Identifier
-
Mp00119:
Dyck paths
—to 321-avoiding permutation (Krattenthaler)⟶
Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
St000391: Binary words ⟶ ℤ
Values
[1,0,1,0] => [1,2] => [1,2] => 0 => 0
[1,1,0,0] => [2,1] => [2,1] => 1 => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => 00 => 0
[1,0,1,1,0,0] => [1,3,2] => [3,1,2] => 10 => 1
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => 10 => 1
[1,1,0,1,0,0] => [2,3,1] => [2,3,1] => 01 => 2
[1,1,1,0,0,0] => [3,1,2] => [1,3,2] => 01 => 2
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => 000 => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [4,1,2,3] => 100 => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [3,1,2,4] => 100 => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,4,1,2] => 010 => 2
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [1,4,2,3] => 010 => 2
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => 100 => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,4,1,3] => 010 => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,3,1,4] => 010 => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,3,4,1] => 001 => 3
[1,1,0,1,1,0,0,0] => [2,4,1,3] => [4,2,1,3] => 110 => 3
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [1,3,2,4] => 010 => 2
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [1,3,4,2] => 001 => 3
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [3,1,4,2] => 101 => 4
[1,1,1,1,0,0,0,0] => [4,1,2,3] => [1,2,4,3] => 001 => 3
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => 0000 => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [5,1,2,3,4] => 1000 => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [4,1,2,3,5] => 1000 => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [4,5,1,2,3] => 0100 => 2
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [1,5,2,3,4] => 0100 => 2
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [3,1,2,4,5] => 1000 => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [3,5,1,2,4] => 0100 => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [3,4,1,2,5] => 0100 => 2
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [3,4,5,1,2] => 0010 => 3
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [5,3,1,2,4] => 1100 => 3
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [1,4,2,3,5] => 0100 => 2
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [1,4,5,2,3] => 0010 => 3
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [4,1,5,2,3] => 1010 => 4
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [1,2,5,3,4] => 0010 => 3
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => 1000 => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,5,1,3,4] => 0100 => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,4,1,3,5] => 0100 => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,4,5,1,3] => 0010 => 3
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [5,2,1,3,4] => 1100 => 3
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,3,1,4,5] => 0100 => 2
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [2,3,5,1,4] => 0010 => 3
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,3,4,1,5] => 0010 => 3
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,3,4,5,1] => 0001 => 4
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [5,2,3,1,4] => 1010 => 4
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [4,2,1,3,5] => 1100 => 3
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [4,2,5,1,3] => 1010 => 4
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [4,5,2,1,3] => 0110 => 5
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [2,1,5,3,4] => 1010 => 4
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [1,3,2,4,5] => 0100 => 2
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [1,3,5,2,4] => 0010 => 3
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [1,3,4,2,5] => 0010 => 3
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [1,3,4,5,2] => 0001 => 4
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [3,1,5,2,4] => 1010 => 4
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [3,1,4,2,5] => 1010 => 4
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [3,1,4,5,2] => 1001 => 5
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [3,4,1,5,2] => 0101 => 6
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [1,5,3,2,4] => 0110 => 5
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [1,2,4,3,5] => 0010 => 3
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [1,2,4,5,3] => 0001 => 4
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [4,1,2,5,3] => 1001 => 5
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [1,4,2,5,3] => 0101 => 6
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [1,2,3,5,4] => 0001 => 4
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 00000 => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 10000 => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 10000 => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [5,6,1,2,3,4] => 01000 => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => 01000 => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 10000 => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [4,6,1,2,3,5] => 01000 => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [4,5,1,2,3,6] => 01000 => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [4,5,6,1,2,3] => 00100 => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [6,4,1,2,3,5] => 11000 => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [1,5,2,3,4,6] => 01000 => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [1,5,6,2,3,4] => 00100 => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [5,1,6,2,3,4] => 10100 => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 00100 => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 10000 => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [3,6,1,2,4,5] => 01000 => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [3,5,1,2,4,6] => 01000 => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [3,5,6,1,2,4] => 00100 => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [6,3,1,2,4,5] => 11000 => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [3,4,1,2,5,6] => 01000 => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [3,4,6,1,2,5] => 00100 => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [3,4,5,1,2,6] => 00100 => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [3,4,5,6,1,2] => 00010 => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [6,3,4,1,2,5] => 10100 => 4
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [5,3,1,2,4,6] => 11000 => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [5,3,6,1,2,4] => 10100 => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [5,6,3,1,2,4] => 01100 => 5
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [6,1,3,2,4,5] => 10100 => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => 01000 => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [1,4,6,2,3,5] => 00100 => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [1,4,5,2,3,6] => 00100 => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [1,4,5,6,2,3] => 00010 => 4
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [4,1,6,2,3,5] => 10100 => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [4,1,5,2,3,6] => 10100 => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [4,1,5,6,2,3] => 10010 => 5
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [4,5,1,6,2,3] => 01010 => 6
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [1,6,4,2,3,5] => 01100 => 5
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [1,2,5,3,4,6] => 00100 => 3
>>> Load all 2115 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [1,2,5,6,3,4] => 00010 => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [5,1,2,6,3,4] => 10010 => 5
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [1,5,2,6,3,4] => 01010 => 6
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [1,2,3,6,4,5] => 00010 => 4
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 10000 => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,6,1,3,4,5] => 01000 => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,5,1,3,4,6] => 01000 => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,5,6,1,3,4] => 00100 => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [6,2,1,3,4,5] => 11000 => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,4,1,3,5,6] => 01000 => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,4,6,1,3,5] => 00100 => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,4,5,1,3,6] => 00100 => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,4,5,6,1,3] => 00010 => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [6,2,4,1,3,5] => 10100 => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [5,2,1,3,4,6] => 11000 => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [5,2,6,1,3,4] => 10100 => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [5,6,2,1,3,4] => 01100 => 5
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [2,1,6,3,4,5] => 10100 => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => 01000 => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [2,3,6,1,4,5] => 00100 => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [2,3,5,1,4,6] => 00100 => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [2,3,5,6,1,4] => 00010 => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [6,2,3,1,4,5] => 10100 => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => 00100 => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [2,3,4,6,1,5] => 00010 => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => 00010 => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => 00001 => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [6,2,3,4,1,5] => 10010 => 5
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [5,2,3,1,4,6] => 10100 => 4
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [5,2,3,6,1,4] => 10010 => 5
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [5,6,2,3,1,4] => 01010 => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [2,6,3,1,4,5] => 01100 => 5
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => 11000 => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [4,2,6,1,3,5] => 10100 => 4
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => 10100 => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [4,2,5,6,1,3] => 10010 => 5
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [4,6,2,1,3,5] => 01100 => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [4,5,2,1,3,6] => 01100 => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [4,5,2,6,1,3] => 01010 => 6
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [4,5,6,2,1,3] => 00110 => 7
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [6,4,2,1,3,5] => 11100 => 6
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [2,1,5,3,4,6] => 10100 => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [2,1,5,6,3,4] => 10010 => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [2,5,1,6,3,4] => 01010 => 6
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [5,2,1,6,3,4] => 11010 => 7
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [2,1,3,6,4,5] => 10010 => 5
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [1,3,2,4,5,6] => 01000 => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [1,3,6,2,4,5] => 00100 => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [1,3,5,2,4,6] => 00100 => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [1,3,5,6,2,4] => 00010 => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [3,1,6,2,4,5] => 10100 => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [1,3,4,2,5,6] => 00100 => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [1,3,4,6,2,5] => 00010 => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [1,3,4,5,2,6] => 00010 => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [1,3,4,5,6,2] => 00001 => 5
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [6,1,3,4,2,5] => 10010 => 5
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [3,1,5,2,4,6] => 10100 => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [3,1,5,6,2,4] => 10010 => 5
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [3,5,1,6,2,4] => 01010 => 6
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [1,6,3,2,4,5] => 01100 => 5
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => 10100 => 4
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [3,1,4,6,2,5] => 10010 => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [3,1,4,5,2,6] => 10010 => 5
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [3,1,4,5,6,2] => 10001 => 6
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [3,4,1,6,2,5] => 01010 => 6
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [3,4,1,5,2,6] => 01010 => 6
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [3,4,1,5,6,2] => 01001 => 7
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [3,4,5,1,6,2] => 00101 => 8
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [6,3,1,4,2,5] => 11010 => 7
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [1,5,3,2,4,6] => 01100 => 5
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [1,5,3,6,2,4] => 01010 => 6
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [5,3,1,6,2,4] => 11010 => 7
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [5,1,6,3,2,4] => 10110 => 8
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [1,3,2,6,4,5] => 01010 => 6
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [1,2,4,3,5,6] => 00100 => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [1,2,4,6,3,5] => 00010 => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [1,2,4,5,3,6] => 00010 => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [1,2,4,5,6,3] => 00001 => 5
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [4,1,2,6,3,5] => 10010 => 5
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [4,1,2,5,3,6] => 10010 => 5
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [4,1,2,5,6,3] => 10001 => 6
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [4,5,1,2,6,3] => 01001 => 7
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [1,4,2,6,3,5] => 01010 => 6
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [1,4,2,5,3,6] => 01010 => 6
