2,4,8,6] => [4,5,2,6,3,8,1,7] => 0101010 => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,3,8,1,2,4,5,7] => [4,5,2,6,7,1,8,3] => 0100101 => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,3,7,1,2,4,5,6] => [4,5,2,6,7,8,3,1] => 0100011 => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,3,7,1,2,4,8,5] => [4,5,2,6,8,1,3,7] => 0100100 => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,5,1,2,8,4,7] => [4,5,2,7,3,1,8,6] => 0101101 => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8,3,5,1,2,7,4,6] => [4,5,2,7,3,8,6,1] => 0101011 => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,3,8,1,2,7,4,5] => [4,5,2,7,8,1,6,3] => 0100101 => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [6,3,5,1,2,7,8,4] => [4,5,2,8,3,1,6,7] => 0101100 => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,5,4,1,2,3,6,7] => [4,5,6,3,2,7,8,1] => 0011001 => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,5,4,1,2,3,8,6] => [4,5,6,3,2,8,1,7] => 0011010 => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,8,4,1,2,3,5,7] => [4,5,6,3,7,1,8,2] => 0010101 => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,4,1,2,3,5,6] => [4,5,6,3,7,8,2,1] => 0010011 => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,1,2,3,8,5] => [4,5,6,3,8,1,2,7] => 0010100 => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,8,5,1,2,3,4,7] => [4,5,6,7,3,1,8,2] => 0001101 => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8,7,5,1,2,3,4,6] => [4,5,6,7,3,8,2,1] => 0001011 => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,7,8,1,2,3,4,5] => [4,5,6,7,8,1,2,3] => 0000100 => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,1,2,3,8,4] => [4,5,6,8,3,1,2,7] => 0001100 => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,4,1,2,7,3,6] => [4,5,7,3,2,8,6,1] => 0011011 => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,8,4,1,2,7,3,5] => [4,5,7,3,8,1,6,2] => 0010101 => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [6,8,5,1,2,7,3,4] => [4,5,7,8,3,1,6,2] => 0001101 => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [6,5,4,1,2,7,8,3] => [4,5,8,3,2,1,6,7] => 0011100 => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,3,4,1,6,2,5,7] => [4,6,2,3,7,5,8,1] => 0100101 => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8,3,4,1,7,2,5,6] => [4,6,2,3,7,8,5,1] => 0100011 => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7,3,4,1,6,2,8,5] => [4,6,2,3,8,5,1,7] => 0100110 => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8,3,5,1,7,2,4,6] => [4,6,2,7,3,8,5,1] => 0101011 => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,3,8,1,6,2,4,5] => [4,6,2,7,8,5,1,3] => 0100110 => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,3,5,1,6,2,8,4] => [4,6,2,8,3,5,1,7] => 0101010 => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,5,4,1,6,2,3,7] => [4,6,7,3,2,5,8,1] => 0011001 => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8,5,4,1,7,2,3,6] => [4,6,7,3,2,8,5,1] => 0011011 => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,8,4,1,6,2,3,5] => [4,6,7,3,8,5,1,2] => 0010110 => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,8,5,1,6,2,3,4] => [4,6,7,8,3,5,1,2] => 0001010 => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,5,4,1,6,2,8,3] => [4,6,8,3,2,5,1,7] => 0011010 => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [5,3,4,1,6,8,2,7] => [4,7,2,3,1,5,8,6] => 0101001 => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,3,4,1,8,7,2,6] => [4,7,2,3,1,8,6,5] => 0101011 => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => [4,7,2,3,8,5,6,1] => 0100101 => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8,3,5,1,6,7,2,4] => [4,7,2,8,3,5,6,1] => 0101001 => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8,5,4,1,6,7,2,3] => [4,7,8,3,2,5,6,1] => 0011001 => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [5,3,4,1,6,7,8,2] => [4,8,2,3,1,5,6,7] => 0101000 => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => [5,1,2,3,6,7,8,4] => 1000001 => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,4,7,1,5,8,6] => [5,1,2,3,6,8,4,7] => 1000010 => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => [5,1,2,3,7,4,8,6] => 1000101 => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,4,8,1,7,5,6] => [5,1,2,3,7,8,6,4] => 1000011 => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [5,1,2,3,8,4,6,7] => 1000100 => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,8,5,1,4,6,7] => [5,1,2,6,4,7,8,3] => 1001001 => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,7,5,1,4,8,6] => [5,1,2,6,4,8,3,7] => 1001010 => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,8,6,1,4,5,7] => [5,1,2,6,7,4,8,3] => 1000101 => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,7,8,1,4,5,6] => [5,1,2,6,7,8,3,4] => 1000010 => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,7,6,1,4,8,5] => [5,1,2,6,8,4,3,7] => 1000110 => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,8,5,1,7,4,6] => [5,1,2,7,4,8,6,3] => 1001011 => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,8,6,1,7,4,5] => [5,1,2,7,8,4,6,3] => 1000101 => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,6,5,1,7,8,4] => [5,1,2,8,4,3,6,7] => 1001100 => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,8,4,5,1,3,6,7] => [5,1,6,3,4,7,8,2] => 1010001 => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,4,5,1,3,8,6] => [5,1,6,3,4,8,2,7] => 1010010 => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,8,4,6,1,3,5,7] => [5,1,6,3,7,4,8,2] => 1010101 => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,7,4,8,1,3,5,6] => [5,1,6,3,7,8,2,4] => 1010010 => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,7,4,6,1,3,8,5] => [5,1,6,3,8,4,2,7] => 1010110 => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,8,6,5,1,3,4,7] => [5,1,6,7,4,3,8,2] => 1001101 => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,8,5,1,3,4,6] => [5,1,6,7,4,8,2,3] => 1001010 => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7,8,6,1,3,4,5] => [5,1,6,7,8,4,2,3] => 1000110 => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,7,6,5,1,3,8,4] => [5,1,6,8,4,3,2,7] => 1001110 => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,6,4,5,1,8,3,7] => [5,1,7,3,4,2,8,6] => 1010101 => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [5,1,7,3,4,8,6,2] => 1010011 => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,6,1,7,3,5] => [5,1,7,3,8,4,6,2] => 1010101 => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,6,5,1,7,3,4] => [5,1,7,8,4,3,6,2] => 1001101 => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,6,4,5,1,7,8,3] => [5,1,8,3,4,2,6,7] => 1010100 => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,3,4,8,1,2,5,6] => [5,6,2,3,7,8,1,4] => 0100010 => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7,3,4,6,1,2,8,5] => [5,6,2,3,8,4,1,7] => 0100110 => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,3,6,5,1,2,4,7] => [5,6,2,7,4,3,8,1] => 0101101 => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,3,8,5,1,2,4,6] => [5,6,2,7,4,8,1,3] => 0101010 => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,8,6,1,2,4,5] => [5,6,2,7,8,4,1,3] => 0100110 => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,6,5,1,2,8,4] => [5,6,2,8,4,3,1,7] => 0101110 => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,6,4,5,1,2,3,7] => [5,6,7,3,4,2,8,1] => 0010101 => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,8,4,5,1,2,3,6] => [5,6,7,3,4,8,1,2] => 0010010 => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,8,4,6,1,2,3,5] => [5,6,7,3,8,4,1,2] => 0010110 => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,6,5,1,2,3,4] => [5,6,7,8,4,3,1,2] => 0001110 => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,6,4,5,1,2,8,3] => [5,6,8,3,4,2,1,7] => 0010110 => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,4,5,1,8,2,7] => [5,7,2,3,4,1,8,6] => 0100101 => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8,3,4,5,1,7,2,6] => [5,7,2,3,4,8,6,1] => 0100011 => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8,3,4,6,1,7,2,5] => [5,7,2,3,8,4,6,1] => 0100101 => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8,3,6,5,1,7,2,4] => [5,7,2,8,4,3,6,1] => 0101101 => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8,6,4,5,1,7,2,3] => [5,7,8,3,4,2,6,1] => 0010101 => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [6,3,4,5,1,7,8,2] => [5,8,2,3,4,1,6,7] => 0100100 => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7] => [6,1,2,3,4,7,8,5] => 1000001 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [6,1,2,3,4,8,5,7] => 1000010 => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,3,4,8,6,1,5,7] => [6,1,2,3,7,5,8,4] => 1000101 => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,4,8,7,1,5,6] => [6,1,2,3,7,8,5,4] => 1000011 => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,4,7,6,1,8,5] => [6,1,2,3,8,5,4,7] => 1000110 => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,3,8,5,6,1,4,7] => [6,1,2,7,4,5,8,3] => 1001001 => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,8,5,7,1,4,6] => [6,1,2,7,4,8,5,3] => 1001011 => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,8,7,6,1,4,5] => [6,1,2,7,8,5,4,3] => 1000111 => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,7,5,6,1,8,4] => [6,1,2,8,4,5,3,7] => 1001010 => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,8,4,5,6,1,3,7] => [6,1,7,3,4,5,8,2] => 1010001 => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,8,4,5,7,1,3,6] => [6,1,7,3,4,8,5,2] => 1010011 => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,4,7,6,1,3,5] => [6,1,7,3,8,5,4,2] => 1010111 => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [6,1,7,8,4,5,3,2] => 1001011 => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,7,4,5,6,1,8,3] => [6,1,8,3,4,5,2,7] => 1010010 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [6,7,2,3,4,5,8,1] => 0100001 => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8,3,4,5,7,1,2,6] => [6,7,2,3,4,8,5,1] => 0100011 => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8,3,4,7,6,1,2,5] => [6,7,2,3,8,5,4,1] => 0100111 => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8,3,7,5,6,1,2,4] => [6,7,2,8,4,5,3,1] => 0101011 => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,7,4,5,6,1,2,3] => [6,7,8,3,4,5,2,1] => 0010011 => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,3,4,5,6,1,8,2] => [6,8,2,3,4,5,1,7] => 0100010 => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => [7,1,2,3,4,5,8,6] => 1000001 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,4,5,8,7,1,6] => [7,1,2,3,4,8,6,5] => 1000011 => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,8,6,7,1,5] => [7,1,2,3,8,5,6,4] => 1000101 => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,8,5,6,7,1,4] => [7,1,2,8,4,5,6,3] => 1001001 => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,4,5,6,7,1,3] => [7,1,8,3,4,5,6,2] => 1010001 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8,3,4,5,6,7,1,2] => [7,8,2,3,4,5,6,1] => 0100001 => 0
[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] => 1000000 => 1
[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] => [2,3,4,5,6,7,8,9,1] => 00000001 => 0
[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] => [2,3,4,5,6,7,9,1,8] => 00000010 => 0
[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] => [2,3,4,5,6,8,1,9,7] => 00000101 => 0
[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] => [2,3,4,5,6,8,9,7,1] => 00000011 => 0
[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] => [2,3,4,5,6,9,1,7,8] => 00000100 => 0
[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] => [2,3,4,5,7,1,8,9,6] => 00001001 => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [9,1,2,3,4,7,5,6,8] => [2,3,4,5,7,8,6,9,1] => 00000101 => 0
[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] => [2,3,4,5,7,8,9,6,1] => 00000011 => 0
[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] => [2,3,4,5,8,1,6,9,7] => 00001001 => 0
[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] => [2,3,4,5,8,1,9,7,6] => 00001011 => 0
[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] => [2,3,4,5,8,9,6,7,1] => 00000101 => 0
[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] => [2,3,4,5,9,1,6,7,8] => 00001000 => 0
[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] => [2,3,4,6,1,7,8,9,5] => 00010001 => 0
[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] => [2,3,4,6,7,5,8,9,1] => 00001001 => 0
[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] => [2,3,4,6,7,8,9,1,5] => 00000010 => 0
[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] => [2,3,4,7,1,8,9,6,5] => 00010011 => 0
[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] => [2,3,4,7,8,5,9,6,1] => 00001011 => 0
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [9,1,2,3,8,7,4,5,6] => [2,3,4,7,8,9,6,5,1] => 00000111 => 0
[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] => [2,3,4,8,1,5,9,7,6] => 00010011 => 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,6,7,8,9,4] => [2,3,4,9,1,5,6,7,8] => 00010000 => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [4,1,2,9,3,5,6,7,8] => [2,3,5,1,6,7,8,9,4] => 00100001 => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [4,1,2,8,3,5,6,9,7] => [2,3,5,1,6,7,9,4,8] => 00100010 => 0
