Identifier
Values
[1,0] => [2,1] => [1,2] => 0 => 0
[1,0,1,0] => [3,1,2] => [1,3,2] => 01 => 1
[1,1,0,0] => [2,3,1] => [1,2,3] => 00 => 0
[1,0,1,0,1,0] => [4,1,2,3] => [1,4,3,2] => 011 => 2
[1,0,1,1,0,0] => [3,1,4,2] => [1,3,4,2] => 001 => 1
[1,1,0,0,1,0] => [2,4,1,3] => [1,2,4,3] => 001 => 1
[1,1,0,1,0,0] => [4,3,1,2] => [1,4,2,3] => 010 => 1
[1,1,1,0,0,0] => [2,3,4,1] => [1,2,3,4] => 000 => 0
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [1,5,4,3,2] => 0111 => 3
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [1,4,5,3,2] => 0011 => 2
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [1,3,5,4,2] => 0011 => 2
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [1,5,3,4,2] => 0101 => 2
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [1,3,4,5,2] => 0001 => 1
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [1,2,5,4,3] => 0011 => 2
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [1,2,4,5,3] => 0001 => 1
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [1,5,4,2,3] => 0110 => 2
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [1,5,3,2,4] => 0110 => 2
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [1,4,5,2,3] => 0010 => 1
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [1,2,3,5,4] => 0001 => 1
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [1,2,5,3,4] => 0010 => 1
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [1,5,2,3,4] => 0100 => 1
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => 0000 => 0
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => 01111 => 4
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [1,5,6,4,3,2] => 00111 => 3
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [1,4,6,5,3,2] => 00111 => 3
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [1,6,4,5,3,2] => 01011 => 3
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [1,4,5,6,3,2] => 00011 => 2
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [1,3,6,5,4,2] => 00111 => 3
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [1,3,5,6,4,2] => 00011 => 2
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [1,6,5,3,4,2] => 01101 => 3
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [1,6,4,2,3,5] => 01100 => 2
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [1,5,6,3,4,2] => 00101 => 2
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [1,3,4,6,5,2] => 00011 => 2
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [1,3,6,4,5,2] => 00101 => 2
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [1,6,3,4,5,2] => 01001 => 2
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [1,3,4,5,6,2] => 00001 => 1
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [1,2,6,5,4,3] => 00111 => 3
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [1,2,5,6,4,3] => 00011 => 2
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [1,2,4,6,5,3] => 00011 => 2
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [1,2,6,4,5,3] => 00101 => 2
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [1,2,4,5,6,3] => 00001 => 1
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [1,6,5,4,2,3] => 01110 => 3
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [1,5,6,4,2,3] => 00110 => 2
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [1,6,5,3,2,4] => 01110 => 3
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [1,5,3,2,6,4] => 01101 => 3
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [1,5,6,3,2,4] => 00110 => 2
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [1,4,6,5,2,3] => 00110 => 2
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [1,6,4,5,2,3] => 01010 => 2
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [1,6,3,2,4,5] => 01100 => 2
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [1,4,5,6,2,3] => 00010 => 1
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [1,2,3,6,5,4] => 00011 => 2
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [1,2,3,5,6,4] => 00001 => 1
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [1,2,6,5,3,4] => 00110 => 2
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [1,2,6,4,3,5] => 00110 => 2
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [1,2,5,6,3,4] => 00010 => 1
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [1,6,5,2,3,4] => 01100 => 2
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [1,6,4,2,3,5] => 01100 => 2
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [1,6,3,4,2,5] => 01010 => 2
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [1,5,6,2,3,4] => 00100 => 1
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [1,2,3,4,6,5] => 00001 => 1
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [1,2,3,6,4,5] => 00010 => 1
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [1,2,6,3,4,5] => 00100 => 1
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [1,6,2,3,4,5] => 01000 => 1
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 00000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [1,7,6,5,4,3,2] => 011111 => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [1,6,7,5,4,3,2] => 001111 => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [1,5,7,6,4,3,2] => 001111 => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => [1,7,5,6,4,3,2] => 010111 => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [1,5,6,7,4,3,2] => 000111 => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [1,4,7,6,5,3,2] => 001111 => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [1,4,6,7,5,3,2] => 000111 => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => [1,7,6,4,5,3,2] => 011011 => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [1,7,5,3,2,4,6] => 011100 => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => [1,6,7,4,5,3,2] => 001011 => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [1,4,5,7,6,3,2] => 000111 => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => [1,4,7,5,6,3,2] => 001011 => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [1,7,4,5,6,3,2] => 010011 => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [1,4,5,6,7,3,2] => 000011 => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [1,3,7,6,5,4,2] => 001111 => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [1,3,6,7,5,4,2] => 000111 => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [1,3,5,7,6,4,2] => 000111 => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [1,3,7,5,6,4,2] => 001011 => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [1,3,5,6,7,4,2] => 000011 => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => [1,7,6,5,3,4,2] => 011101 => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => [1,6,7,5,3,4,2] => 001101 => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [1,7,6,4,2,3,5] => 011100 => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [1,6,4,2,3,7,5] => 011001 => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [1,6,7,4,2,3,5] => 001100 => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [1,5,7,6,3,4,2] => 001101 => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => [1,7,5,6,3,4,2] => 010101 => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [1,7,4,2,3,5,6] => 011000 => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => [1,5,6,7,3,4,2] => 000101 => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [1,3,4,7,6,5,2] => 000111 => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [1,3,4,6,7,5,2] => 000011 => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [1,3,7,6,4,5,2] => 001101 => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [1,3,7,5,2,4,6] => 001100 => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [1,3,6,7,4,5,2] => 000101 => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [1,7,6,3,4,5,2] => 011001 => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [1,7,5,2,3,4,6] => 011000 => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [1,7,4,5,2,3,6] => 010100 => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => [1,6,7,3,4,5,2] => 001001 => 2