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [1,4,2,5,6,3] => 01001 => 7
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [1,4,5,2,6,3] => 00101 => 8
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => 10101 => 9
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [1,2,6,4,3,5] => 00110 => 7
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [1,2,3,5,4,6] => 00010 => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [1,2,3,5,6,4] => 00001 => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [5,1,2,3,6,4] => 10001 => 6
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [1,5,2,3,6,4] => 01001 => 7
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [1,2,5,3,6,4] => 00101 => 8
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [1,2,3,4,6,5] => 00001 => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 100000 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 100000 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [6,7,1,2,3,4,5] => 010000 => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => [1,7,2,3,4,5,6] => 010000 => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 100000 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [5,7,1,2,3,4,6] => 010000 => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [5,6,1,2,3,4,7] => 010000 => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [5,6,7,1,2,3,4] => 001000 => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6] => [7,5,1,2,3,4,6] => 110000 => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => 010000 => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => [1,6,7,2,3,4,5] => 001000 => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,4,5] => [6,1,7,2,3,4,5] => 101000 => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => 001000 => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 100000 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [4,7,1,2,3,5,6] => 010000 => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [4,6,1,2,3,5,7] => 010000 => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [4,6,7,1,2,3,5] => 001000 => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => [7,4,1,2,3,5,6] => 110000 => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [4,5,1,2,3,6,7] => 010000 => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [4,5,7,1,2,3,6] => 001000 => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [4,5,6,1,2,3,7] => 001000 => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [4,5,6,7,1,2,3] => 000100 => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6] => [7,4,5,1,2,3,6] => 101000 => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,7] => [6,4,1,2,3,5,7] => 110000 => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,7,5] => [6,4,7,1,2,3,5] => 101000 => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,3,5] => [6,7,4,1,2,3,5] => 011000 => 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [7,1,4,2,3,5,6] => 101000 => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => [1,5,2,3,4,6,7] => 010000 => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => [1,5,7,2,3,4,6] => 001000 => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,3,6,4,7] => [1,5,6,2,3,4,7] => 001000 => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,3,6,7,4] => [1,5,6,7,2,3,4] => 000100 => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6] => [5,1,7,2,3,4,6] => 101000 => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => [5,1,6,2,3,4,7] => 101000 => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,3,7,4] => [5,1,6,7,2,3,4] => 100100 => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,3,4] => [5,6,1,7,2,3,4] => 010100 => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [1,7,5,2,3,4,6] => 011000 => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => [1,2,6,3,4,5,7] => 001000 => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => [1,2,6,7,3,4,5] => 000100 => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,3,7,4,5] => [6,1,2,7,3,4,5] => 100100 => 5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,3,4,5] => [1,6,2,7,3,4,5] => 010100 => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => [1,2,3,7,4,5,6] => 000100 => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 100000 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [3,7,1,2,4,5,6] => 010000 => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [3,6,1,2,4,5,7] => 010000 => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [3,6,7,1,2,4,5] => 001000 => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => [7,3,1,2,4,5,6] => 110000 => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [3,5,1,2,4,6,7] => 010000 => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [3,5,7,1,2,4,6] => 001000 => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [3,5,6,1,2,4,7] => 001000 => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [3,5,6,7,1,2,4] => 000100 => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6] => [7,3,5,1,2,4,6] => 101000 => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => [6,3,1,2,4,5,7] => 110000 => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,7,5] => [6,3,7,1,2,4,5] => 101000 => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => [6,7,3,1,2,4,5] => 011000 => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => [7,1,3,2,4,5,6] => 101000 => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [3,4,1,2,5,6,7] => 010000 => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [3,4,7,1,2,5,6] => 001000 => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [3,4,6,1,2,5,7] => 001000 => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [3,4,6,7,1,2,5] => 000100 => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => [7,3,4,1,2,5,6] => 101000 => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [3,4,5,1,2,6,7] => 001000 => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [3,4,5,7,1,2,6] => 000100 => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [3,4,5,6,1,2,7] => 000100 => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [3,4,5,6,7,1,2] => 000010 => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6] => [7,3,4,5,1,2,6] => 100100 => 5
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,7] => [6,3,4,1,2,5,7] => 101000 => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,2,7,5] => [6,3,4,7,1,2,5] => 100100 => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,2,5] => [6,7,3,4,1,2,5] => 010100 => 6
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [3,7,4,1,2,5,6] => 011000 => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,6,7] => [5,3,1,2,4,6,7] => 110000 => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6] => [5,3,7,1,2,4,6] => 101000 => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,6,4,7] => [5,3,6,1,2,4,7] => 101000 => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => [5,3,6,7,1,2,4] => 100100 => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6] => [5,7,3,1,2,4,6] => 011000 => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,2,4,7] => [5,6,3,1,2,4,7] => 011000 => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,2,7,4] => [5,6,3,7,1,2,4] => 010100 => 6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,2,4] => [5,6,7,3,1,2,4] => 001100 => 7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [7,5,3,1,2,4,6] => 111000 => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => [6,1,3,2,4,5,7] => 101000 => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,2,4,7,5] => [6,1,3,7,2,4,5] => 100100 => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,4,5] => [6,7,1,3,2,4,5] => 010100 => 6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,4,5] => [1,6,7,3,2,4,5] => 001100 => 7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => [3,1,2,7,4,5,6] => 100100 => 5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => [1,4,2,3,5,6,7] => 010000 => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => [1,4,7,2,3,5,6] => 001000 => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => [1,4,6,2,3,5,7] => 001000 => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => [1,4,6,7,2,3,5] => 000100 => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => [4,1,7,2,3,5,6] => 101000 => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,3,6,7] => [1,4,5,2,3,6,7] => 001000 => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6] => [1,4,5,7,2,3,6] => 000100 => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,5,6,3,7] => [1,4,5,6,2,3,7] => 000100 => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => [1,4,5,6,7,2,3] => 000010 => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6] => [7,1,4,5,2,3,6] => 100100 => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,7] => [4,1,6,2,3,5,7] => 101000 => 4
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,7,5] => [4,1,6,7,2,3,5] => 100100 => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,7,3,5] => [4,6,1,7,2,3,5] => 010100 => 6
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,7,3,5,6] => [1,7,4,2,3,5,6] => 011000 => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => [4,1,5,2,3,6,7] => 101000 => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => [4,1,5,7,2,3,6] => 100100 => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,2,6,3,7] => [4,1,5,6,2,3,7] => 100100 => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,2,6,7,3] => [4,1,5,6,7,2,3] => 100010 => 6
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6] => [4,5,1,7,2,3,6] => 010100 => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => [4,5,1,6,2,3,7] => 010100 => 6
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,2,7,3] => [4,5,1,6,7,2,3] => 010010 => 7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,2,3] => [4,5,6,1,7,2,3] => 001010 => 8
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [7,4,1,5,2,3,6] => 110100 => 7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,7] => [1,6,4,2,3,5,7] => 011000 => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,7,5] => [1,6,4,7,2,3,5] => 010100 => 6
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,7,3,5] => [6,4,1,7,2,3,5] => 110100 => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => [6,1,7,4,2,3,5] => 101100 => 8
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => [1,7,2,4,3,5,6] => 010100 => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => [1,2,5,3,4,6,7] => 001000 => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => [1,2,5,7,3,4,6] => 000100 => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,6,4,7] => [1,2,5,6,3,4,7] => 000100 => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,6,7,4] => [1,2,5,6,7,3,4] => 000010 => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6] => [5,1,2,7,3,4,6] => 100100 => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,6,3,4,7] => [5,1,2,6,3,4,7] => 100100 => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,7,4] => [5,1,2,6,7,3,4] => 100010 => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,2,6,7,3,4] => [5,6,1,2,7,3,4] => 010010 => 7
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6] => [1,5,2,7,3,4,6] => 010100 => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,2,3,4,7] => [1,5,2,6,3,4,7] => 010100 => 6
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,2,3,7,4] => [1,5,2,6,7,3,4] => 010010 => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,2,7,3,4] => [1,5,6,2,7,3,4] => 001010 => 8
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => [5,1,6,2,7,3,4] => 101010 => 9
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6] => [1,2,7,5,3,4,6] => 001100 => 7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => [1,2,3,6,4,5,7] => 000100 => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [1,2,3,6,7,4,5] => 000010 => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,2,3,7,4,5] => [6,1,2,3,7,4,5] => 100010 => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => [1,6,2,3,7,4,5] => 010010 => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,2,3,4,5] => [1,2,6,3,7,4,5] => 001010 => 8
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => [1,2,3,4,7,5,6] => 000010 => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 100000 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,7,1,3,4,5,6] => 010000 => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,6,1,3,4,5,7] => 010000 => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,6,7,1,3,4,5] => 001000 => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => [7,2,1,3,4,5,6] => 110000 => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,5,1,3,4,6,7] => 010000 => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,5,7,1,3,4,6] => 001000 => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,5,6,1,3,4,7] => 001000 => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,5,6,7,1,3,4] => 000100 => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,4,6] => [7,2,5,1,3,4,6] => 101000 => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => [6,2,1,3,4,5,7] => 110000 => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,4,7,5] => [6,2,7,1,3,4,5] => 101000 => 4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,4,5] => [6,7,2,1,3,4,5] => 011000 => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => [2,1,7,3,4,5,6] => 101000 => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,4,1,3,5,6,7] => 010000 => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,4,7,1,3,5,6] => 001000 => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,4,6,1,3,5,7] => 001000 => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,4,6,7,1,3,5] => 000100 => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => [7,2,4,1,3,5,6] => 101000 => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,4,5,1,3,6,7] => 001000 => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,4,5,7,1,3,6] => 000100 => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,4,5,6,1,3,7] => 000100 => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,4,5,6,7,1,3] => 000010 => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,3,6] => [7,2,4,5,1,3,6] => 100100 => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,7] => [6,2,4,1,3,5,7] => 101000 => 4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,7,5] => [6,2,4,7,1,3,5] => 100100 => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,3,5] => [6,7,2,4,1,3,5] => 010100 => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,3,5,6] => [2,7,4,1,3,5,6] => 011000 => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [5,2,1,3,4,6,7] => 110000 => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => [5,2,7,1,3,4,6] => 101000 => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4,7] => [5,2,6,1,3,4,7] => 101000 => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,3,6,7,4] => [5,2,6,7,1,3,4] => 100100 => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6] => [5,7,2,1,3,4,6] => 011000 => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,3,4,7] => [5,6,2,1,3,4,7] => 011000 => 5