[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] => [2,3,5,6,4,7,8,9,1] => 00010001 => 0
[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] => [2,3,5,6,7,8,9,4,1] => 00000011 => 0
[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] => [2,3,6,1,7,8,9,4,5] => 00100010 => 0
[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] => [2,3,6,7,4,8,9,1,5] => 00010010 => 0
[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] => [2,3,7,1,4,8,9,6,5] => 00100011 => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [4,1,2,5,6,7,9,3,8] => [2,3,8,1,4,5,6,9,7] => 00100001 => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,3] => [2,3,9,1,4,5,6,7,8] => 00100000 => 0
[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] => [2,4,1,5,6,7,8,9,3] => 01000001 => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,8,2,4,5,6,9,7] => [2,4,1,5,6,7,9,3,8] => 01000010 => 0
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,6,2,4,7,8,9,5] => [2,4,1,5,9,3,6,7,8] => 01001000 => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,9,6,8] => [2,4,1,6,3,8,5,9,7] => 01010101 => 0
[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] => [2,4,5,6,7,8,9,3,1] => 00000011 => 0
[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] => [2,5,1,3,6,7,8,9,4] => 01000001 => 0
[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] => [2,5,1,6,7,8,9,4,3] => 01000011 => 0
[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] => [2,5,6,3,7,8,9,4,1] => 00100011 => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,1,8,9,2,3,4,5,6] => [2,5,6,7,8,9,1,3,4] => 00000100 => 0
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,1,4,5,7,2,8,9,6] => [2,6,1,3,4,9,5,7,8] => 01000100 => 0
[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] => [2,6,1,3,7,8,9,4,5] => 01000010 => 0
[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] => [2,6,9,3,4,5,1,7,8] => 00100100 => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,4,5,6,9,2,7,8] => [2,7,1,3,4,5,8,9,6] => 01000001 => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,4,5,6,8,2,9,7] => [2,7,1,3,4,5,9,6,8] => 01000010 => 0
[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] => [2,7,8,9,4,5,6,3,1] => 00010011 => 0
[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] => [2,7,9,3,4,5,6,1,8] => 00100010 => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,9,2,8] => [2,8,1,3,4,5,6,9,7] => 01000001 => 0
[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] => [2,8,1,3,9,5,6,7,4] => 01001001 => 0
[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] => [2,8,1,9,4,5,6,7,3] => 01010001 => 0
[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] => [2,8,9,3,4,5,6,7,1] => 00100001 => 0
[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] => [2,9,1,3,4,5,6,7,8] => 01000000 => 0
[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] => [3,1,4,5,6,7,8,9,2] => 10000001 => 1
[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] => [3,1,4,5,6,7,9,2,8] => 10000010 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,7,1,3,4,5,9,6,8] => [3,1,4,5,6,8,2,9,7] => 10000101 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,7,1,3,4,5,8,9,6] => [3,1,4,5,6,9,2,7,8] => 10000100 => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,5,1,3,6,7,8,9,4] => [3,1,4,9,2,5,6,7,8] => 10010000 => 1
[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] => [3,1,5,2,7,4,9,6,8] => 10101010 => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1,5,6,7,9,3,8] => [3,1,8,2,4,5,6,9,7] => 10100001 => 1
[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] => [3,1,9,2,4,5,6,7,8] => 10100000 => 1
[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] => [3,4,2,5,6,7,8,9,1] => 01000001 => 0
[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] => [3,4,5,6,1,7,8,9,2] => 00010001 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => [3,4,5,6,7,8,2,9,1] => 00000101 => 0
[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] => [3,4,5,6,7,8,9,1,2] => 00000010 => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [9,4,1,6,2,8,3,5,7] => [3,5,7,2,8,4,9,6,1] => 00101011 => 0
[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] => [3,9,2,1,4,5,6,7,8] => 01100000 => 0