>>> Load all 673 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [1,3,4,5,7,6,2] => 000011 => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [1,3,4,7,5,6,2] => 000101 => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [1,3,7,4,5,6,2] => 001001 => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => [1,7,3,4,5,6,2] => 010001 => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,3,4,5,6,7,2] => 000001 => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [1,2,7,6,5,4,3] => 001111 => 4
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [1,2,6,7,5,4,3] => 000111 => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [1,2,5,7,6,4,3] => 000111 => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [1,2,7,5,6,4,3] => 001011 => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [1,2,5,6,7,4,3] => 000011 => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [1,2,4,7,6,5,3] => 000111 => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [1,2,4,6,7,5,3] => 000011 => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [1,2,7,6,4,5,3] => 001101 => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [1,2,7,5,3,4,6] => 001100 => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => [1,2,6,7,4,5,3] => 000101 => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [1,2,4,5,7,6,3] => 000011 => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => [1,2,4,7,5,6,3] => 000101 => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [1,2,7,4,5,6,3] => 001001 => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [1,2,4,5,6,7,3] => 000001 => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => [1,7,6,5,4,2,3] => 011110 => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => [1,6,7,5,4,2,3] => 001110 => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [1,5,7,6,4,2,3] => 001110 => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => [1,7,5,6,4,2,3] => 010110 => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => [1,5,6,7,4,2,3] => 000110 => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => [1,7,6,5,3,2,4] => 011110 => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => [1,6,7,5,3,2,4] => 001110 => 3
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [1,5,3,2,7,6,4] => 011011 => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [1,7,5,3,2,6,4] => 011101 => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [1,5,3,2,6,7,4] => 011001 => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [1,5,7,6,3,2,4] => 001110 => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [1,7,5,6,3,2,4] => 010110 => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [1,5,6,3,2,7,4] => 001101 => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => [1,5,6,7,3,2,4] => 000110 => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [1,4,7,6,5,2,3] => 001110 => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [1,4,6,7,5,2,3] => 000110 => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => [1,7,6,4,5,2,3] => 011010 => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [1,7,5,2,3,4,6] => 011000 => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => [1,6,7,4,5,2,3] => 001010 => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [1,7,6,3,2,4,5] => 011100 => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => [1,7,5,2,4,6,3] => 011001 => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [1,6,3,2,7,4,5] => 011010 => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [1,6,7,3,2,4,5] => 001100 => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [1,4,5,7,6,2,3] => 000110 => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [1,4,7,5,6,2,3] => 001010 => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [1,7,4,5,6,2,3] => 010010 => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [1,7,3,2,4,5,6] => 011000 => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,4,5,6,7,2,3] => 000010 => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [1,2,3,7,6,5,4] => 000111 => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [1,2,3,6,7,5,4] => 000011 => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [1,2,3,5,7,6,4] => 000011 => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => [1,2,3,7,5,6,4] => 000101 => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [1,2,3,5,6,7,4] => 000001 => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [1,2,7,6,5,3,4] => 001110 => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => [1,2,6,7,5,3,4] => 000110 => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [1,2,7,6,4,3,5] => 001110 => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [1,2,6,4,3,7,5] => 001101 => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => [1,2,6,7,4,3,5] => 000110 => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => [1,2,5,7,6,3,4] => 000110 => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => [1,2,7,5,6,3,4] => 001010 => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [1,2,7,4,3,5,6] => 001100 => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => [1,2,5,6,7,3,4] => 000010 => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => [1,7,6,5,2,3,4] => 011100 => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [1,6,7,5,2,3,4] => 001100 => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [1,7,6,4,2,3,5] => 011100 => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [1,6,4,2,3,7,5] => 011001 => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [1,6,7,4,2,3,5] => 001100 => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [1,7,6,3,4,2,5] => 011010 => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [1,6,3,4,2,7,5] => 010101 => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => [1,6,3,5,2,7,4] => 010101 => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [1,6,7,3,4,2,5] => 001010 => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => [1,5,7,6,2,3,4] => 001100 => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => [1,7,5,6,2,3,4] => 010100 => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [1,7,4,2,3,5,6] => 011000 => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [1,7,3,4,2,5,6] => 010100 => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => [1,5,6,7,2,3,4] => 000100 => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [1,2,3,4,7,6,5] => 000011 => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [1,2,3,4,6,7,5] => 000001 => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => [1,2,3,7,6,4,5] => 000110 => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => [1,2,3,7,5,4,6] => 000110 => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => [1,2,3,6,7,4,5] => 000010 => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => [1,2,7,6,3,4,5] => 001100 => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [1,2,7,5,3,4,6] => 001100 => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [1,2,7,4,5,3,6] => 001010 => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => [1,2,6,7,3,4,5] => 000100 => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [1,7,6,2,3,4,5] => 011000 => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [1,7,5,2,3,4,6] => 011000 => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [1,7,4,5,2,3,6] => 010100 => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => [1,7,3,4,5,2,6] => 010010 => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [1,6,7,2,3,4,5] => 001000 => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [1,2,3,4,5,7,6] => 000001 => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => [1,2,3,4,7,5,6] => 000010 => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => [1,2,3,7,4,5,6] => 000100 => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => [1,2,7,3,4,5,6] => 001000 => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => [1,7,2,3,4,5,6] => 010000 => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => 000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [1,7,8,6,5,4,3,2] => 0011111 => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => [1,6,8,7,5,4,3,2] => 0011111 => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,1,2,3,4,7,5,6] => [1,8,6,7,5,4,3,2] => 