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,3,7,4] => [5,6,2,7,1,3,4] => 010100 => 6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,3,4] => [5,6,7,2,1,3,4] => 001100 => 7
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6] => [7,5,2,1,3,4,6] => 111000 => 6
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => [2,1,6,3,4,5,7] => 101000 => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,3,4,7,5] => [2,1,6,7,3,4,5] => 100100 => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,7,4,5] => [2,6,1,7,3,4,5] => 010100 => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,3,4,5] => [6,2,1,7,3,4,5] => 110100 => 7
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => [2,1,3,7,4,5,6] => 100100 => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => 010000 => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [2,3,7,1,4,5,6] => 001000 => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [2,3,6,1,4,5,7] => 001000 => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [2,3,6,7,1,4,5] => 000100 => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,5,6] => [7,2,3,1,4,5,6] => 101000 => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [2,3,5,1,4,6,7] => 001000 => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [2,3,5,7,1,4,6] => 000100 => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [2,3,5,6,1,4,7] => 000100 => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [2,3,5,6,7,1,4] => 000010 => 5
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6] => [7,2,3,5,1,4,6] => 100100 => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => [6,2,3,1,4,5,7] => 101000 => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,7,5] => [6,2,3,7,1,4,5] => 100100 => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => [6,7,2,3,1,4,5] => 010100 => 6
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,4,5,6] => [2,7,3,1,4,5,6] => 011000 => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => 001000 => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [2,3,4,7,1,5,6] => 000100 => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [2,3,4,6,1,5,7] => 000100 => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [2,3,4,6,7,1,5] => 000010 => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,5,6] => [7,2,3,4,1,5,6] => 100100 => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => 000100 => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [2,3,4,5,7,1,6] => 000010 => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => 000010 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => 000001 => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6] => [7,2,3,4,5,1,6] => 100010 => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,7] => [6,2,3,4,1,5,7] => 100100 => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => [6,2,3,4,7,1,5] => 100010 => 6
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,1,5] => [6,7,2,3,4,1,5] => 010010 => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [2,7,3,4,1,5,6] => 010100 => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,6,7] => [5,2,3,1,4,6,7] => 101000 => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6] => [5,2,3,7,1,4,6] => 100100 => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,6,4,7] => [5,2,3,6,1,4,7] => 100100 => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,6,7,4] => [5,2,3,6,7,1,4] => 100010 => 6
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,7,4,6] => [5,7,2,3,1,4,6] => 010100 => 6
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,1,4,7] => [5,6,2,3,1,4,7] => 010100 => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,1,7,4] => [5,6,2,3,7,1,4] => 010010 => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,1,4] => [5,6,7,2,3,1,4] => 001010 => 8
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [7,5,2,3,1,4,6] => 110100 => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,7] => [2,6,3,1,4,5,7] => 011000 => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,1,4,7,5] => [2,6,3,7,1,4,5] => 010100 => 6
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,4,5] => [2,6,7,3,1,4,5] => 001100 => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,4,5] => [6,2,7,3,1,4,5] => 101100 => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6] => [2,3,1,7,4,5,6] => 010100 => 6
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7] => [4,2,1,3,5,6,7] => 110000 => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,5,7,6] => [4,2,7,1,3,5,6] => 101000 => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,7] => [4,2,6,1,3,5,7] => 101000 => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,7,5] => [4,2,6,7,1,3,5] => 100100 => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,7,5,6] => [4,7,2,1,3,5,6] => 011000 => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,5,3,6,7] => [4,2,5,1,3,6,7] => 101000 => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6] => [4,2,5,7,1,3,6] => 100100 => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,5,6,3,7] => [4,2,5,6,1,3,7] => 100100 => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,3] => [4,2,5,6,7,1,3] => 100010 => 6
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,1,5,7,3,6] => [4,7,2,5,1,3,6] => 010100 => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,7] => [4,6,2,1,3,5,7] => 011000 => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,7,5] => [4,6,2,7,1,3,5] => 010100 => 6
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,7,3,5] => [4,6,7,2,1,3,5] => 001100 => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,7,3,5,6] => [7,4,2,1,3,5,6] => 111000 => 6
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,1,3,6,7] => [4,5,2,1,3,6,7] => 011000 => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6] => [4,5,2,7,1,3,6] => 010100 => 6
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,1,6,3,7] => [4,5,2,6,1,3,7] => 010100 => 6
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,1,6,7,3] => [4,5,2,6,7,1,3] => 010010 => 7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6] => [4,5,7,2,1,3,6] => 001100 => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,1,3,7] => [4,5,6,2,1,3,7] => 001100 => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,1,7,3] => [4,5,6,2,7,1,3] => 001010 => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,1,3] => [4,5,6,7,2,1,3] => 000110 => 9
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [7,4,5,2,1,3,6] => 101100 => 8
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,7] => [6,4,2,1,3,5,7] => 111000 => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,7,5] => [6,4,2,7,1,3,5] => 110100 => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,7,3,5] => [6,4,7,2,1,3,5] => 101100 => 8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,1,3,5] => [6,7,4,2,1,3,5] => 011100 => 9
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6] => [7,2,1,4,3,5,6] => 110100 => 7
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,6,7] => [2,1,5,3,4,6,7] => 101000 => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [2,1,5,7,3,4,6] => 100100 => 5
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,6,4,7] => [2,1,5,6,3,4,7] => 100100 => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,6,7,4] => [2,1,5,6,7,3,4] => 100010 => 6
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6] => [2,5,1,7,3,4,6] => 010100 => 6
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1,6,3,4,7] => [2,5,1,6,3,4,7] => 010100 => 6
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,1,6,3,7,4] => [2,5,1,6,7,3,4] => 010010 => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,1,6,7,3,4] => [2,5,6,1,7,3,4] => 001010 => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,1,7,3,4,6] => [5,2,1,7,3,4,6] => 110100 => 7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,1,3,4,7] => [5,2,1,6,3,4,7] => 110100 => 7
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,1,3,7,4] => [5,2,1,6,7,3,4] => 110010 => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,1,7,3,4] => [5,2,6,1,7,3,4] => 101010 => 9
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,1,3,4] => [5,6,2,1,7,3,4] => 011010 => 10
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,1,3,4,6] => [2,1,7,5,3,4,6] => 101100 => 8
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => [2,1,3,6,4,5,7] => 100100 => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,7,5] => [2,1,3,6,7,4,5] => 100010 => 6
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,1,3,7,4,5] => [2,6,1,3,7,4,5] => 010010 => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,1,7,3,4,5] => [6,2,1,3,7,4,5] => 110010 => 8
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,1,3,4,5] => [2,1,6,3,7,4,5] => 101010 => 9
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6] => [2,1,3,4,7,5,6] => 100010 => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => [1,3,2,4,5,6,7] => 010000 => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => [1,3,7,2,4,5,6] => 001000 => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => [1,3,6,2,4,5,7] => 001000 => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,4,6,7,5] => [1,3,6,7,2,4,5] => 000100 => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,4,7,5,6] => [3,1,7,2,4,5,6] => 101000 => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => [1,3,5,2,4,6,7] => 001000 => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => [1,3,5,7,2,4,6] => 000100 => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,6,4,7] => [1,3,5,6,2,4,7] => 000100 => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,6,7,4] => [1,3,5,6,7,2,4] => 000010 => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6] => [7,1,3,5,2,4,6] => 100100 => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => [3,1,6,2,4,5,7] => 101000 => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,2,6,4,7,5] => [3,1,6,7,2,4,5] => 100100 => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,6,7,4,5] => [3,6,1,7,2,4,5] => 010100 => 6
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => [1,7,3,2,4,5,6] => 011000 => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7] => [1,3,4,2,5,6,7] => 001000 => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,4,2,5,7,6] => [1,3,4,7,2,5,6] => 000100 => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,7] => [1,3,4,6,2,5,7] => 000100 => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,7,5] => [1,3,4,6,7,2,5] => 000010 => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,7,5,6] => [7,1,3,4,2,5,6] => 100100 => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2,6,7] => [1,3,4,5,2,6,7] => 000100 => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6] => [1,3,4,5,7,2,6] => 000010 => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,2,7] => [1,3,4,5,6,2,7] => 000010 => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,2] => [1,3,4,5,6,7,2] => 000001 => 6
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6] => [7,1,3,4,5,2,6] => 100010 => 6
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,7] => [6,1,3,4,2,5,7] => 100100 => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,7,5] => [6,1,3,4,7,2,5] => 100010 => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,4,6,7,2,5] => [6,7,1,3,4,2,5] => 010010 => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,4,7,2,5,6] => [3,7,1,4,2,5,6] => 010100 => 6
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [3,1,5,2,4,6,7] => 101000 => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6] => [3,1,5,7,2,4,6] => 100100 => 5
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4,7] => [3,1,5,6,2,4,7] => 100100 => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,6,7,4] => [3,1,5,6,7,2,4] => 100010 => 6
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6] => [3,5,1,7,2,4,6] => 010100 => 6
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,6,2,4,7] => [3,5,1,6,2,4,7] => 010100 => 6
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,6,2,7,4] => [3,5,1,6,7,2,4] => 010010 => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,6,7,2,4] => [3,5,6,1,7,2,4] => 001010 => 8
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6] => [7,3,1,5,2,4,6] => 110100 => 7
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,7] => [1,6,3,2,4,5,7] => 011000 => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,6,2,4,7,5] => [1,6,3,7,2,4,5] => 010100 => 6
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,7,4,5] => [6,3,1,7,2,4,5] => 110100 => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,6,7,2,4,5] => [6,1,7,3,2,4,5] => 101100 => 8
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6] => [1,3,2,7,4,5,6] => 010100 => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7] => [3,1,4,2,5,6,7] => 101000 => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,5,7,6] => [3,1,4,7,2,5,6] => 100100 => 5
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,7] => [3,1,4,6,2,5,7] => 100100 => 5
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,7,5] => [3,1,4,6,7,2,5] => 100010 => 6
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,7,5,6] => [3,4,1,7,2,5,6] => 010100 => 6
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,1,5,2,6,7] => [3,1,4,5,2,6,7] => 100100 => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6] => [3,1,4,5,7,2,6] => 100010 => 6
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,1,5,6,2,7] => [3,1,4,5,6,2,7] => 100010 => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,2] => [3,1,4,5,6,7,2] => 100001 => 7