[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] => [4,1,2,5,6,7,8,9,3] => 10000001 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,8,1,4,5,6,9,7] => [4,1,2,5,6,7,9,3,8] => 10000010 => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,6,1,4,7,8,9,5] => [4,1,2,5,9,3,6,7,8] => 10001000 => 1
[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] => [4,1,2,8,3,5,6,9,7] => 10010001 => 1
[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] => [4,1,5,3,6,7,8,9,2] => 10100001 => 1
[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] => [4,1,5,6,7,8,9,3,2] => 10000011 => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,9,4,1,6,3,8,5,7] => [4,1,6,3,8,5,9,7,2] => 10101011 => 1
[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] => [4,5,2,3,6,7,8,9,1] => 01000001 => 0
[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] => [4,5,2,6,7,8,9,3,1] => 01000011 => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9,8,4,1,2,3,5,6,7] => [4,5,6,3,7,8,9,2,1] => 00100011 => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [6,7,9,1,2,3,4,5,8] => [4,5,6,7,8,1,2,9,3] => 00001001 => 0
[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] => [4,5,6,7,8,9,2,3,1] => 00000101 => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,8,1,2,3,4,9,5] => [4,5,6,7,9,1,2,3,8] => 00001000 => 0
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [9,8,5,1,7,2,3,4,6] => [4,6,7,8,3,9,5,2,1] => 00010111 => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [9,5,4,1,8,7,2,3,6] => [4,7,8,3,2,9,6,5,1] => 00110111 => 0
[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] => [5,1,2,3,6,7,8,9,4] => 10000001 => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [2,3,4,6,1,7,9,5,8] => [5,1,2,3,8,4,6,9,7] => 10001001 => 1
[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] => [5,1,2,6,4,7,8,9,3] => 10010001 => 1
[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] => [5,1,2,6,7,8,9,4,3] => 10000011 => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,7,8,9,1,3,4,5,6] => [5,1,6,7,8,9,2,3,4] => 10000100 => 1
[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] => [5,8,2,3,4,1,6,9,7] => 01001001 => 0
[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] => [6,1,2,3,4,7,8,9,5] => 10000001 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [2,3,4,5,8,1,6,9,7] => [6,1,2,3,4,7,9,5,8] => 10000010 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [2,3,4,5,7,1,9,6,8] => [6,1,2,3,4,8,5,9,7] => 10000101 => 1
[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] => [6,1,2,3,4,9,5,7,8] => 10000100 => 1
[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] => [6,1,2,3,7,5,8,9,4] => 10001001 => 1
[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] => [6,1,2,7,4,5,8,9,3] => 10010001 => 1
[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] => [6,1,2,7,4,5,9,3,8] => 10010010 => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [2,3,9,5,6,1,8,4,7] => [6,1,2,8,4,5,9,7,3] => 10010011 => 1
[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] => [6,7,8,3,4,5,2,9,1] => 00100101 => 0
[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] => [6,8,2,3,4,5,1,9,7] => 01000101 => 0
[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] => [7,1,2,3,4,5,8,9,6] => 10000001 => 1
[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] => [7,1,2,3,4,5,9,6,8] => 10000010 => 1
[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] => [7,1,2,3,4,8,6,9,5] => 10000101 => 1
[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] => [7,1,2,3,8,5,6,9,4] => 10001001 => 1
[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] => [7,1,2,8,4,5,6,9,3] => 10010001 => 1
[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] => [7,1,8,3,4,5,6,9,2] => 10100001 => 1
[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] => [7,1,9,3,4,5,6,2,8] => 10100010 => 1
[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] => [7,8,2,3,4,5,6,9,1] => 01000001 => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [9,3,4,5,6,8,1,2,7] => [7,8,2,3,4,5,9,6,1] => 01000011 => 0
[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] => [8,1,2,3,4,5,6,9,7] => 10000001 => 1
[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] => [8,1,2,3,4,5,9,7,6] => 10000011 => 1
[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] => [8,1,2,3,4,9,6,7,5] => 10000101 => 1
[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] => [8,1,2,3,9,5,6,7,4] => 10001001 => 1