0101111 => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [1,6,7,8,5,4,3,2] => 0001111 => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => [1,5,8,7,6,4,3,2] => 0011111 => 5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,1,2,3,6,4,5,7] => [1,8,7,5,6,4,3,2] => 0110111 => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,1,2,3,6,4,8,5] => [1,7,8,5,6,4,3,2] => 0010111 => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,1,2,3,6,7,4,5] => [1,8,5,6,7,4,3,2] => 0100111 => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [1,5,6,7,8,4,3,2] => 0000111 => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => [1,4,8,7,6,5,3,2] => 0011111 => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => [1,4,7,8,6,5,3,2] => 0001111 => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [1,4,6,8,7,5,3,2] => 0001111 => 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [4,1,2,8,3,7,5,6] => [1,4,8,6,7,5,3,2] => 0010111 => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [1,4,6,7,8,5,3,2] => 0000111 => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,1,2,5,3,4,6,7] => [1,8,7,6,4,5,3,2] => 0111011 => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,1,2,5,3,4,8,6] => [1,7,8,6,4,5,3,2] => 0011011 => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,1,2,6,3,4,5,7] => [1,8,7,5,3,2,4,6] => 0111100 => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,1,2,8,3,4,5,6] => [1,7,5,3,2,4,8,6] => 0111001 => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,1,2,5,3,8,4,7] => [1,6,8,7,4,5,3,2] => 0011011 => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [8,1,2,5,3,7,4,6] => [1,8,6,7,4,5,3,2] => 0101011 => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [8,1,2,6,3,7,4,5] => [1,8,5,3,2,4,6,7] => 0111000 => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [6,1,2,5,3,7,8,4] => [1,6,7,8,4,5,3,2] => 0001011 => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => [1,4,5,8,7,6,3,2] => 0001111 => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [1,4,5,7,8,6,3,2] => 0000111 => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [4,1,2,8,7,3,5,6] => [1,4,8,6,3,2,5,7] => 0011100 => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,1,2,5,6,3,4,7] => [1,8,7,4,5,6,3,2] => 0110011 => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [8,1,2,5,7,3,4,6] => [1,8,6,3,2,4,5,7] => 0111000 => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,8,7,3,6] => [1,4,5,8,6,7,3,2] => 0001011 => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,1,2,8,6,7,3,5] => [1,4,8,5,6,7,3,2] => 0010011 => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => [1,8,4,5,6,7,3,2] => 0100011 => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [1,4,5,6,7,8,3,2] => 0000011 => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [1,3,8,7,6,5,4,2] => 0011111 => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => [1,3,7,8,6,5,4,2] => 0001111 => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,6,2,4,8,5,7] => [1,3,6,8,7,5,4,2] => 0001111 => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [1,3,6,7,8,5,4,2] => 0000111 => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [1,3,5,8,7,6,4,2] => 0001111 => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [1,3,5,7,8,6,4,2] => 0000111 => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,8,2,6,4,5,7] => [1,3,8,7,5,6,4,2] => 0011011 => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [3,1,8,2,7,4,5,6] => [1,3,8,6,4,2,5,7] => 0011100 => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,1,7,2,6,4,8,5] => [1,3,7,8,5,6,4,2] => 0001011 => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [1,3,5,6,8,7,4,2] => 0000111 => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,1,8,2,6,7,4,5] => [1,3,8,5,6,7,4,2] => 0010011 => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [1,3,5,6,7,8,4,2] => 0000011 => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,1,4,2,3,5,6,7] => [1,8,7,6,5,3,4,2] => 0111101 => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,1,4,2,3,5,8,6] => [1,7,8,6,5,3,4,2] => 0011101 => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,1,4,2,3,8,5,7] => [1,6,8,7,5,3,4,2] => 0011101 => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [8,1,4,2,3,7,5,6] => [1,8,6,7,5,3,4,2] => 0101101 => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,1,4,2,3,7,8,5] => [1,6,7,8,5,3,4,2] => 0001101 => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,1,5,2,3,4,6,7] => [1,8,7,6,4,2,3,5] => 0111100 => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,1,5,2,3,4,8,6] => [1,7,8,6,4,2,3,5] => 0011100 => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7] => [1,6,4,2,3,8,7,5] => 0110011 => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,1,7,2,3,4,5,6] => [1,8,6,4,2,3,7,5] => 0111001 => 4
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,1,7,2,3,4,8,5] => [1,6,4,2,3,7,8,5] => 0110001 => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,1,5,2,3,8,4,7] => [1,6,8,7,4,2,3,5] => 0011100 => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [8,1,5,2,3,7,4,6] => [1,8,6,7,4,2,3,5] => 0101100 => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,1,8,2,3,7,4,5] => [1,6,7,4,2,3,8,5] => 0011001 => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,1,5,2,3,7,8,4] => [1,6,7,8,4,2,3,5] => 0001100 => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [5,1,4,2,8,3,6,7] => [1,5,8,7,6,3,4,2] => 0011101 => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,1,4,2,7,3,8,6] => [1,5,7,8,6,3,4,2] => 0001101 => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,1,4,2,6,3,5,7] => [1,8,7,5,6,3,4,2] => 0110101 => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [8,1,4,2,7,3,5,6] => [1,8,6,3,4,2,5,7] => 0110100 => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [7,1,4,2,6,3,8,5] => [1,7,8,5,6,3,4,2] => 0010101 => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,1,5,2,6,3,4,7] => [1,8,7,4,2,3,5,6] => 0111000 => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [8,1,5,2,7,3,4,6] => [1,8,6,3,5,7,4,2] => 0110011 => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [7,1,8,2,6,3,4,5] => [1,7,4,2,3,8,5,6] => 0110010 => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [7,1,5,2,6,3,8,4] => [1,7,8,4,2,3,5,6] => 0011000 => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,1,4,2,8,7,3,6] => [1,5,8,6,7,3,4,2] => 0010101 => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [8,1,4,2,6,7,3,5] => [1,8,5,6,7,3,4,2] => 0100101 => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [8,1,5,2,6,7,3,4] => [1,8,4,2,3,5,6,7] => 0110000 => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [5,1,4,2,6,7,8,3] => [1,5,6,7,8,3,4,2] => 0000101 => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,8,2,5,6,7] => [1,3,4,8,7,6,5,2] => 0001111 => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,4,8,2,7,5,6] => [1,3,4,8,6,7,5,2] => 0001011 => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [1,3,4,6,7,8,5,2] => 0000011 => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,8,6,2,4,5,7] => [1,3,8,7,5,2,4,6] => 0011100 => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,7,8,2,4,5,6] => [1,3,7,5,2,4,8,6] => 0011001 => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,7,6,2,4,8,5] => [1,3,7,8,5,2,4,6] => 0001100 => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,6,5,2,8,4,7] => [1,3,6,8,7,4,5,2] => 0001101 => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,8,5,2,7,4,6] => [1,3,8,6,7,4,5,2] => 0010101 => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,8,6,2,7,4,5] => [1,3,8,5,2,4,6,7] => 0011000 => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,1,4,5,2,3,6,7] => [1,8,7,6,3,4,5,2] => 0111001 => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,1,4,5,2,3,8,6] => [1,7,8,6,3,4,5,2] => 0011001 => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,1,4,6,2,3,5,7] => [1,8,7,5,2,3,4,6] => 0111000 => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,1,4,8,2,3,5,6] => [1,7,5,2,3,4,8,6] => 0110001 => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,1,6,5,2,3,4,7] => [1,8,7,4,5,2,3,6] => 0110100 => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,1,8,5,2,3,4,6] => [1,7,4,5,2,3,8,6] => 0101001 => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [7,1,8,6,2,3,4,5] => [1,7,4,6,3,8,5,2] => 0101011 => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [7,1,6,5,2,3,8,4] => [1,7,8,4,5,2,3,6] => 0010100 => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,1,4,5,2,8,3,7] => [1,6,8,7,3,4,5,2] => 0011001 => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [8,1,4,5,2,7,3,6] => [1,8,6,7,3,4,5,2] => 0101001 => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [8,1,6,5,2,7,3,4] => [1,8,4,5,2,3,6,7] => 0101000 => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [6,1,4,5,2,7,8,3] => [1,6,7,8,3,4,5,2] => 0001001 => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => [1,3,4,5,8,7,6,2] => 0000111 => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,1,4,5,7,2,8,6] => [1,3,4,5,7,8,6,2] => 0000011 => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,8,5,6,2,4,7] => [1,3,8,7,4,5,6,2] => 0011001 => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,8,5,7,2,4,6] => [1,3,8,6,2,4,5,7] => 0011000 => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,1,7,5,6,2,8,4] => [1,3,7,8,4,5,6,2] => 0001001 => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,1,4,5,6,2,3,7] => [1,8,7,3,4,5,6,2] => 0110001 => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [8,1,4,5,7,2,3,6] => [1,8,6,2,3,4,5,7] => 0110000 => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [8,1,4,7,6,2,3,5] => [1,8,5,6,2,3,4,7] => 0101000 => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [8,1,7,5,6,2,3,4] => [1,8,4,5,6,2,3,7] => 0100100 => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [7,1,4,5,6,2,8,3] => [1,7,8,3,4,5,6,2] => 0010001 => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [1,3,4,5,6,8,7,2] => 0000011 => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,1,4,5,8,7,2,6] => [1,3,4,5,8,6,7,2] => 0000101 => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,1,4,8,6,7,2,5] => [1,3,4,8,5,6,7,2] => 0001001 => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,8,5,6,7,2,4] => [1,3,8,4,5,6,7,2] => 0010001 => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [8,1,4,5,6,7,2,3] => [1,8,3,4,5,6,7,2] => 0100001 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,3,4,5,6,7,8,2] => 0000001 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => [1,2,8,7,6,5,4,3] => 0011111 => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => [1,2,7,8,6,5,4,3] => 0001111 => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,8,1,3,4,7,5,6] => [1,2,8,6,7,5,4,3] => 0010111 => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,6,1,3,4,7,8,5] => [1,2,6,7,8,5,4,3] => 0000111 => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7] => [1,2,5,8,7,6,4,3] => 0001111 => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,8,1,3,6,4,5,7] => [1,2,8,7,5,6,4,3] => 0011011 => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,8,1,3,7,4,5,6] => [1,2,8,6,4,3,5,7] => 0011100 => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,7,1,3,6,4,8,5] => [1,2,7,8,5,6,4,3] => 0001011 => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,5,1,3,6,8,4,7] => [1,2,5,6,8,7,4,3] => 0000111 => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,5,1,3,8,7,4,6] => [1,2,5,8,6,7,4,3] => 0001011 => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,8,1,3,6,7,4,5] => [1,2,8,5,6,7,4,3] => 0010011 => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,1,3,6,7,8,4] => [1,2,5,6,7,8,4,3] => 0000011 => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => [1,2,4,8,7,6,5,3] => 0001111 => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,7,3,5,8,6] => [1,2,4,7,8,6,5,3] => 0000111 => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [1,2,4,6,8,7,5,3] => 0000111 => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [1,2,4,6,7,8,5,3] => 0000011 => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,7,1,5,3,4,8,6] => [1,2,7,8,6,4,5,3] => 0001101 => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,7,1,8,3,4,5,6] => [1,2,7,5,3,4,8,6] => 0011001 => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,7,1,6,3,4,8,5] => [1,2,7,8,5,3,4,6] => 0001100 => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,6,1,5,3,8,4,7] => [1,2,6,8,7,4,5,3] => 0001101 => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,8,1,6,3,7,4,5] => [1,2,8,5,3,4,6,7] => 0011000 => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,6,1,5,3,7,8,4] => [1,2,6,7,8,4,5,3] => 0000101 => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => [1,2,4,5,8,7,6,3] => 0000111 => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,5,7,3,8,6] => [1,2,4,5,7,8,6,3] => 0000011 => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,8,7,3,5,6] => [1,2,4,8,6,3,5,7] => 0001100 => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,4,1,7,6,3,8,5] => [1,2,4,7,8,5,6,3] => 0000101 => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,8,1,5,6,3,4,7] => [1,2,8,7,4,5,6,3] => 0011001 => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,8,1,5,7,3,4,6] => [1,2,8,6,3,4,5,7] => 0011000 => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,8,1,7,6,3,4,5] => [1,2,8,5,6,3,4,7] => 0010100 => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,7,1,5,6,3,8,4] => [1,2,7,8,4,5,6,3] => 0001001 => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1,5,6,8,3,7] => [1,2,4,5,6,8,7,3] => 0000011 => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,8,7,3,6] => [1,2,4,5,8,6,7,3] => 0000101 => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1,8,6,7,3,5] => [1,2,4,8,5,6,7,3] => 0001001 => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,8,1,5,6,7,3,4] => [1,2,8,4,5,6,7,3] => 0010001 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [1,2,4,5,6,7,8,3] => 0000001 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => [1,8,7,6,5,4,2,3] => 0111110 => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,3,1,2,4,5,8,6] => [1,7,8,6,5,4,2,3] => 0011110 => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [8,3,1,2,4,7,5,6] => [1,8,6,7,5,4,2,3] => 0101110 => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,3,1,2,7,4,8,6] => [1,5,7,8,6,4,2,3] => 0001110 => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,3,1,2,6,4,5,7] => [1,8,7,5,6,4,2,3] => 0110110 => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [8,3,1,2,7,4,5,6] => [1,8,6,4,2,3,5,7] => 0111000 => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [7,3,1,2,6,4,8,5] => [1,7,8,5,6,4,2,3] => 0010110 => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,1,2,6,8,4,7] => [1,5,6,8,7,4,2,3] => 0001110 => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,1,2,8,7,4,6] => [1,5,8,6,7,4,2,3] => 0010110 => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [8,3,1,2,6,7,4,5] => [1,8,5,6,7,4,2,3] => 0100110 => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,3,1,2,6,7,8,4] => [1,5,6,7,8,4,2,3] => 0000110 => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => [1,8,7,6,5,3,2,4] => 0111110 => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,4,1,2,3,5,8,6] => [1,7,8,6,5,3,2,4] => 0011110 => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,1,2,3,8,5,7] => [1,6,8,7,5,3,2,4] => 0011110 => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [8,4,1,2,3,7,5,6] => [1,8,6,7,5,3,2,4] => 0101110 => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,8,1,2,3,4,6,7] => [1,5,3,2,8,7,6,4] => 0110111 => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [1,8,7,5,3,2,6,4] => 0111101 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6] => [1,8,6,4,2,7,5,3] => 0111011 => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [5,6,1,2,3,8,4,7] => [1,5,3,2,6,8,7,4] => 0110011 => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,8,1,2,3,7,4,6] => [1,5,3,2,8,6,7,4] => 0110101 => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,6,1,2,3,7,4,5] => [1,8,5,3,2,6,7,4] => 0111001 => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,1,2,3,7,8,4] => [1,5,3,2,6,7,8,4] => 0110001 => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,2,8,3,6,7] => [1,5,8,7,6,3,2,4] => 0011110 => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,4,1,2,7,3,8,6] => [1,5,7,8,6,3,2,4] => 0001110 => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,4,1,2,7,3,5,6] => [1,8,6,3,2,4,5,7] => 0111000 => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7,4,1,2,6,3,8,5] => [1,7,8,5,6,3,2,4] => 0010110 => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [5,8,1,2,6,3,4,7] => [1,5,6,3,2,8,7,4] => 0011011 => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,8,1,2,7,3,4,6] => [1,5,7,4,2,8,6,3] => 0011011 => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,7,1,2,6,3,8,4] => [1,5,6,3,2,7,8,4] => 0011001 => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [5,4,1,2,6,8,3,7] => [1,5,6,8,7,3,2,4] => 0001110 => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8,4,1,2,6,7,3,5] => [1,8,5,6,7,3,2,4] => 0100110 => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,8,1,2,6,7,3,4] => [1,5,6,7,3,2,8,4] => 0001101 => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,4,1,2,6,7,8,3] => [1,5,6,7,8,3,2,4] => 0000110 => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3,1,8,2,7,5,6] => [1,4,8,6,7,5,2,3] => 0010110 => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,3,1,5,2,4,6,7] => [1,8,7,6,4,5,2,3] => 0111010 => 4
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,3,1,6,2,4,5,7] => [1,8,7,5,2,3,4,6] => 0111000 => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,3,1,8,2,4,5,6] => [1,7,5,2,3,4,8,6] => 0110001 => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8,3,1,5,2,7,4,6] => [1,8,6,7,4,5,2,3] => 0101010 => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,4,1,5,2,3,6,7] => [1,8,7,6,3,2,4,5] => 0111100 => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,4,1,5,2,3,8,6] => [1,7,8,6,3,2,4,5] => 0011100 => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,4,1,6,2,3,5,7] => [1,8,7,5,2,4,6,3] => 0111001 => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,4,1,8,2,3,5,6] => [1,7,5,2,4,8,6,3] => 0110011 => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,8,1,5,2,3,4,7] => [1,6,3,2,8,7,4,5] => 0110110 => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8,7,1,5,2,3,4,6] => [1,8,6,3,2,7,4,5] => 0111010 => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8,7,1,6,2,3,4,5] => [1,8,5,2,7,4,6,3] => 0110101 => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [6,7,1,5,2,3,8,4] => [1,6,3,2,7,8,4,5] => 0110010 => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,4,1,5,2,8,3,7] => [1,6,8,7,3,2,4,5] => 0011100 => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8,4,1,5,2,7,3,6] => [1,8,6,7,3,2,4,5] => 0101100 => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [6,8,1,5,2,7,3,4] => [1,6,7,3,2,8,4,5] => 0011010 => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [6,4,1,5,2,7,8,3] => [1,6,7,8,3,2,4,5] => 0001100 => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [4,3,1,5,8,2,6,7] => [1,4,5,8,7,6,2,3] => 0001110 => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [4,3,1,8,7,2,5,6] => [1,4,8,6,2,3,5,7] => 0011000 => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,3,1,7,6,2,8,5] => [1,4,7,8,5,6,2,3] => 0001010 => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,3,1,5,6,2,4,7] => [1,8,7,4,5,6,2,3] => 0110010 => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8,3,1,5,7,2,4,6] => [1,8,6,2,3,4,5,7] => 0110000 => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8,3,1,7,6,2,4,5] => [1,8,5,6,2,3,4,7] => 0101000 => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7,3,1,5,6,2,8,4] => [1,7,8,4,5,6,2,3] => 0010010 => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,1,5,6,2,3,7] => [1,8,7,3,2,4,5,6] => 0111000 => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8,4,1,7,6,2,3,5] => [1,8,5,6,2,4,7,3] => 0101001 => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [1,7,3,2,8,4,5,6] => 0110100 => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [4,3,1,5,6,8,2,7] => [1,4,5,6,8,7,2,3] => 0000110 => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,3,1,8,6,7,2,5] => [1,4,8,5,6,7,2,3] => 0010010 => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8,3,1,5,6,7,2,4] => [1,8,4,5,6,7,2,3] => 0100010 => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8,4,1,5,6,7,2,3] => [1,8,3,2,4,5,6,7] => 0110000 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,4,5,6,7,8,2,3] => 0000010 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => [1,2,3,8,7,6,5,4] => 0001111 => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,3,7,1,4,5,8,6] => [1,2,3,7,8,6,5,4] => 0000111 => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7] => [1,2,3,6,8,7,5,4] => 0000111 => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,3,8,1,4,7,5,6] => [1,2,3,8,6,7,5,4] => 0001011 => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => [1,2,3,6,7,8,5,4] => 0000011 => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => [1,2,3,5,8,7,6,4] => 0000111 => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [1,2,3,5,7,8,6,4] => 0000011 => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,3,8,1,6,4,5,7] => [1,2,3,8,7,5,6,4] => 0001101 => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,3,8,1,7,4,5,6] => [1,2,3,8,6,4,5,7] => 0001100 => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,3,7,1,6,4,8,5] => [1,2,3,7,8,5,6,4] => 0000101 => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [1,2,3,5,6,8,7,4] => 0000011 => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,3,5,1,8,7,4,6] => [1,2,3,5,8,6,7,4] => 0000101 => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,3,8,1,6,7,4,5] => [1,2,3,8,5,6,7,4] => 0001001 => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [1,2,3,5,6,7,8,4] => 0000001 => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,8,4,1,3,5,6,7] => [1,2,8,7,6,5,3,4] => 0011110 => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,7,4,1,3,5,8,6] => [1,2,7,8,6,5,3,4] => 0001110 => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,6,4,1,3,8,5,7] => [1,2,6,8,7,5,3,4] => 0001110 => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,8,4,1,3,7,5,6] => [1,2,8,6,7,5,3,4] => 0010110 => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,6,4,1,3,7,8,5] => [1,2,6,7,8,5,3,4] => 0000110 => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,8,5,1,3,4,6,7] => [1,2,8,7,6,4,3,5] => 0011110 => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,7,5,1,3,4,8,6] => [1,2,7,8,6,4,3,5] => 0001110 => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,8,7,1,3,4,5,6] => [1,2,8,6,4,3,7,5] => 0011101 => 4
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => [1,2,6,4,3,7,8,5] => 0011001 => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,6,5,1,3,8,4,7] => [1,2,6,8,7,4,3,5] => 0001110 => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,6,8,1,3,7,4,5] => [1,2,6,7,4,3,8,5] => 0001101 => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,6,5,1,3,7,8,4] => [1,2,6,7,8,4,3,5] => 0000110 => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,5,4,1,8,3,6,7] => [1,2,5,8,7,6,3,4] => 0001110 => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,5,4,1,7,3,8,6] => [1,2,5,7,8,6,3,4] => 0000110 => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,8,4,1,6,3,5,7] => [1,2,8,7,5,6,3,4] => 0011010 => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,8,4,1,7,3,5,6] => [1,2,8,6,3,4,5,7] => 0011000 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,7,4,1,6,3,8,5] => [1,2,7,8,5,6,3,4] => 0001010 => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,8,5,1,7,3,4,6] => [1,2,8,6,3,5,7,4] => 0011001 => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,7,5,1,6,3,8,4] => [1,2,7,8,4,3,5,6] => 0001100 => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,5,4,1,6,8,3,7] => [1,2,5,6,8,7,3,4] => 0000110 => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,5,4,1,8,7,3,6] => [1,2,5,8,6,7,3,4] => 0001010 => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,8,4,1,6,7,3,5] => [1,2,8,5,6,7,3,4] => 0010010 => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,8,5,1,6,7,3,4] => [1,2,8,4,3,5,6,7] => 0011000 => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,5,4,1,6,7,8,3] => [1,2,5,6,7,8,3,4] => 0000010 => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,3,4,1,2,5,6,7] => [1,8,7,6,5,2,3,4] => 0111100 => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,3,4,1,2,8,5,7] => [1,6,8,7,5,2,3,4] => 0011100 => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [8,3,4,1,2,7,5,6] => [1,8,6,7,5,2,3,4] => 0101100 => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,3,4,1,2,7,8,5] => [1,6,7,8,5,2,3,4] => 0001100 => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,3,5,1,2,4,6,7] => [1,8,7,6,4,2,3,5] => 0111100 => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,3,5,1,2,4,8,6] => [1,7,8,6,4,2,3,5] => 0011100 => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,3,8,1,2,4,5,7] => [1,6,4,2,3,8,7,5] => 0110011 => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,3,7,1,2,4,5,6] => [1,8,6,4,2,3,7,5] => 0111001 => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,3,7,1,2,4,8,5] => [1,6,4,2,3,7,8,5] => 0110001 => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,5,1,2,8,4,7] => [1,6,8,7,4,2,3,5] => 0011100 => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8,3,5,1,2,7,4,6] => [1,8,6,7,4,2,3,5] => 0101100 => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,3,8,1,2,7,4,5] => [1,6,7,4,2,3,8,5] => 0011001 => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [6,3,5,1,2,7,8,4] => [1,6,7,8,4,2,3,5] => 0001100 => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,5,4,1,2,3,6,7] => [1,8,7,6,3,4,2,5] => 0111010 => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,5,4,1,2,3,8,6] => [1,7,8,6,3,4,2,5] => 0011010 => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,8,4,1,2,3,5,7] => [1,6,3,4,2,8,7,5] => 0101011 => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,8,5,1,2,3,4,7] => [1,6,3,5,2,8,7,4] => 0101011 => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8,7,5,1,2,3,4,6] => [1,8,6,3,5,2,7,4] => 0110101 => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,7,8,1,2,3,4,5] => [1,6,3,8,5,2,7,4] => 0101101 => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,1,2,3,8,4] => [1,6,3,5,2,7,8,4] => 0101001 => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,5,4,1,2,8,3,7] => [1,6,8,7,3,4,2,5] => 0011010 => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,4,1,2,7,3,6] => [1,8,6,7,3,4,2,5] => 0101010 => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,8,4,1,2,7,3,5] => [1,6,7,3,4,2,8,5] => 0010101 => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [6,5,4,1,2,7,8,3] => [1,6,7,8,3,4,2,5] => 0001010 => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,3,4,1,8,2,6,7] => [1,5,8,7,6,2,3,4] => 0011100 => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,3,4,1,7,2,8,6] => [1,5,7,8,6,2,3,4] => 0001100 => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,3,4,1,6,2,5,7] => [1,8,7,5,6,2,3,4] => 0110100 => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8,3,4,1,7,2,5,6] => [1,8,6,2,3,4,5,7] => 0110000 => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,3,5,1,6,2,4,7] => [1,8,7,4,2,3,5,6] => 0111000 => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,3,8,1,6,2,4,5] => [1,7,4,2,3,8,5,6] => 0110010 => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,3,5,1,6,2,8,4] => [1,7,8,4,2,3,5,6] => 0011000 => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,5,4,1,6,2,3,7] => [1,8,7,3,4,2,5,6] => 0110100 => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8,5,4,1,7,2,3,6] => [1,8,6,2,5,7,3,4] => 0110010 => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,8,4,1,6,2,3,5] => [1,7,3,4,2,8,5,6] => 0101010 => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,8,5,1,6,2,3,4] => [1,7,3,5,6,2,8,4] => 0100101 => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,5,4,1,6,2,8,3] => [1,7,8,3,4,2,5,6] => 0010100 => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => [1,8,5,6,7,2,3,4] => 0100100 => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8,3,5,1,6,7,2,4] => [1,8,4,2,3,5,6,7] => 0110000 => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8,5,4,1,6,7,2,3] => [1,8,3,4,2,5,6,7] => 0101000 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [5,3,4,1,6,7,8,2] => [1,5,6,7,8,2,3,4] => 0000100 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => [1,2,3,4,8,7,6,5] => 0000111 => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,4,7,1,5,8,6] => [1,2,3,4,7,8,6,5] => 0000011 => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => [1,2,3,4,6,8,7,5] => 0000011 => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,4,8,1,7,5,6] => [1,2,3,4,8,6,7,5] => 0000101 => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [1,2,3,4,6,7,8,5] => 0000001 => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,8,5,1,4,6,7] => [1,2,3,8,7,6,4,5] => 0001110 => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,7,5,1,4,8,6] => [1,2,3,7,8,6,4,5] => 0000110 => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,8,6,1,4,5,7] => [1,2,3,8,7,5,4,6] => 0001110 => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,7,8,1,4,5,6] => [1,2,3,7,5,4,8,6] => 0001101 => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,7,6,1,4,8,5] => [1,2,3,7,8,5,4,6] => 0000110 => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,6,5,1,8,4,7] => [1,2,3,6,8,7,4,5] => 0000110 => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,8,5,1,7,4,6] => [1,2,3,8,6,7,4,5] => 0001010 => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,8,6,1,7,4,5] => [1,2,3,8,5,4,6,7] => 0001100 => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,6,5,1,7,8,4] => [1,2,3,6,7,8,4,5] => 0000010 => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,8,4,5,1,3,6,7] => [1,2,8,7,6,3,4,5] => 0011100 => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,4,5,1,3,8,6] => [1,2,7,8,6,3,4,5] => 0001100 => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,7,4,8,1,3,5,6] => [1,2,7,5,3,4,8,6] => 0011001 => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,7,4,6,1,3,8,5] => [1,2,7,8,5,3,4,6] => 0001100 => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,8,6,5,1,3,4,7] => [1,2,8,7,4,5,3,6] => 0011010 => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,8,5,1,3,4,6] => [1,2,7,4,5,3,8,6] => 0010101 => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7,8,6,1,3,4,5] => [1,2,7,4,6,3,8,5] => 0010101 => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,7,6,5,1,3,8,4] => [1,2,7,8,4,5,3,6] => 0001010 => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,6,4,5,1,8,3,7] => [1,2,6,8,7,3,4,5] => 0001100 => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,6,1,7,3,5] => [1,2,8,5,3,4,6,7] => 0011000 => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,6,5,1,7,3,4] => [1,2,8,4,5,3,6,7] => 0010100 => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,6,4,5,1,7,8,3] => [1,2,6,7,8,3,4,5] => 0000100 => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [8,3,4,5,1,2,6,7] => [1,8,7,6,2,3,4,5] => 0111000 => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,3,4,5,1,2,8,6] => [1,7,8,6,2,3,4,5] => 0011000 => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,3,4,6,1,2,5,7] => [1,8,7,5,2,3,4,6] => 0111000 => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,3,4,8,1,2,5,6] => [1,7,5,2,3,4,8,6] => 0110001 => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,3,6,5,1,2,4,7] => [1,8,7,4,5,2,3,6] => 0110100 => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,3,8,5,1,2,4,6] => [1,7,4,5,2,3,8,6] => 0101001 => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,8,6,1,2,4,5] => [1,7,4,6,2,3,8,5] => 0101001 => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,6,5,1,2,8,4] => [1,7,8,4,5,2,3,6] => 0010100 => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,6,4,5,1,2,3,7] => [1,8,7,3,4,5,2,6] => 0110010 => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,8,4,5,1,2,3,6] => [1,7,3,4,5,2,8,6] => 0100101 => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,6,5,1,2,3,4] => [1,7,3,6,2,8,4,5] => 0101010 => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,6,4,5,1,2,8,3] => [1,7,8,3,4,5,2,6] => 0010010 => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,4,5,1,8,2,7] => [1,6,8,7,2,3,4,5] => 0011000 => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8,3,4,5,1,7,2,6] => [1,8,6,7,2,3,4,5] => 0101000 => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8,3,6,5,1,7,2,4] => [1,8,4,5,2,3,6,7] => 0101000 => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8,6,4,5,1,7,2,3] => [1,8,3,4,5,2,6,7] => 0100100 => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [6,3,4,5,1,7,8,2] => [1,6,7,8,2,3,4,5] => 0001000 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7] => [1,2,3,4,5,8,7,6] => 0000011 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [1,2,3,4,5,7,8,6] => 0000001 => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,3,4,8,6,1,5,7] => [1,2,3,4,8,7,5,6] => 0000110 => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,4,8,7,1,5,6] => [1,2,3,4,8,6,5,7] => 0000110 => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,4,7,6,1,8,5] => [1,2,3,4,7,8,5,6] => 0000010 => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,3,8,5,6,1,4,7] => [1,2,3,8,7,4,5,6] => 0001100 => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,8,5,7,1,4,6] => [1,2,3,8,6,4,5,7] => 0001100 => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,8,7,6,1,4,5] => [1,2,3,8,5,6,4,7] => 0001010 => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,7,5,6,1,8,4] => [1,2,3,7,8,4,5,6] => 0000100 => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,8,4,5,6,1,3,7] => [1,2,8,7,3,4,5,6] => 0011000 => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,8,4,5,7,1,3,6] => [1,2,8,6,3,4,5,7] => 0011000 => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,4,7,6,1,3,5] => [1,2,8,5,6,3,4,7] => 0010100 => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [1,2,8,4,5,6,3,7] => 0010010 => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,7,4,5,6,1,8,3] => [1,2,7,8,3,4,5,6] => 0001000 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [1,8,7,2,3,4,5,6] => 0110000 => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8,3,4,5,7,1,2,6] => [1,8,6,2,3,4,5,7] => 0110000 => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8,3,4,7,6,1,2,5] => [1,8,5,6,2,3,4,7] => 0101000 => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8,3,7,5,6,1,2,4] => [1,8,4,5,6,2,3,7] => 0100100 => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,7,4,5,6,1,2,3] => [1,8,3,4,5,6,2,7] => 0100010 => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,3,4,5,6,1,8,2] => [1,7,8,2,3,4,5,6] => 0010000 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => [1,2,3,4,5,6,8,7] => 0000001 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,4,5,8,7,1,6] => [1,2,3,4,5,8,6,7] => 0000010 => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,8,6,7,1,5] => [1,2,3,4,8,5,6,7] => 0000100 => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,8,5,6,7,1,4] => [1,2,3,8,4,5,6,7] => 0001000 => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,4,5,6,7,1,3] => [1,2,8,3,4,5,6,7] => 0010000 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8,3,4,5,6,7,1,2] => [1,8,2,3,4,5,6,7] => 0100000 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[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] => [1,9,8,7,6,5,4,3,2] => 01111111 => 7
[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] => [1,8,9,7,6,5,4,3,2] => 00111111 => 6
[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] => [1,7,9,8,6,5,4,3,2] => 00111111 => 6
[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] => [1,7,8,9,6,5,4,3,2] => 00011111 => 5
[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] => [1,6,9,8,7,5,4,3,2] => 00111111 => 6
[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] => [1,6,7,8,9,5,4,3,2] => 00001111 => 4
[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] => [1,9,8,7,5,6,4,3,2] => 01110111 => 6
[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] => [1,5,6,7,8,9,4,3,2] => 00000111 => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [9,1,2,5,6,7,8,3,4] => [1,9,4,5,6,7,8,3,2] => 01000011 => 3
[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] => [1,4,5,6,7,8,9,3,2] => 00000011 => 2
[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] => [1,3,9,8,7,6,5,4,2] => 00111111 => 6
[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] => [1,3,5,7,9,8,6,4,2] => 00001111 => 4
[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] => [1,3,4,5,6,9,8,7,2] => 00000111 => 3
[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] => [1,8,9,3,4,5,6,7,2] => 00100001 => 2
[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] => [1,3,4,5,6,7,9,8,2] => 00000011 => 2
[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] => [1,3,9,4,5,6,7,8,2] => 00100001 => 2
[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] => [1,9,3,4,5,6,7,8,2] => 01000001 => 2
[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] => [1,3,4,5,6,7,8,9,2] => 00000001 => 1
[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] => [1,2,9,8,7,6,5,4,3] => 00111111 => 6
[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] => [1,2,4,6,8,9,7,5,3] => 00000111 => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,5,9,3,6,7,8] => [1,2,4,5,9,8,7,6,3] => 00001111 => 4
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,9,1,5,6,7,8,3,4] => [1,2,9,4,5,6,7,8,3] => 00100001 => 2
[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] => [1,2,4,5,6,7,8,9,3] => 00000001 => 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] => [1,9,8,7,6,5,4,2,3] => 01111110 => 6
[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] => [1,9,8,7,6,5,3,2,4] => 01111110 => 6
[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] => [1,9,8,6,4,2,7,5,3] => 01111011 => 6
[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] => [1,8,6,4,2,9,7,5,3] => 01110111 => 6
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [5,4,1,2,6,7,8,9,3] => [1,5,6,7,8,9,3,2,4] => 00000110 => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [9,4,1,5,6,7,8,2,3] => [1,9,3,2,4,5,6,7,8] => 01100000 => 2
[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] => [1,4,5,6,7,8,9,2,3] => 00000010 => 1
[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] => [1,2,3,9,8,7,6,5,4] => 00011111 => 5
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,8,1,6,7,4,9,5] => [1,2,3,8,9,5,6,7,4] => 00001001 => 2
[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] => [1,2,3,5,6,7,9,8,4] => 00000011 => 2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,9,1,6,7,8,4,5] => [1,2,3,9,5,6,7,8,4] => 00010001 => 2
[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] => [1,2,3,5,6,7,8,9,4] => 00000001 => 1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [2,9,5,1,6,7,8,3,4] => [1,2,9,4,3,5,6,7,8] => 00110000 => 2
[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] => [1,9,8,7,6,5,2,3,4] => 01111100 => 5
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [9,5,4,1,2,3,6,7,8] => [1,9,8,7,6,3,4,2,5] => 01111010 => 5
[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] => [1,5,6,7,8,9,2,3,4] => 00000100 => 1
[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] => [1,2,3,4,9,8,7,6,5] => 00001111 => 4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [2,3,4,9,1,7,8,5,6] => [1,2,3,4,9,6,7,8,5] => 00001001 => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,6,1,7,8,9,5] => [1,2,3,4,6,7,8,9,5] => 00000001 => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [2,3,9,6,1,7,8,4,5] => [1,2,3,9,5,4,6,7,8] => 00011000 => 2
[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] => [1,6,7,8,9,2,3,4,5] => 00001000 => 1
[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] => [1,2,3,4,5,9,8,7,6] => 00000111 => 3