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6] => [3,7,1,4,5,2,6] => 010010 => 7
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,7] => [3,4,1,6,2,5,7] => 010100 => 6
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,7,5] => [3,4,1,6,7,2,5] => 010010 => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,7,2,5] => [3,4,6,1,7,2,5] => 001010 => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,1,7,2,5,6] => [7,3,1,4,2,5,6] => 110100 => 7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,1,2,6,7] => [3,4,1,5,2,6,7] => 010100 => 6
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => [3,4,1,5,7,2,6] => 010010 => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,1,6,2,7] => [3,4,1,5,6,2,7] => 010010 => 7
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,1,6,7,2] => [3,4,1,5,6,7,2] => 010001 => 8
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6] => [3,4,5,1,7,2,6] => 001010 => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,1,2,7] => [3,4,5,1,6,2,7] => 001010 => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,1,7,2] => [3,4,5,1,6,7,2] => 001001 => 9
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => [3,4,5,6,1,7,2] => 000101 => 10
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [7,3,4,1,5,2,6] => 101010 => 9
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,7] => [6,3,1,4,2,5,7] => 110100 => 7
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,1,2,7,5] => [6,3,1,4,7,2,5] => 110010 => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,1,7,2,5] => [6,3,4,1,7,2,5] => 101010 => 9
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,1,2,5] => [6,7,3,1,4,2,5] => 011010 => 10
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,1,2,5,6] => [3,1,7,4,2,5,6] => 101100 => 8
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,6,7] => [1,5,3,2,4,6,7] => 011000 => 5
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [1,5,3,7,2,4,6] => 010100 => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,6,4,7] => [1,5,3,6,2,4,7] => 010100 => 6
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,6,7,4] => [1,5,3,6,7,2,4] => 010010 => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6] => [5,3,1,7,2,4,6] => 110100 => 7
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,6,2,4,7] => [5,3,1,6,2,4,7] => 110100 => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,6,2,7,4] => [5,3,1,6,7,2,4] => 110010 => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,6,7,2,4] => [5,3,6,1,7,2,4] => 101010 => 9
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6] => [5,1,7,3,2,4,6] => 101100 => 8
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,1,2,4,7] => [5,1,6,3,2,4,7] => 101100 => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,1,2,7,4] => [5,1,6,3,7,2,4] => 101010 => 9
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,1,7,2,4] => [5,6,3,1,7,2,4] => 011010 => 10
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,1,2,4] => [5,6,1,7,3,2,4] => 010110 => 11
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6] => [1,7,5,3,2,4,6] => 011100 => 9
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,7] => [1,3,2,6,4,5,7] => 010100 => 6
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,7,5] => [1,3,2,6,7,4,5] => 010010 => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,1,2,7,4,5] => [1,3,6,2,7,4,5] => 001010 => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,1,7,2,4,5] => [3,1,6,2,7,4,5] => 101010 => 9
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,1,2,4,5] => [1,6,3,2,7,4,5] => 011010 => 10
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6] => [1,3,2,4,7,5,6] => 010010 => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => [1,2,4,3,5,6,7] => 001000 => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => [1,2,4,7,3,5,6] => 000100 => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => [1,2,4,6,3,5,7] => 000100 => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,7,5] => [1,2,4,6,7,3,5] => 000010 => 5
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => [4,1,2,7,3,5,6] => 100100 => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,5,3,6,7] => [1,2,4,5,3,6,7] => 000100 => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6] => [1,2,4,5,7,3,6] => 000010 => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,5,6,3,7] => [1,2,4,5,6,3,7] => 000010 => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,3] => [1,2,4,5,6,7,3] => 000001 => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6] => [7,1,2,4,5,3,6] => 100010 => 6
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,7] => [4,1,2,6,3,5,7] => 100100 => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,7,5] => [4,1,2,6,7,3,5] => 100010 => 6
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,7,3,5] => [4,6,1,2,7,3,5] => 010010 => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,7,3,5,6] => [1,4,2,7,3,5,6] => 010100 => 6
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [4,1,2,5,3,6,7] => 100100 => 5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6] => [4,1,2,5,7,3,6] => 100010 => 6
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3,7] => [4,1,2,5,6,3,7] => 100010 => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,5,2,6,7,3] => [4,1,2,5,6,7,3] => 100001 => 7
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6] => [4,5,1,2,7,3,6] => 010010 => 7
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,5,6,2,3,7] => [4,5,1,2,6,3,7] => 010010 => 7
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,5,6,2,7,3] => [4,5,1,2,6,7,3] => 010001 => 8
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,2,3] => [4,5,6,1,2,7,3] => 001001 => 9
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6] => [7,4,1,2,5,3,6] => 110010 => 8
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,7] => [1,4,2,6,3,5,7] => 010100 => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,7,5] => [1,4,2,6,7,3,5] => 010010 => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,7,3,5] => [1,4,6,2,7,3,5] => 001010 => 8
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,7,2,3,5] => [4,1,6,2,7,3,5] => 101010 => 9
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6] => [1,2,7,4,3,5,6] => 001100 => 7
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,6,7] => [1,4,2,5,3,6,7] => 010100 => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [1,4,2,5,7,3,6] => 010010 => 7
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,1,2,6,3,7] => [1,4,2,5,6,3,7] => 010010 => 7
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,1,2,6,7,3] => [1,4,2,5,6,7,3] => 010001 => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6] => [1,4,5,2,7,3,6] => 001010 => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,1,6,2,3,7] => [1,4,5,2,6,3,7] => 001010 => 8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,1,6,2,7,3] => [1,4,5,2,6,7,3] => 001001 => 9
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,1,6,7,2,3] => [1,4,5,6,2,7,3] => 000101 => 10
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6] => [4,1,5,2,7,3,6] => 101010 => 9
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,1,2,3,7] => [4,1,5,2,6,3,7] => 101010 => 9
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,1,2,7,3] => [4,1,5,2,6,7,3] => 101001 => 10
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,1,7,2,3] => [4,1,5,6,2,7,3] => 100101 => 11
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,2,3] => [4,5,1,6,2,7,3] => 010101 => 12
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,1,2,3,6] => [1,7,4,2,5,3,6] => 011010 => 10
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,7] => [1,2,6,4,3,5,7] => 001100 => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,7,5] => [1,2,6,4,7,3,5] => 001010 => 8
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,7,3,5] => [6,1,4,2,7,3,5] => 101010 => 9
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,7,2,3,5] => [1,6,4,2,7,3,5] => 011010 => 10
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,1,2,3,5] => [1,6,2,7,4,3,5] => 010110 => 11
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6] => [1,2,4,3,7,5,6] => 001010 => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => [1,2,3,5,4,6,7] => 000100 => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => [1,2,3,5,7,4,6] => 000010 => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,6,4,7] => [1,2,3,5,6,4,7] => 000010 => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => [1,2,3,5,6,7,4] => 000001 => 6
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6] => [5,1,2,3,7,4,6] => 100010 => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,6,3,4,7] => [5,1,2,3,6,4,7] => 100010 => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,6,3,7,4] => [5,1,2,3,6,7,4] => 100001 => 7
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,6,7,3,4] => [5,6,1,2,3,7,4] => 010001 => 8
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6] => [1,5,2,3,7,4,6] => 010010 => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,6,2,3,4,7] => [1,5,2,3,6,4,7] => 010010 => 7
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => [1,5,2,3,6,7,4] => 010001 => 8
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,6,2,7,3,4] => [1,5,6,2,3,7,4] => 001001 => 9
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,6,7,2,3,4] => [5,1,6,2,3,7,4] => 101001 => 10
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6] => [1,2,5,3,7,4,6] => 001010 => 8
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,7] => [1,2,5,3,6,4,7] => 001010 => 8
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,1,2,3,7,4] => [1,2,5,3,6,7,4] => 001001 => 9
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,1,2,7,3,4] => [1,2,5,6,3,7,4] => 000101 => 10
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,1,7,2,3,4] => [5,1,2,6,3,7,4] => 100101 => 11
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,1,2,3,4] => [1,5,2,6,3,7,4] => 010101 => 12
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6] => [1,2,3,7,5,4,6] => 000110 => 9
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [1,2,3,4,6,5,7] => 000010 => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,7,5] => [1,2,3,4,6,7,5] => 000001 => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,7,4,5] => [6,1,2,3,4,7,5] => 100001 => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1,2,7,3,4,5] => [1,6,2,3,4,7,5] => 010001 => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1,7,2,3,4,5] => [1,2,6,3,4,7,5] => 001001 => 9
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5] => [1,2,3,6,4,7,5] => 000101 => 10
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [1,2,3,4,5,7,6] => 000001 => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 1000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [7,8,1,2,3,4,5,6] => 0100000 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => [1,8,2,3,4,5,6,7] => 0100000 => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => 1000000 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [6,8,1,2,3,4,5,7] => 0100000 => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [6,7,1,2,3,4,5,8] => 0100000 => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [6,7,8,1,2,3,4,5] => 0010000 => 3
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,5,7] => [8,6,1,2,3,4,5,7] => 1100000 => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,5,6,8] => [1,7,2,3,4,5,6,8] => 0100000 => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,5,8,6] => [1,7,8,2,3,4,5,6] => 0010000 => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,5,6] => [7,1,8,2,3,4,5,6] => 1010000 => 4
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,5,6,7] => [1,2,8,3,4,5,6,7] => 0010000 => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1000000 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [5,8,1,2,3,4,6,7] => 0100000 => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [5,7,1,2,3,4,6,8] => 0100000 => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [5,7,8,1,2,3,4,6] => 0010000 => 3
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => [8,5,1,2,3,4,6,7] => 1100000 => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [5,6,8,1,2,3,4,7] => 0010000 => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [5,6,7,1,2,3,4,8] => 0010000 => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [5,6,7,8,1,2,3,4] => 0001000 => 4
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,4,7] => [8,5,6,1,2,3,4,7] => 1010000 => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,4,6,8] => [7,5,1,2,3,4,6,8] => 1100000 => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,4,8,6] => [7,5,8,1,2,3,4,6] => 1010000 => 4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,4,6] => [7,8,5,1,2,3,4,6] => 0110000 => 5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,4,6,7] => [8,1,5,2,3,4,6,7] => 1010000 => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,4,5,7,8] => [1,6,2,3,4,5,7,8] => 0100000 => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => [1,6,8,2,3,4,5,7] => 0010000 => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5,8] => [1,6,7,2,3,4,5,8] => 0010000 => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,4,7,8,5] => [1,6,7,8,2,3,4,5] => 0001000 => 4
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,4,8,5,7] => [6,1,8,2,3,4,5,7] => 1010000 => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,4,5,8] => [6,1,7,2,3,4,5,8] => 1010000 => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,4,8,5] => [6,1,7,8,2,3,4,5] => 1001000 => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,4,5] => [6,7,1,8,2,3,4,5] => 0101000 => 6
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,4,5,7] => [1,8,6,2,3,4,5,7] => 0110000 => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,4,5,6,8] => [1,2,7,3,4,5,6,8] => 0010000 => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,4,5,8,6] => [1,2,7,8,3,4,5,6] => 0001000 => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,4,8,5,6] => [7,1,2,8,3,4,5,6] => 1001000 => 5
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,4,5,6] => [1,7,2,8,3,4,5,6] => 0101000 => 6