[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] => [8,9,2,3,4,5,6,7,1] => 01000001 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => 10000000 => 1
[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] => [9,1,2,3,4,5,6,7,10,8] => 100000001 => 1
[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] => [2,10,1,3,4,5,6,7,8,9] => 010000000 => 0
[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] => [8,9,2,3,4,5,6,7,10,1] => 010000001 => 0
[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] => [2,9,10,3,4,5,6,7,8,1] => 001000001 => 0
[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] => [2,11,1,3,4,5,6,7,8,9,10] => 0100000000 => 0
[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] => [9,10,2,3,4,5,6,7,8,11,1] => 0100000001 => 0
[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] => [8,1,9,3,4,5,6,7,10,2] => 101000001 => 1
[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] => [7,9,2,3,4,5,6,1,10,8] => 010000101 => 0
[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] => [2,9,1,10,4,5,6,7,8,3] => 010100001 => 0
[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] => [2,8,10,3,4,5,6,7,1,9] => 001000010 => 0
[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] => [2,10,11,3,4,5,6,7,8,9,1] => 0010000001 => 0
[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] => [2,12,1,3,4,5,6,7,8,9,10,11] => 01000000000 => 0
[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] => [8,1,2,3,4,5,9,7,10,6] => 100000101 => 1
[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] => [8,1,2,3,4,5,6,9,10,7] => 100000001 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,10,2,9] => [2,9,1,3,4,5,6,7,10,8] => 010000001 => 0
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,10,3] => [2,3,10,1,4,5,6,7,8,9] => 001000000 => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,11,2,10] => [2,10,1,3,4,5,6,7,8,11,9] => 0100000001 => 0
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,10,11,3] => [2,3,11,1,4,5,6,7,8,9,10] => 0010000000 => 0
[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] => [3,4,5,6,7,8,9,10,2,1] => 000000011 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,10,1,2,3,4,5,9,6,7] => [3,4,5,6,7,9,10,1,8,2] => 000000101 => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,10,1,2,3,4,8,5,6,7] => [3,4,5,6,8,9,10,7,1,2] => 000000110 => 0
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,10,1,2,3,9,8,4,6,7] => [3,4,5,8,1,9,10,7,6,2] => 000100111 => 0
[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] => [3,5,2,7,4,9,6,10,8,1] => 010101011 => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,7,1,9,2,3,4,5,6,8] => [3,5,6,7,8,9,2,10,4,1] => 000001011 => 0
[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] => [4,1,5,6,7,8,9,10,2,3] => 100000010 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,7,9,1,2,3,4,5,6,8] => [4,5,6,7,8,9,2,10,3,1] => 000001011 => 0
[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] => [4,5,6,7,8,9,10,3,2,1] => 000000111 => 0
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,10,5,1,7,4,9,6,8] => [5,1,2,7,4,9,6,10,8,3] => 100101011 => 1
[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] => [5,6,7,8,9,10,1,2,3,4] => 000001000 => 0
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => [2,3,10,5,6,1,8,9,4,7] => [6,1,2,9,4,5,10,7,8,3] => 100100101 => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,9,4,5,6,7,8,1,10,3] => [8,1,10,3,4,5,6,7,2,9] => 101000010 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [10,3,4,5,6,7,9,1,2,8] => [8,9,2,3,4,5,6,10,7,1] => 010000011 => 0
[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] => [9,1,2,3,4,5,6,10,8,7] => 100000011 => 1
[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] => [9,1,2,3,4,5,10,7,8,6] => 100000101 => 1
[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] => [9,1,2,3,4,10,6,7,8,5] => 100001001 => 1
[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] => 100000000 => 1
[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] => [2,3,4,5,6,7,8,9,10,1] => 000000001 => 0
[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] => [2,3,4,5,6,7,8,10,1,9] => 000000010 => 0
[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] => [2,3,4,5,6,7,9,10,8,1] => 000000011 => 0
[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] => [2,3,4,5,6,8,9,10,7,1] => 000000011 => 0