[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] => [1,2,3,4,5,8,9,7,6] => 00000011 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [2,3,4,5,9,1,8,6,7] => [1,2,3,4,5,9,7,8,6] => 00000101 => 2
[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] => [1,2,3,4,5,7,8,9,6] => 00000001 => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [2,3,4,9,7,1,8,5,6] => [1,2,3,4,9,6,5,7,8] => 00001100 => 2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,4,5,6,1,2,9,3] => [1,8,9,3,4,5,6,2,7] => 00100010 => 2
[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] => [1,7,8,9,2,3,4,5,6] => 00010000 => 1
[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] => [1,2,3,4,5,6,9,8,7] => 00000011 => 2
[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] => [1,2,3,4,5,6,8,9,7] => 00000001 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [2,3,4,5,9,8,1,6,7] => [1,2,3,4,5,9,7,6,8] => 00000110 => 2
[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] => [1,8,9,2,3,4,5,6,7] => 00100000 => 1
[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] => [1,2,3,4,5,6,7,9,8] => 00000001 => 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] => [1,2,3,4,5,6,9,7,8] => 00000010 => 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] => [1,2,3,4,5,9,6,7,8] => 00000100 => 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] => [1,2,3,4,9,5,6,7,8] => 00001000 => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,3,9,5,6,7,8,1,4] => [1,2,3,9,4,5,6,7,8] => 00010000 => 1
[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] => [1,2,9,3,4,5,6,7,8] => 00100000 => 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] => [1,9,2,3,4,5,6,7,8] => 01000000 => 1
[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] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[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] => [1,2,3,4,5,6,7,8,10,9] => 000000001 => 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] => [1,3,4,5,6,7,8,9,10,2] => 000000001 => 1
[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] => [1,2,3,4,5,6,7,8,9,11,10] => 0000000001 => 1
[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] => [1,10,3,4,5,6,7,8,9,2] => 010000001 => 2
[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] => [1,3,4,5,6,7,8,9,10,11,2] => 0000000001 => 1
[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] => [1,3,4,5,6,7,8,9,10,11,12,2] => 00000000001 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,9,1,10,8] => [1,2,3,4,5,6,7,9,10,8] => 000000001 => 1
[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] => [1,2,4,5,6,7,8,9,10,3] => 000000001 => 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] => [1,2,3,4,5,6,7,10,9,8] => 000000011 => 2
[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] => [1,3,4,5,6,7,8,10,9,2] => 000000011 => 2
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,10,1,5,6,7,8,9,3,4] => [1,2,10,4,5,6,7,8,9,3] => 001000001 => 2
[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] => [1,4,5,6,7,8,9,10,3,2] => 000000011 => 2
[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] => [1,2,3,4,5,6,7,8,10,11,9] => 0000000001 => 1
[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] => [1,10,8,6,4,2,9,7,5,3] => 011110111 => 7
[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] => [1,4,5,6,7,8,9,10,2,3] => 000000010 => 1
[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] => [1,5,6,7,8,9,10,2,3,4] => 000000100 => 1
[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] => [1,6,7,8,9,10,2,3,4,5] => 000001000 => 1
[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] => [1,7,8,9,10,2,3,4,5,6] => 000010000 => 1
[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] => [1,8,9,10,2,3,4,5,6,7] => 000100000 => 1
[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] => [1,9,10,2,3,4,5,6,7,8] => 001000000 => 1
[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] => [1,2,3,4,5,6,7,10,8,9] => 000000010 => 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] => [1,2,3,4,5,6,10,7,8,9] => 000000100 => 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] => [1,2,3,4,5,10,6,7,8,9] => 000001000 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [2,3,4,10,6,7,8,9,1,5] => [1,2,3,4,10,5,6,7,8,9] => 000010000 => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [2,3,10,5,6,7,8,9,1,4] => [1,2,3,10,4,5,6,7,8,9] => 000100000 => 1
[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] => [1,2,10,3,4,5,6,7,8,9] => 001000000 => 1
[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] => [1,10,2,3,4,5,6,7,8,9] => 010000000 => 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] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[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] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 8
[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] => [1,9,10,8,7,6,5,4,3,2] => 001111111 => 7
[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] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 9
[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] => [1,8,9,10,7,6,5,4,3,2] => 000111111 => 6
[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] => [1,12,11,10,9,8,7,6,5,4,3,2] => 01111111111 => 10
[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] => [1,7,8,9,10,6,5,4,3,2] => 000011111 => 5
[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] => [1,6,7,8,9,10,5,4,3,2] => 000001111 => 4
[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] => [1,5,6,7,8,9,10,4,3,2] => 000000111 => 3
[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] => [1,5,10,9,8,7,6,4,3,2] => 001111111 => 7
[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] => [1,4,10,9,8,7,6,5,3,2] => 001111111 => 7
[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] => [1,3,5,10,9,8,7,6,4,2] => 000111111 => 6
[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] => [1,3,5,7,9,10,8,6,4,2] => 000001111 => 4
[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] => [1,2,10,9,8,7,6,5,4,3] => 001111111 => 7
[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] => [1,2,4,6,8,10,9,7,5,3] => 000001111 => 4
[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] => [1,2,3,10,9,8,7,6,5,4] => 000111111 => 6
[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] => [1,2,3,5,6,7,8,9,10,4] => 000000001 => 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] => [1,2,3,4,10,9,8,7,6,5] => 000011111 => 5
[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] => [1,2,3,4,6,7,8,9,10,5] => 000000001 => 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] => [1,2,3,4,5,10,9,8,7,6] => 000001111 => 4
[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] => [1,2,3,4,5,7,8,9,10,6] => 000000001 => 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] => [1,2,3,4,5,6,10,9,8,7] => 000000111 => 3
[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] => [1,2,3,4,5,6,8,9,10,7] => 000000001 => 1
[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] => [1,8,6,4,2,10,9,7,5,3] => 011101111 => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,7,8,11,10,1,9] => [1,2,3,4,5,6,7,8,11,9,10] => 0000000010 => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,7,8,9,12,11,1,10] => [1,2,3,4,5,6,7,8,9,12,10,11] => 00000000010 => 1
[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] => [1,11,2,3,4,5,6,7,8,9,10] => 0100000000 => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,10,1,7,8,9,5,6] => [1,2,3,4,10,6,7,8,9,5] => 000010001 => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [2,3,4,5,6,10,1,9,7,8] => [1,2,3,4,5,6,10,8,9,7] => 000000101 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [2,3,4,5,10,1,8,9,6,7] => [1,2,3,4,5,10,7,8,9,6] => 000001001 => 2
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,10,1,6,7,8,9,4,5] => [1,2,3,10,5,6,7,8,9,4] => 000100001 => 2
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Description
The number of ones in a binary word.
This is also known as the Hamming weight of the 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
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.