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 0001000 => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => 1000000 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [4,8,1,2,3,5,6,7] => 0100000 => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [4,7,1,2,3,5,6,8] => 0100000 => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [4,7,8,1,2,3,5,6] => 0010000 => 3
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,6,7] => [8,4,1,2,3,5,6,7] => 1100000 => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [4,6,1,2,3,5,7,8] => 0100000 => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [4,6,8,1,2,3,5,7] => 0010000 => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [4,6,7,1,2,3,5,8] => 0010000 => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [4,6,7,8,1,2,3,5] => 0001000 => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => [7,4,1,2,3,5,6,8] => 1100000 => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,8,6] => [7,4,8,1,2,3,5,6] => 1010000 => 4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,5,6] => [7,8,4,1,2,3,5,6] => 0110000 => 5
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => [8,1,4,2,3,5,6,7] => 1010000 => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [4,5,1,2,3,6,7,8] => 0100000 => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6,8,7] => [4,5,8,1,2,3,6,7] => 0010000 => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [4,5,7,8,1,2,3,6] => 0001000 => 4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,6,7] => [8,4,5,1,2,3,6,7] => 1010000 => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [4,5,6,1,2,3,7,8] => 0010000 => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [4,5,6,8,1,2,3,7] => 0001000 => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [4,5,6,7,1,2,3,8] => 0001000 => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [4,5,6,7,8,1,2,3] => 0000100 => 5
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,3,7] => [8,4,5,6,1,2,3,7] => 1001000 => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,4,5,7,3,6,8] => [7,4,5,1,2,3,6,8] => 1010000 => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,4,5,7,3,8,6] => [7,4,5,8,1,2,3,6] => 1001000 => 5
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,3,6] => [7,8,4,5,1,2,3,6] => 0101000 => 6
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,3,6,7] => [4,8,5,1,2,3,6,7] => 0110000 => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,3,5,7,8] => [6,4,1,2,3,5,7,8] => 1100000 => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,6,3,5,8,7] => [6,4,8,1,2,3,5,7] => 1010000 => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,3,7,5,8] => [6,4,7,1,2,3,5,8] => 1010000 => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,4,6,3,7,8,5] => [6,4,7,8,1,2,3,5] => 1001000 => 5
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,3,8,5,7] => [6,8,4,1,2,3,5,7] => 0110000 => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,6,7,3,8,5] => [6,7,4,8,1,2,3,5] => 0101000 => 6
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,3,5] => [6,7,8,4,1,2,3,5] => 0011000 => 7
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,3,5,7] => [8,6,4,1,2,3,5,7] => 1110000 => 6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,3,5,6,8] => [7,1,4,2,3,5,6,8] => 1010000 => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,3,5,8,6] => [7,1,4,8,2,3,5,6] => 1001000 => 5
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,7,3,8,5,6] => [7,8,1,4,2,3,5,6] => 0101000 => 6
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,3,5,6] => [1,7,8,4,2,3,5,6] => 0011000 => 7
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,3,5,6,7] => [8,1,2,4,3,5,6,7] => 1001000 => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => 0100000 => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,3,4,6,8,7] => [1,5,8,2,3,4,6,7] => 0010000 => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => [1,5,7,2,3,4,6,8] => 0010000 => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,3,4,7,8,6] => [1,5,7,8,2,3,4,6] => 0001000 => 4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => [5,1,8,2,3,4,6,7] => 1010000 => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,4,7,8] => [1,5,6,2,3,4,7,8] => 0010000 => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,8,7] => [1,5,6,8,2,3,4,7] => 0001000 => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,3,6,7,4,8] => [1,5,6,7,2,3,4,8] => 0001000 => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,3,6,7,8,4] => [1,5,6,7,8,2,3,4] => 0000100 => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,8,6] => [5,1,7,8,2,3,4,6] => 1001000 => 5
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,3,7,8,4,6] => [5,7,1,8,2,3,4,6] => 0101000 => 6
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,3,4,7,8] => [5,1,6,2,3,4,7,8] => 1010000 => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,3,7,8,4] => [5,1,6,7,8,2,3,4] => 1000100 => 6
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,5,6,3,8,4,7] => [5,6,1,8,2,3,4,7] => 0101000 => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,5,6,7,3,4,8] => [5,6,1,7,2,3,4,8] => 0101000 => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,3,8,4] => [5,6,1,7,8,2,3,4] => 0100100 => 7
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,3,4] => [5,6,7,1,8,2,3,4] => 0010100 => 8
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,3,4,7] => [8,5,1,6,2,3,4,7] => 1101000 => 7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,3,4,6,8] => [1,7,5,2,3,4,6,8] => 0110000 => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,3,4,8,6] => [1,7,5,8,2,3,4,6] => 0101000 => 6
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,3,8,4,6] => [7,5,1,8,2,3,4,6] => 1101000 => 7
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,5,7,8,3,4,6] => [7,1,8,5,2,3,4,6] => 1011000 => 8
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,3,4,6,7] => [1,8,2,5,3,4,6,7] => 0101000 => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,3,4,5,7,8] => [1,2,6,3,4,5,7,8] => 0010000 => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => [1,2,6,8,3,4,5,7] => 0001000 => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,6,3,4,7,5,8] => [1,2,6,7,3,4,5,8] => 0001000 => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,3,4,7,8,5] => [1,2,6,7,8,3,4,5] => 0000100 => 5
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,3,4,8,5,7] => [6,1,2,8,3,4,5,7] => 1001000 => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,6,3,7,4,5,8] => [6,1,2,7,3,4,5,8] => 1001000 => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,8,5] => [6,1,2,7,8,3,4,5] => 1000100 => 6
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,3,7,8,4,5] => [6,7,1,2,8,3,4,5] => 0100100 => 7
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,3,8,4,5,7] => [1,6,2,8,3,4,5,7] => 0101000 => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,3,4,5,8] => [1,6,2,7,3,4,5,8] => 0101000 => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,6,7,3,4,8,5] => [1,6,2,7,8,3,4,5] => 0100100 => 7
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,6,7,3,8,4,5] => [1,6,7,2,8,3,4,5] => 0010100 => 8
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,3,4,5] => [6,1,7,2,8,3,4,5] => 1010100 => 9
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,6,8,3,4,5,7] => [1,2,8,6,3,4,5,7] => 0011000 => 7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,3,4,5,6,8] => [1,2,3,7,4,5,6,8] => 0001000 => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,3,4,5,8,6] => [1,2,3,7,8,4,5,6] => 0000100 => 5
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,3,4,8,5,6] => [7,1,2,3,8,4,5,6] => 1000100 => 6
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,3,8,4,5,6] => [1,7,2,3,8,4,5,6] => 0100100 => 7
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,3,4,5,6] => [1,2,7,3,8,4,5,6] => 0010100 => 8
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [1,2,3,4,8,5,6,7] => 0000100 => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => 1000000 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [3,8,1,2,4,5,6,7] => 0100000 => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [3,7,1,2,4,5,6,8] => 0100000 => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [3,7,8,1,2,4,5,6] => 0010000 => 3
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => [8,3,1,2,4,5,6,7] => 1100000 => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [3,6,1,2,4,5,7,8] => 0100000 => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [3,6,8,1,2,4,5,7] => 0010000 => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,2,4,6,7,5,8] => [3,6,7,1,2,4,5,8] => 0010000 => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [3,6,7,8,1,2,4,5] => 0001000 => 4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,5,7] => [8,3,6,1,2,4,5,7] => 1010000 => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,5,6,8] => [7,3,1,2,4,5,6,8] => 1100000 => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,5,8,6] => [7,3,8,1,2,4,5,6] => 1010000 => 4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,7,8,5,6] => [7,8,3,1,2,4,5,6] => 0110000 => 5
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => [8,1,3,2,4,5,6,7] => 1010000 => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [3,5,1,2,4,6,7,8] => 0100000 => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [3,5,7,1,2,4,6,8] => 0010000 => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [3,5,7,8,1,2,4,6] => 0001000 => 4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => [8,3,5,1,2,4,6,7] => 1010000 => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [3,5,6,1,2,4,7,8] => 0010000 => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [3,5,6,8,1,2,4,7] => 0001000 => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [3,5,6,7,1,2,4,8] => 0001000 => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [3,5,6,7,8,1,2,4] => 0000100 => 5
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,4,7] => [8,3,5,6,1,2,4,7] => 1001000 => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,4,6,8] => [7,3,5,1,2,4,6,8] => 1010000 => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,8,6] => [7,3,5,8,1,2,4,6] => 1001000 => 5
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,4,6] => [7,8,3,5,1,2,4,6] => 0101000 => 6
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,4,6,7] => [3,8,5,1,2,4,6,7] => 0110000 => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => [6,3,1,2,4,5,7,8] => 1100000 => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5,8] => [6,3,7,1,2,4,5,8] => 1010000 => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,7,8,5] => [6,3,7,8,1,2,4,5] => 1001000 => 5
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,8,5,7] => [6,8,3,1,2,4,5,7] => 0110000 => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,4,5,8] => [6,7,3,1,2,4,5,8] => 0110000 => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,4,8,5] => [6,7,3,8,1,2,4,5] => 0101000 => 6
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,4,5] => [6,7,8,3,1,2,4,5] => 0011000 => 7
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => [7,1,3,2,4,5,6,8] => 1010000 => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,4,5,8,6] => [7,1,3,8,2,4,5,6] => 1001000 => 5
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,8,5,6] => [7,8,1,3,2,4,5,6] => 0101000 => 6
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => [3,1,2,8,4,5,6,7] => 1001000 => 5
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [3,4,1,2,5,6,7,8] => 0100000 => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [3,4,8,1,2,5,6,7] => 0010000 => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [3,4,7,8,1,2,5,6] => 0001000 => 4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,6,7] => [8,3,4,1,2,5,6,7] => 1010000 => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [3,4,6,8,1,2,5,7] => 0001000 => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [3,4,6,7,1,2,5,8] => 0001000 => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [3,4,6,7,8,1,2,5] => 0000100 => 5
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,5,7] => [8,3,4,6,1,2,5,7] => 1001000 => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,4,2,7,5,6,8] => [7,3,4,1,2,5,6,8] => 1010000 => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,8,6] => [7,3,4,8,1,2,5,6] => 1001000 => 5
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,5,6] => [7,8,3,4,1,2,5,6] => 0101000 => 6
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [3,4,5,1,2,6,7,8] => 0010000 => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,5,2,6,8,7] => [3,4,5,8,1,2,6,7] => 0001000 => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [3,4,5,7,1,2,6,8] => 0001000 => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [3,4,5,7,8,1,2,6] => 0000100 => 5
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,6,7] => [8,3,4,5,1,2,6,7] => 1001000 => 5
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [3,4,5,6,1,2,7,8] => 0001000 => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [3,4,5,6,8,1,2,7] => 0000100 => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [3,4,5,6,7,1,2,8] => 0000100 => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [3,4,5,6,7,8,1,2] => 0000010 => 6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,2,7] => [8,3,4,5,6,1,2,7] => 1000100 => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,2,8,6] => [7,3,4,5,8,1,2,6] => 1000100 => 6
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,2,6] => [7,8,3,4,5,1,2,6] => 0100100 => 7
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,3,4,6,2,5,8,7] => [6,3,4,8,1,2,5,7] => 1001000 => 5
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,4,6,2,8,5,7] => [6,8,3,4,1,2,5,7] => 0101000 => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,2,5,8] => [6,7,3,4,1,2,5,8] => 0101000 => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,2,8,5] => [6,7,3,4,8,1,2,5] => 0100100 => 7
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,2,5] => [6,7,8,3,4,1,2,5] => 0010100 => 8
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,8,2,5,7] => [8,6,3,4,1,2,5,7] => 1101000 => 7
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,2,5,8,6] => [3,7,4,8,1,2,5,6] => 0101000 => 6
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,7,8,2,5,6] => [7,3,8,4,1,2,5,6] => 1011000 => 8