[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] => [2,3,4,5,7,8,9,10,1,6] => 000000010 => 0
[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] => [2,3,4,6,7,8,9,10,5,1] => 000000011 => 0
[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] => [2,3,5,6,7,8,9,10,4,1] => 000000011 => 0
[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] => [2,4,5,6,7,8,9,10,1,3] => 000000010 => 0
[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] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000001 => 0
[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] => [2,3,4,5,6,7,8,9,11,1,10] => 0000000010 => 0
[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] => [2,3,4,5,6,7,10,1,8,9] => 000000100 => 0
[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] => [2,3,4,5,6,7,8,10,11,9,1] => 0000000011 => 0
[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] => [2,3,4,5,6,9,1,10,8,7] => 000001011 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [11,1,2,3,4,5,6,10,7,8,9] => [2,3,4,5,6,7,9,10,11,8,1] => 0000000011 => 0
[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] => [2,3,4,5,8,1,9,10,7,6] => 000010011 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [10,1,2,3,4,5,11,6,7,8,9] => [2,3,4,5,6,8,9,10,11,1,7] => 0000000010 => 0
[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] => [2,3,4,7,1,8,9,10,5,6] => 000100010 => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [11,1,2,3,4,10,5,6,7,8,9] => [2,3,4,5,7,8,9,10,11,6,1] => 0000000011 => 0
[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] => [2,3,6,1,7,8,9,10,5,4] => 001000011 => 0
[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] => [2,3,4,6,7,8,9,10,11,5,1] => 0000000011 => 0
[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] => [2,5,1,6,7,8,9,10,4,3] => 010000011 => 0
[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] => [2,3,5,6,7,8,9,10,11,1,4] => 0000000010 => 0
[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] => [2,4,5,6,7,8,9,10,11,3,1] => 0000000011 => 0
[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] => [3,4,5,6,7,8,9,10,11,2,1] => 0000000011 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [2,3,4,5,6,7,8,9,10,11,12,1] => 00000000001 => 0
[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] => [2,3,4,5,6,7,8,9,10,12,1,11] => 00000000010 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [9,1,2,3,4,5,6,7,10,11,8] => [2,3,4,5,6,7,8,11,1,9,10] => 0000000100 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,1,2,3,4,5,8,9,10,6] => [2,3,4,5,6,10,1,7,8,9] => 000001000 => 0
[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] => [3,4,5,6,7,8,9,10,11,12,1,2] => 00000000010 => 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [10,1,2,3,4,9,8,5,6,7] => [2,3,4,5,8,9,10,7,6,1] => 000000111 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [8,1,2,3,4,5,6,9,10,11,7] => [2,3,4,5,6,7,11,1,8,9,10] => 0000001000 => 0
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,1,2,3,4,7,8,9,10,5] => [2,3,4,5,10,1,6,7,8,9] => 000010000 => 0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8,1,2,9,10,3,4,5,6,7] => [2,3,6,7,8,9,10,1,4,5] => 000000100 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [7,1,2,3,4,5,8,9,10,11,6] => [2,3,4,5,6,11,1,7,8,9,10] => 0000010000 => 0
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,1,2,3,6,7,8,9,10,4] => [2,3,4,10,1,5,6,7,8,9] => 000100000 => 0
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,7,8,9,10,11,5] => [2,3,4,5,11,1,6,7,8,9,10] => 0000100000 => 0
[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] => [2,3,4,5,6,7,9,1,10,8] => 000000101 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,1,2,3,4,5,10,6,8,9] => [2,3,4,5,6,8,1,9,10,7] => 000001001 => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,1,2,3,4,10,5,7,8,9] => [2,3,4,5,7,1,8,9,10,6] => 000010001 => 0
[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] => [2,3,4,6,1,7,8,9,10,5] => 000100001 => 0
[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] => [2,3,5,1,6,7,8,9,10,4] => 001000001 => 0
[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] => [2,4,1,5,6,7,8,9,10,3] => 010000001 => 0
[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] => [2,4,1,5,6,7,8,10,3,9] => 010000010 => 0