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,2,5,6,7] => [1,8,3,4,2,5,6,7] => 0101000 => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,2,4,6,7,8] => [5,3,1,2,4,6,7,8] => 1100000 => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,8] => [5,3,7,1,2,4,6,8] => 1010000 => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,2,4,7,8,6] => [5,3,7,8,1,2,4,6] => 1001000 => 5
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,3,5,2,4,8,6,7] => [5,8,3,1,2,4,6,7] => 0110000 => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,3,5,2,6,4,7,8] => [5,3,6,1,2,4,7,8] => 1010000 => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,2,6,7,4,8] => [5,3,6,7,1,2,4,8] => 1001000 => 5
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,2,6,8,4,7] => [5,8,3,6,1,2,4,7] => 0101000 => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,2,7,4,6,8] => [5,7,3,1,2,4,6,8] => 0110000 => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,8,6] => [5,7,3,8,1,2,4,6] => 0101000 => 6
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,2,7,8,4,6] => [5,7,8,3,1,2,4,6] => 0011000 => 7
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,2,8,4,6,7] => [8,5,3,1,2,4,6,7] => 1110000 => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,2,7,4,8] => [5,6,3,7,1,2,4,8] => 0101000 => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,5,6,2,7,8,4] => [5,6,3,7,8,1,2,4] => 0100100 => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,2,8,4] => [5,6,7,3,8,1,2,4] => 0010100 => 8
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,2,4] => [5,6,7,8,3,1,2,4] => 0001100 => 9
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,2,4,7] => [8,5,6,3,1,2,4,7] => 1011000 => 8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,2,4,6,8] => [7,5,3,1,2,4,6,8] => 1110000 => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,2,4,8,6] => [7,5,3,8,1,2,4,6] => 1101000 => 7
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,2,8,4,6] => [7,5,8,3,1,2,4,6] => 1011000 => 8
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,2,4,6] => [7,8,5,3,1,2,4,6] => 0111000 => 9
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,2,4,6,7] => [8,5,1,3,2,4,6,7] => 1101000 => 7
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,2,7,4,8,5] => [6,7,1,3,8,2,4,5] => 0100100 => 7
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,2,7,8,4,5] => [6,7,8,1,3,2,4,5] => 0010100 => 8
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,6,2,8,4,5,7] => [1,6,8,3,2,4,5,7] => 0011000 => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,6,7,2,4,5,8] => [1,6,7,3,2,4,5,8] => 0011000 => 7
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,2,8,4,5] => [1,6,7,8,3,2,4,5] => 0001100 => 9
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,6,8,2,4,5,7] => [8,1,6,3,2,4,5,7] => 1011000 => 8
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,7,2,4,5,8,6] => [3,1,2,7,8,4,5,6] => 1000100 => 6
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,7,2,4,8,5,6] => [3,7,1,2,8,4,5,6] => 0100100 => 7
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,7,2,8,4,5,6] => [7,3,1,2,8,4,5,6] => 1100100 => 8
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [3,1,2,4,8,5,6,7] => 1000100 => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 0100000 => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,2,3,5,6,8,7] => [1,4,8,2,3,5,6,7] => 0010000 => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,3,5,7,6,8] => [1,4,7,2,3,5,6,8] => 0010000 => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,2,3,5,7,8,6] => [1,4,7,8,2,3,5,6] => 0001000 => 4
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => [4,1,8,2,3,5,6,7] => 1010000 => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => [1,4,6,2,3,5,7,8] => 0010000 => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => [1,4,6,8,2,3,5,7] => 0001000 => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,2,3,6,7,5,8] => [1,4,6,7,2,3,5,8] => 0001000 => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,2,3,6,7,8,5] => [1,4,6,7,8,2,3,5] => 0000100 => 5
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,2,3,6,8,5,7] => [8,1,4,6,2,3,5,7] => 1001000 => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => [4,1,7,2,3,5,6,8] => 1010000 => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,2,3,7,5,8,6] => [4,1,7,8,2,3,5,6] => 1001000 => 5
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,2,3,7,8,5,6] => [4,7,1,8,2,3,5,6] => 0101000 => 6
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => [1,8,4,2,3,5,6,7] => 0110000 => 5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,3,6,7,8] => [1,4,5,2,3,6,7,8] => 0010000 => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,3,6,8,7] => [1,4,5,8,2,3,6,7] => 0001000 => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,8] => [1,4,5,7,2,3,6,8] => 0001000 => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,3,7,8,6] => [1,4,5,7,8,2,3,6] => 0000100 => 5
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,8,6,7] => [8,1,4,5,2,3,6,7] => 1001000 => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3,7,8] => [1,4,5,6,2,3,7,8] => 0001000 => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,2,5,6,3,8,7] => [1,4,5,6,8,2,3,7] => 0000100 => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,2,5,6,7,3,8] => [1,4,5,6,7,2,3,8] => 0000100 => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,8,3] => [1,4,5,6,7,8,2,3] => 0000010 => 6
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,2,5,6,8,3,7] => [8,1,4,5,6,2,3,7] => 1000100 => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,2,5,7,3,6,8] => [7,1,4,5,2,3,6,8] => 1001000 => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,8,6] => [7,1,4,5,8,2,3,6] => 1000100 => 6
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,2,5,7,8,3,6] => [7,8,1,4,5,2,3,6] => 0100100 => 7
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,2,5,8,3,6,7] => [4,8,1,5,2,3,6,7] => 0101000 => 6
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,6,3,5,7,8] => [4,1,6,2,3,5,7,8] => 1010000 => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,6,3,5,8,7] => [4,1,6,8,2,3,5,7] => 1001000 => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5,8] => [4,1,6,7,2,3,5,8] => 1001000 => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,3,7,8,5] => [4,1,6,7,8,2,3,5] => 1000100 => 6
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,8,5,7] => [4,6,1,8,2,3,5,7] => 0101000 => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,2,6,7,3,5,8] => [4,6,1,7,2,3,5,8] => 0101000 => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,6,7,3,8,5] => [4,6,1,7,8,2,3,5] => 0100100 => 7
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,2,6,7,8,3,5] => [4,6,7,1,8,2,3,5] => 0010100 => 8
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,2,6,8,3,5,7] => [8,4,1,6,2,3,5,7] => 1101000 => 7
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,7,3,5,6,8] => [1,7,4,2,3,5,6,8] => 0110000 => 5
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,8,5,6] => [7,4,1,8,2,3,5,6] => 1101000 => 7
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,2,7,8,3,5,6] => [7,1,8,4,2,3,5,6] => 1011000 => 8
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,8,3,5,6,7] => [1,8,2,4,3,5,6,7] => 0101000 => 6
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,2,3,6,7,8] => [4,1,5,2,3,6,7,8] => 1010000 => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,2,3,7,6,8] => [4,1,5,7,2,3,6,8] => 1001000 => 5
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,2,3,8,6,7] => [4,5,1,8,2,3,6,7] => 0101000 => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,2,6,3,7,8] => [4,1,5,6,2,3,7,8] => 1001000 => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,8,7] => [4,1,5,6,8,2,3,7] => 1000100 => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,7,3,8] => [4,1,5,6,7,2,3,8] => 1000100 => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,2,6,7,8,3] => [4,1,5,6,7,8,2,3] => 1000010 => 7
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,6,8,3,7] => [4,8,1,5,6,2,3,7] => 0100100 => 7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,4,5,2,7,3,6,8] => [4,5,1,7,2,3,6,8] => 0101000 => 6
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,8,6] => [4,5,1,7,8,2,3,6] => 0100100 => 7
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,2,8,3,6,7] => [8,4,1,5,2,3,6,7] => 1101000 => 7
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,2,3,7,8] => [4,5,1,6,2,3,7,8] => 0101000 => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,4,5,6,2,3,8,7] => [4,5,1,6,8,2,3,7] => 0100100 => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,2,7,3,8] => [4,5,1,6,7,2,3,8] => 0100100 => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,5,6,2,7,8,3] => [4,5,1,6,7,8,2,3] => 0100010 => 8
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,5,6,2,8,3,7] => [4,5,6,1,8,2,3,7] => 0010100 => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,2,3,8] => [4,5,6,1,7,2,3,8] => 0010100 => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,2,8,3] => [4,5,6,1,7,8,2,3] => 0010010 => 9
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,2,3] => [4,5,6,7,1,8,2,3] => 0001010 => 10
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,4,5,7,2,3,6,8] => [7,4,1,5,2,3,6,8] => 1101000 => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,5,7,2,3,8,6] => [7,4,1,5,8,2,3,6] => 1100100 => 8
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,4,5,7,2,8,3,6] => [7,4,5,1,8,2,3,6] => 1010100 => 9
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,4,5,7,8,2,3,6] => [7,8,4,1,5,2,3,6] => 0110100 => 10
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,2,3,6,7] => [4,1,8,5,2,3,6,7] => 1011000 => 8
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,2,3,5,7,8] => [1,6,4,2,3,5,7,8] => 0110000 => 5
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,4,6,2,3,5,8,7] => [1,6,4,8,2,3,5,7] => 0101000 => 6
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,6,2,3,7,8,5] => [1,6,4,7,8,2,3,5] => 0100100 => 7
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,2,3,8,5,7] => [6,4,1,8,2,3,5,7] => 1101000 => 7
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,2,7,3,5,8] => [6,4,1,7,2,3,5,8] => 1101000 => 7
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,2,7,3,8,5] => [6,4,1,7,8,2,3,5] => 1100100 => 8
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,4,6,2,7,8,3,5] => [6,4,7,1,8,2,3,5] => 1010100 => 9
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,2,8,3,5,7] => [6,1,8,4,2,3,5,7] => 1011000 => 8
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,2,3,5,8] => [6,1,7,4,2,3,5,8] => 1011000 => 8
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,2,3,8,5] => [6,1,7,4,8,2,3,5] => 1010100 => 9
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,2,8,3,5] => [6,7,4,1,8,2,3,5] => 0110100 => 10
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,2,3,5] => [6,7,1,8,4,2,3,5] => 0101100 => 11
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,2,3,5,7] => [1,8,6,4,2,3,5,7] => 0111000 => 9
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,2,3,5,6,8] => [1,7,2,4,3,5,6,8] => 0101000 => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,7,2,3,5,8,6] => [1,7,2,4,8,3,5,6] => 0100100 => 7
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => [1,4,2,3,8,5,6,7] => 0100100 => 7
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,2,3,4,6,7,8] => [1,2,5,3,4,6,7,8] => 0010000 => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,2,3,4,6,8,7] => [1,2,5,8,3,4,6,7] => 0001000 => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => [1,2,5,7,3,4,6,8] => 0001000 => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,2,3,4,7,8,6] => [1,2,5,7,8,3,4,6] => 0000100 => 5
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => [5,1,2,8,3,4,6,7] => 1001000 => 5
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,2,3,6,4,7,8] => [1,2,5,6,3,4,7,8] => 0001000 => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,3,6,7,8,4] => [1,2,5,6,7,8,3,4] => 0000010 => 6
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,2,3,6,8,4,7] => [8,1,2,5,6,3,4,7] => 1000100 => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,5,2,3,7,4,6,8] => [5,1,2,7,3,4,6,8] => 1001000 => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,3,7,4,8,6] => [5,1,2,7,8,3,4,6] => 1000100 => 6
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,2,3,7,8,4,6] => [5,7,1,2,8,3,4,6] => 0100100 => 7
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,2,3,8,4,6,7] => [1,5,2,8,3,4,6,7] => 0101000 => 6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,6,3,4,7,8] => [5,1,2,6,3,4,7,8] => 1001000 => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,6,3,4,8,7] => [5,1,2,6,8,3,4,7] => 1000100 => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4,8] => [5,1,2,6,7,3,4,8] => 1000100 => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,7,8,4] => [5,1,2,6,7,8,3,4] => 1000010 => 7
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,8,4,7] => [5,6,1,2,8,3,4,7] => 0100100 => 7
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,2,6,7,3,4,8] => [5,6,1,2,7,3,4,8] => 0100100 => 7
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,6,7,3,8,4] => [5,6,1,2,7,8,3,4] => 0100010 => 8
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,2,6,7,8,3,4] => [5,6,7,1,2,8,3,4] => 0010010 => 9
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,2,6,8,3,4,7] => [8,5,1,2,6,3,4,7] => 1100100 => 8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,7,3,4,6,8] => [1,5,2,7,3,4,6,8] => 0101000 => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,7,3,4,8,6] => [1,5,2,7,8,3,4,6] => 0100100 => 7
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,8,4,6] => [1,5,7,2,8,3,4,6] => 0010100 => 8
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,2,7,8,3,4,6] => [5,1,7,2,8,3,4,6] => 1010100 => 9
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,8,3,4,6,7] => [1,2,8,5,3,4,6,7] => 0011000 => 7
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,2,3,4,7,8] => [1,5,2,6,3,4,7,8] => 0101000 => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,2,3,4,8,7] => [1,5,2,6,8,3,4,7] => 0100100 => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,5,6,2,3,7,4,8] => [1,5,2,6,7,3,4,8] => 0100100 => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,6,2,3,7,8,4] => [1,5,2,6,7,8,3,4] => 0100010 => 8
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,8,4,7] => [1,5,6,2,8,3,4,7] => 0010100 => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,5,6,2,7,3,4,8] => [1,5,6,2,7,3,4,8] => 0010100 => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,2,7,3,8,4] => [1,5,6,2,7,8,3,4] => 0010010 => 9
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,2,7,8,3,4] => [1,5,6,7,2,8,3,4] => 0001010 => 10
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,5,6,2,8,3,4,7] => [5,1,6,2,8,3,4,7] => 1010100 => 9
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,5,6,7,2,3,4,8] => [5,1,6,2,7,3,4,8] => 1010100 => 9
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,5,6,7,2,8,3,4] => [5,1,6,7,2,8,3,4] => 1001010 => 11
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,5,6,8,2,3,4,7] => [1,8,5,2,6,3,4,7] => 0110100 => 10
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,5,7,2,3,4,6,8] => [1,2,7,5,3,4,6,8] => 0011000 => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,7,2,3,4,8,6] => [1,2,7,5,8,3,4,6] => 0010100 => 8
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,5,7,2,3,8,4,6] => [7,1,5,2,8,3,4,6] => 1010100 => 9
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,2,8,3,4,6] => [1,7,5,2,8,3,4,6] => 0110100 => 10
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,5,7,8,2,3,4,6] => [1,7,2,8,5,3,4,6] => 0101100 => 11
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [1,2,8,3,5,4,6,7] => 0010100 => 8
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,2,3,4,5,7,8] => [1,2,3,6,4,5,7,8] => 0001000 => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => [1,2,3,6,8,4,5,7] => 0000100 => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,2,3,4,7,5,8] => [1,2,3,6,7,4,5,8] => 0000100 => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,3,4,7,8,5] => [1,2,3,6,7,8,4,5] => 0000010 => 6
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,2,3,4,8,5,7] => [6,1,2,3,8,4,5,7] => 1000100 => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,6,2,3,7,4,5,8] => [6,1,2,3,7,4,5,8] => 1000100 => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,8,5] => [6,1,2,3,7,8,4,5] => 1000010 => 7
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,2,3,7,8,4,5] => [6,7,1,2,3,8,4,5] => 0100010 => 8
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,6,2,3,8,4,5,7] => [1,6,2,3,8,4,5,7] => 0100100 => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,7,3,4,5,8] => [1,6,2,3,7,4,5,8] => 0100100 => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,7,3,4,8,5] => [1,6,2,3,7,8,4,5] => 0100010 => 8
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,8,4,5] => [1,6,7,2,3,8,4,5] => 0010010 => 9
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,2,7,8,3,4,5] => [6,1,7,2,3,8,4,5] => 1010010 => 10
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,8,3,4,5,7] => [1,2,6,3,8,4,5,7] => 0010100 => 8
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,2,3,4,5,8] => [1,2,6,3,7,4,5,8] => 0010100 => 8
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,7,2,3,4,8,5] => [1,2,6,3,7,8,4,5] => 0010010 => 9
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,6,7,2,3,8,4,5] => [1,2,6,7,3,8,4,5] => 0001010 => 10
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,2,8,3,4,5] => [6,1,2,7,3,8,4,5] => 1001010 => 11
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,2,3,4,5] => [1,6,2,7,3,8,4,5] => 0101010 => 12
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [1,2,3,8,6,4,5,7] => 0001100 => 9
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,8] => [1,2,3,4,7,5,6,8] => 0000100 => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => [1,2,3,4,7,8,5,6] => 0000010 => 6
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,2,3,4,8,5,6] => [7,1,2,3,4,8,5,6] => 1000010 => 7
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,2,3,8,4,5,6] => [1,7,2,3,4,8,5,6] => 0100010 => 8
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,8,3,4,5,6] => [1,2,7,3,4,8,5,6] => 0010010 => 9
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [1,2,3,7,4,8,5,6] => 0001010 => 10
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [1,2,3,4,5,8,6,7] => 0000010 => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => 1000000 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,8,1,3,4,5,6,7] => 0100000 => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,7,1,3,4,5,6,8] => 0100000 => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [2,7,8,1,3,4,5,6] => 0010000 => 3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,6,7] => [8,2,1,3,4,5,6,7] => 1100000 => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [2,6,1,3,4,5,7,8] => 0100000 => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,6,8,1,3,4,5,7] => 0010000 => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,4,6,7,5,8] => [2,6,7,1,3,4,5,8] => 0010000 => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [2,6,7,8,1,3,4,5] => 0001000 => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,7,5,6,8] => [7,2,1,3,4,5,6,8] => 1100000 => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,5,8,6] => [7,2,8,1,3,4,5,6] => 1010000 => 4
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,5,6] => [7,8,2,1,3,4,5,6] => 0110000 => 5
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,5,6,7] => [2,1,8,3,4,5,6,7] => 1010000 => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [2,5,1,3,4,6,7,8] => 0100000 => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [2,5,8,1,3,4,6,7] => 0010000 => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [2,5,7,8,1,3,4,6] => 0001000 => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [2,5,6,8,1,3,4,7] => 0001000 => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [2,5,6,7,8,1,3,4] => 0000100 => 5
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,3,5,6,8,4,7] => [8,2,5,6,1,3,4,7] => 1001000 => 5
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,7,8,4,6] => [7,8,2,5,1,3,4,6] => 0101000 => 6
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,3,5,8,4,6,7] => [2,8,5,1,3,4,6,7] => 0110000 => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,6,4,5,7,8] => [6,2,1,3,4,5,7,8] => 1100000 => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,4,5,8,7] => [6,2,8,1,3,4,5,7] => 1010000 => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,6,4,7,8,5] => [6,2,7,8,1,3,4,5] => 1001000 => 5
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,4,8,5,7] => [6,8,2,1,3,4,5,7] => 0110000 => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,6,7,4,8,5] => [6,7,2,8,1,3,4,5] => 0101000 => 6
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,4,5] => [6,7,8,2,1,3,4,5] => 0011000 => 7
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,7,4,5,6,8] => [2,1,7,3,4,5,6,8] => 1010000 => 4
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,7,4,8,5,6] => [2,7,1,8,3,4,5,6] => 0101000 => 6
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,4,5,6] => [7,2,1,8,3,4,5,6] => 1101000 => 7
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,4,5,6,7] => [2,1,3,8,4,5,6,7] => 1001000 => 5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,4,1,3,5,6,7,8] => 0100000 => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,4,8,1,3,5,6,7] => 0010000 => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [2,4,7,8,1,3,5,6] => 0001000 => 4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => [8,2,4,1,3,5,6,7] => 1010000 => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,4,6,1,3,5,7,8] => 0010000 => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,4,6,8,1,3,5,7] => 0001000 => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [2,4,6,7,1,3,5,8] => 0001000 => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,4,6,7,8,1,3,5] => 0000100 => 5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,5,7] => [8,2,4,6,1,3,5,7] => 1001000 => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,8,6] => [7,2,4,8,1,3,5,6] => 1001000 => 5
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,5,6] => [7,8,2,4,1,3,5,6] => 0101000 => 6
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => [2,8,4,1,3,5,6,7] => 0110000 => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [2,4,5,1,3,6,7,8] => 0010000 => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [2,4,5,8,1,3,6,7] => 0001000 => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3,7,8,6] => [2,4,5,7,8,1,3,6] => 0000100 => 5
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,4,5,6,3,7,8] => [2,4,5,6,1,3,7,8] => 0001000 => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,4,5,6,8,1,3,7] => 0000100 => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [2,4,5,6,7,1,3,8] => 0000100 => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,4,5,6,7,8,1,3] => 0000010 => 6
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,3,7] => [8,2,4,5,6,1,3,7] => 1000100 => 6
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,3,6] => [7,8,2,4,5,1,3,6] => 0100100 => 7
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,3,6,7] => [2,8,4,5,1,3,6,7] => 0101000 => 6
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,3,5,7,8] => [6,2,4,1,3,5,7,8] => 1010000 => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,3,5,8,7] => [6,2,4,8,1,3,5,7] => 1001000 => 5
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,3,7,8,5] => [6,2,4,7,8,1,3,5] => 1000100 => 6
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,3,8,5,7] => [6,8,2,4,1,3,5,7] => 0101000 => 6
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,3,5] => [6,7,8,2,4,1,3,5] => 0010100 => 8
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,3,5,7] => [8,6,2,4,1,3,5,7] => 1101000 => 7
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,7,3,8,5,6] => [2,7,8,4,1,3,5,6] => 0011000 => 7
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,3,5,6] => [7,2,8,4,1,3,5,6] => 1011000 => 8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => [5,2,1,3,4,6,7,8] => 1100000 => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => [5,2,8,1,3,4,6,7] => 1010000 => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,8,7] => [5,2,6,8,1,3,4,7] => 1001000 => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,3,6,7,4,8] => [5,2,6,7,1,3,4,8] => 1001000 => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,3,6,7,8,4] => [5,2,6,7,8,1,3,4] => 1000100 => 6
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,8,6] => [5,7,2,8,1,3,4,6] => 0101000 => 6
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,8,4,6,7] => [8,5,2,1,3,4,6,7] => 1110000 => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,3,4,7,8] => [5,6,2,1,3,4,7,8] => 0110000 => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,3,4,8,7] => [5,6,2,8,1,3,4,7] => 0101000 => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,5,6,3,7,4,8] => [5,6,2,7,1,3,4,8] => 0101000 => 6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,5,6,7,3,4,8] => [5,6,7,2,1,3,4,8] => 0011000 => 7
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,3,8,4] => [5,6,7,2,8,1,3,4] => 0010100 => 8
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,3,4] => [5,6,7,8,2,1,3,4] => 0001100 => 9
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,3,4,7] => [8,5,6,2,1,3,4,7] => 1011000 => 8
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,3,8,4,6] => [7,5,8,2,1,3,4,6] => 1011000 => 8
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,3,4,6] => [7,8,5,2,1,3,4,6] => 0111000 => 9
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => [2,1,6,8,3,4,5,7] => 1001000 => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,3,4,7,8,5] => [2,1,6,7,8,3,4,5] => 1000100 => 6
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,3,4,8,5,7] => [2,6,1,8,3,4,5,7] => 0101000 => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,7,4,5,8] => [2,6,1,7,3,4,5,8] => 0101000 => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,8,5] => [2,6,1,7,8,3,4,5] => 0100100 => 7
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,3,7,8,4,5] => [2,6,7,1,8,3,4,5] => 0010100 => 8
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,3,4,8,5] => [6,2,1,7,8,3,4,5] => 1100100 => 8
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,3,8,4,5] => [6,2,7,1,8,3,4,5] => 1010100 => 9
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,3,4,5] => [6,7,2,1,8,3,4,5] => 0110100 => 10
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,3,4,5,8,6] => [2,1,3,7,8,4,5,6] => 1000100 => 6
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,3,4,8,5,6] => [2,7,1,3,8,4,5,6] => 0100100 => 7
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,3,4,5,6] => [2,1,7,3,8,4,5,6] => 1010100 => 9
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [2,1,3,4,8,5,6,7] => 1000100 => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => 0100000 => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [2,3,8,1,4,5,6,7] => 0010000 => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [2,3,7,1,4,5,6,8] => 0010000 => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [2,3,7,8,1,4,5,6] => 0001000 => 4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,6,7] => [8,2,3,1,4,5,6,7] => 1010000 => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,4,6,5,7,8] => [2,3,6,1,4,5,7,8] => 0010000 => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [2,3,6,8,1,4,5,7] => 0001000 => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [2,3,6,7,1,4,5,8] => 0001000 => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [2,3,6,7,8,1,4,5] => 0000100 => 5
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,3,1,4,6,8,5,7] => [8,2,3,6,1,4,5,7] => 1001000 => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,7,5,6,8] => [7,2,3,1,4,5,6,8] => 1010000 => 4
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,5,6] => [7,8,2,3,1,4,5,6] => 0101000 => 6
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [2,3,5,1,4,6,7,8] => 0010000 => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [2,3,5,7,1,4,6,8] => 0001000 => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,4,7,8,6] => [2,3,5,7,8,1,4,6] => 0000100 => 5
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [2,3,5,6,1,4,7,8] => 0001000 => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,6,4,8,7] => [2,3,5,6,8,1,4,7] => 0000100 => 5
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [2,3,5,6,7,1,4,8] => 0000100 => 5