[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] => [2,4,1,6,3,8,5,10,7,9] => 010101010 => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,10,2,5,6,7,8,9] => [2,5,1,3,6,7,8,9,10,4] => 010000001 => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,1,4,5,6,7,9,2,10,8] => [2,8,1,3,4,5,6,10,7,9] => 010000010 => 0
[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] => [3,1,4,5,6,7,8,9,10,2] => 100000001 => 1
[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] => [3,1,4,5,6,7,8,10,2,9] => 100000010 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,8,1,3,4,5,6,10,7,9] => [3,1,4,5,6,7,9,2,10,8] => 100000101 => 1
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,6,7,8,9,10,4] => [3,1,4,10,2,5,6,7,8,9] => 100100000 => 1
[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] => [3,1,5,2,7,4,9,6,10,8] => 101010101 => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,4,1,5,6,7,8,10,3,9] => [3,1,9,2,4,5,6,7,10,8] => 101000001 => 1
[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] => [4,1,2,5,6,7,8,9,10,3] => 100000001 => 1
[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] => [4,1,2,10,3,5,6,7,8,9] => 100100000 => 1
[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] => [5,1,2,3,6,7,8,9,10,4] => 100000001 => 1
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,6,1,7,8,9,10,5] => [5,1,2,3,10,4,6,7,8,9] => 100010000 => 1
[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] => [6,1,2,3,4,7,8,9,10,5] => 100000001 => 1
[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] => [7,1,2,3,4,5,8,9,10,6] => 100000001 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [2,3,4,5,6,8,1,10,7,9] => [7,1,2,3,4,5,9,6,10,8] => 100000101 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,1,2,3,4,5,6,7,11,8,10] => [2,3,4,5,6,7,8,10,1,11,9] => 0000000101 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,1,2,3,4,5,6,11,7,9,10] => [2,3,4,5,6,7,9,1,10,11,8] => 0000001001 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,1,2,3,4,5,11,6,8,9,10] => [2,3,4,5,6,8,1,9,10,11,7] => 0000010001 => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,11,5,7,8,9,10] => [2,3,4,5,7,1,8,9,10,11,6] => 0000100001 => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,2,3,11,4,6,7,8,9,10] => [2,3,4,6,1,7,8,9,10,11,5] => 0001000001 => 0
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,6,7,8,9,10,11,4] => [2,3,4,11,1,5,6,7,8,9,10] => 0001000000 => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,11,3,5,6,7,8,9,10] => [2,3,5,1,6,7,8,9,10,11,4] => 0010000001 => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,11,2,4,5,6,7,8,9,10] => [2,4,1,5,6,7,8,9,10,11,3] => 0100000001 => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,10,1,3,4,5,6,7,8,11,9] => [3,1,4,5,6,7,8,9,11,2,10] => 1000000010 => 1
[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] => 1000000000 => 1
[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] => [3,4,5,6,1,7,8,9,10,2] => 000100001 => 0
[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] => [3,4,5,6,7,8,9,1,10,2] => 000000101 => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [7,8,9,10,1,2,3,4,5,11,6] => [5,6,7,8,9,11,1,2,3,4,10] => 0000010000 => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,3,4,1,2,5,6,7,8,9] => [4,5,2,3,6,7,8,9,10,1] => 010000001 => 0
[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] => [7,1,2,3,4,8,6,9,10,5] => 100001001 => 1
[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] => [6,1,2,3,7,5,8,9,10,4] => 100010001 => 1
[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] => [5,1,2,6,4,7,8,9,10,3] => 100100001 => 1
[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] => [4,1,5,3,6,7,8,9,10,2] => 101000001 => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,1,5,2,3,4,6,7,8,9] => [2,4,5,6,3,7,8,9,10,1] => 000100001 => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,1,2,5,3,4,6,7,8,9] => [2,3,5,6,4,7,8,9,10,1] => 000100001 => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,11,9,1,2,3,4,5,6,7,8] => [4,5,6,7,8,9,10,11,3,1,2] => 0000000110 => 0
[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] => 10000000000 => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,10,4,1,6,3,8,5,7,9] => [4,1,6,3,8,5,9,7,10,2] => 101010101 => 1
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Description
The number of leading ones in a binary word.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
Map
inverse
Description
Sends a permutation to its inverse.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.