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [2,3,5,6,7,8,1,4] => 0000010 => 6
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,4,7] => [8,2,3,5,6,1,4,7] => 1000100 => 6
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,4,6] => [7,8,2,3,5,1,4,6] => 0100100 => 7
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,4,5,7,8] => [6,2,3,1,4,5,7,8] => 1010000 => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,4,5,8,7] => [6,2,3,8,1,4,5,7] => 1001000 => 5
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5,8] => [6,2,3,7,1,4,5,8] => 1001000 => 5
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,7,8,5] => [6,2,3,7,8,1,4,5] => 1000100 => 6
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,8,5,7] => [6,8,2,3,1,4,5,7] => 0101000 => 6
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,6,7,4,5,8] => [6,7,2,3,1,4,5,8] => 0101000 => 6
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,4,8,5] => [6,7,2,3,8,1,4,5] => 0100100 => 7
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,4,5] => [6,7,8,2,3,1,4,5] => 0010100 => 8
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,8,5,6] => [2,7,8,3,1,4,5,6] => 0011000 => 7
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,4,5,6] => [7,2,8,3,1,4,5,6] => 1011000 => 8
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,4,5,6,7] => [2,3,1,8,4,5,6,7] => 0101000 => 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => 0010000 => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [2,3,4,8,1,5,6,7] => 0001000 => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [2,3,4,7,1,5,6,8] => 0001000 => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [2,3,4,7,8,1,5,6] => 0000100 => 5
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,6,7] => [8,2,3,4,1,5,6,7] => 1001000 => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [2,3,4,6,1,5,7,8] => 0001000 => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [2,3,4,6,8,1,5,7] => 0000100 => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [2,3,4,6,7,1,5,8] => 0000100 => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [2,3,4,6,7,8,1,5] => 0000010 => 6
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,5,6,8] => [7,2,3,4,1,5,6,8] => 1001000 => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,8,6] => [7,2,3,4,8,1,5,6] => 1000100 => 6
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,5,6] => [7,8,2,3,4,1,5,6] => 0100100 => 7
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,5,6,7] => [2,8,3,4,1,5,6,7] => 0101000 => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7,8] => 0001000 => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [2,3,4,5,8,1,6,7] => 0000100 => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [2,3,4,5,7,1,6,8] => 0000100 => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [2,3,4,5,7,8,1,6] => 0000010 => 6
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,6,7] => [8,2,3,4,5,1,6,7] => 1000100 => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7,8] => 0000100 => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [2,3,4,5,6,8,1,7] => 0000010 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1,8] => 0000010 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1] => 0000001 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,1,7] => [8,2,3,4,5,6,1,7] => 1000010 => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,1,6,8] => [7,2,3,4,5,1,6,8] => 1000100 => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,1,8,6] => [7,2,3,4,5,8,1,6] => 1000010 => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,1,6] => [7,8,2,3,4,5,1,6] => 0100010 => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,1,6,7] => [2,8,3,4,5,1,6,7] => 0100100 => 7
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,4,6,1,5,8,7] => [6,2,3,4,8,1,5,7] => 1000100 => 6
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,1,7,8,5] => [6,2,3,4,7,8,1,5] => 1000010 => 7
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,1,8,5,7] => [6,8,2,3,4,1,5,7] => 0100100 => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,1,5,8] => [6,7,2,3,4,1,5,8] => 0100100 => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,1,8,5] => [6,7,2,3,4,8,1,5] => 0100010 => 8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,1,5] => [6,7,8,2,3,4,1,5] => 0010010 => 9
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,1,5,7] => [8,6,2,3,4,1,5,7] => 1100100 => 8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,1,5,6,8] => [2,7,3,4,1,5,6,8] => 0101000 => 6
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,1,8,5,6] => [2,7,8,3,4,1,5,6] => 0010100 => 8
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,1,5,6] => [7,2,8,3,4,1,5,6] => 1010100 => 9
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,1,5,6,7] => [2,3,8,4,1,5,6,7] => 0011000 => 7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,1,4,6,7,8] => [5,2,3,1,4,6,7,8] => 1010000 => 4
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,4,8,6,7] => [5,8,2,3,1,4,6,7] => 0101000 => 6
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,1,6,4,7,8] => [5,2,3,6,1,4,7,8] => 1001000 => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,1,6,7,8,4] => [5,2,3,6,7,8,1,4] => 1000010 => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,8,6] => [5,7,2,3,8,1,4,6] => 0100100 => 7
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,1,7,8,4,6] => [5,7,8,2,3,1,4,6] => 0010100 => 8
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,1,7,8,4] => [5,6,2,3,7,8,1,4] => 0100010 => 8
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,1,8,4,7] => [5,6,8,2,3,1,4,7] => 0010100 => 8
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,1,4,8] => [5,6,7,2,3,1,4,8] => 0010100 => 8
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,1,8,4] => [5,6,7,2,3,8,1,4] => 0010010 => 9
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,1,4] => [5,6,7,8,2,3,1,4] => 0001010 => 10
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,1,4,7] => [8,5,6,2,3,1,4,7] => 1010100 => 9
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,5,7,1,4,6,8] => [7,5,2,3,1,4,6,8] => 1101000 => 7
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,1,8,4,6] => [7,5,8,2,3,1,4,6] => 1010100 => 9
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,1,4,5,8,7] => [2,6,3,8,1,4,5,7] => 0101000 => 6
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,6,1,4,7,5,8] => [2,6,3,7,1,4,5,8] => 0101000 => 6
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,1,4,7,8,5] => [2,6,3,7,8,1,4,5] => 0100100 => 7
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,6,1,7,4,5,8] => [2,6,7,3,1,4,5,8] => 0011000 => 7
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,6,1,7,8,4,5] => [2,6,7,8,3,1,4,5] => 0001100 => 9
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,1,8,4,5,7] => [6,2,8,3,1,4,5,7] => 1011000 => 8
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,6,7,1,4,5,8] => [6,2,7,3,1,4,5,8] => 1011000 => 8
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,6,7,1,4,8,5] => [6,2,7,3,8,1,4,5] => 1010100 => 9
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,6,7,1,8,4,5] => [6,2,7,8,3,1,4,5] => 1001100 => 10
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,1,4,5] => [6,7,2,8,3,1,4,5] => 0101100 => 11
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,6,8,1,4,5,7] => [2,8,6,3,1,4,5,7] => 0111000 => 9
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,1,4,5,8,6] => [2,3,1,7,8,4,5,6] => 0100100 => 7
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,7,1,8,4,5,6] => [7,2,3,1,8,4,5,6] => 1010100 => 9
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,7,8,1,4,5,6] => [2,7,3,1,8,4,5,6] => 0110100 => 10
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [2,3,1,4,8,5,6,7] => 0100100 => 7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7,8] => [4,2,1,3,5,6,7,8] => 1100000 => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5,6,8,7] => [4,2,8,1,3,5,6,7] => 1010000 => 4
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,1,3,5,8,6,7] => [4,8,2,1,3,5,6,7] => 0110000 => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,1,3,6,5,7,8] => [4,2,6,1,3,5,7,8] => 1010000 => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [4,2,6,8,1,3,5,7] => 1001000 => 5
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,4,1,3,6,7,5,8] => [4,2,6,7,1,3,5,8] => 1001000 => 5
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,1,3,6,7,8,5] => [4,2,6,7,8,1,3,5] => 1000100 => 6
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,1,3,6,8,5,7] => [4,8,2,6,1,3,5,7] => 0101000 => 6
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,1,3,7,5,8,6] => [4,7,2,8,1,3,5,6] => 0101000 => 6
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,1,3,7,8,5,6] => [4,7,8,2,1,3,5,6] => 0011000 => 7
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,1,3,8,5,6,7] => [8,4,2,1,3,5,6,7] => 1110000 => 6
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,3,6,7,8] => [4,2,5,1,3,6,7,8] => 1010000 => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,3,6,8,7] => [4,2,5,8,1,3,6,7] => 1001000 => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,8] => [4,2,5,7,1,3,6,8] => 1001000 => 5
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,8,6,7] => [4,8,2,5,1,3,6,7] => 0101000 => 6
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,1,5,6,7,3,8] => [4,2,5,6,7,1,3,8] => 1000100 => 6
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,8,3] => [4,2,5,6,7,8,1,3] => 1000010 => 7
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,1,5,6,8,3,7] => [4,8,2,5,6,1,3,7] => 0100100 => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,8,6] => [4,7,2,5,8,1,3,6] => 0100100 => 7
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,1,5,7,8,3,6] => [4,7,8,2,5,1,3,6] => 0010100 => 8
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,4,1,5,8,3,6,7] => [8,4,2,5,1,3,6,7] => 1101000 => 7
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,1,6,3,5,7,8] => [4,6,2,1,3,5,7,8] => 0110000 => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7] => [4,6,2,8,1,3,5,7] => 0101000 => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5,8] => [4,6,2,7,1,3,5,8] => 0101000 => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,7,8,5] => [4,6,2,7,8,1,3,5] => 0100100 => 7
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,7] => [4,6,8,2,1,3,5,7] => 0011000 => 7
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,4,1,6,7,3,5,8] => [4,6,7,2,1,3,5,8] => 0011000 => 7
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,1,6,7,3,8,5] => [4,6,7,2,8,1,3,5] => 0010100 => 8
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,1,6,7,8,3,5] => [4,6,7,8,2,1,3,5] => 0001100 => 9
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,1,6,8,3,5,7] => [8,4,6,2,1,3,5,7] => 1011000 => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,1,7,3,5,8,6] => [7,4,2,8,1,3,5,6] => 1101000 => 7
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,8,5,6] => [7,4,8,2,1,3,5,6] => 1011000 => 8
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,1,7,8,3,5,6] => [7,8,4,2,1,3,5,6] => 0111000 => 9
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,1,3,6,7,8] => [4,5,2,1,3,6,7,8] => 0110000 => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,1,3,7,6,8] => [4,5,2,7,1,3,6,8] => 0101000 => 6
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,1,3,7,8,6] => [4,5,2,7,8,1,3,6] => 0100100 => 7
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,4,5,1,6,3,7,8] => [4,5,2,6,1,3,7,8] => 0101000 => 6
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,8,7] => [4,5,2,6,8,1,3,7] => 0100100 => 7
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,4,5,1,6,7,3,8] => [4,5,2,6,7,1,3,8] => 0100100 => 7
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,1,6,7,8,3] => [4,5,2,6,7,8,1,3] => 0100010 => 8
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,1,6,8,3,7] => [4,5,8,2,6,1,3,7] => 0010100 => 8
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,8,6] => [4,5,7,2,8,1,3,6] => 0010100 => 8
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,1,7,8,3,6] => [4,5,7,8,2,1,3,6] => 0001100 => 9
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,1,3,7,8] => [4,5,6,2,1,3,7,8] => 0011000 => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,4,5,6,1,7,3,8] => [4,5,6,2,7,1,3,8] => 0010100 => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,1,3,8] => [4,5,6,7,2,1,3,8] => 0001100 => 9
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,1,8,3] => [4,5,6,7,2,8,1,3] => 0001010 => 10
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,1,3] => [4,5,6,7,8,2,1,3] => 0000110 => 11
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,1,3,7] => [8,4,5,6,2,1,3,7] => 1001100 => 10
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,4,5,7,1,3,8,6] => [7,4,5,2,8,1,3,6] => 1010100 => 9
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,4,5,7,1,8,3,6] => [7,4,5,8,2,1,3,6] => 1001100 => 10
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,4,5,8,1,3,6,7] => [4,8,5,2,1,3,6,7] => 0111000 => 9
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,1,3,5,7,8] => [6,4,2,1,3,5,7,8] => 1110000 => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,1,3,5,8,7] => [6,4,2,8,1,3,5,7] => 1101000 => 7
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,4,6,1,3,7,5,8] => [6,4,2,7,1,3,5,8] => 1101000 => 7
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,1,3,7,8,5] => [6,4,2,7,8,1,3,5] => 1100100 => 8
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,1,3,8,5,7] => [6,4,8,2,1,3,5,7] => 1011000 => 8
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,1,7,3,8,5] => [6,4,7,2,8,1,3,5] => 1010100 => 9
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,1,7,8,3,5] => [6,4,7,8,2,1,3,5] => 1001100 => 10
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,1,8,3,5,7] => [6,8,4,2,1,3,5,7] => 0111000 => 9
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,1,3,8,5] => [6,7,4,2,8,1,3,5] => 0110100 => 10
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,4,6,7,1,8,3,5] => [6,7,4,8,2,1,3,5] => 0101100 => 11
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,1,3,5] => [6,7,8,4,2,1,3,5] => 0011100 => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,1,3,5,7] => [8,6,4,2,1,3,5,7] => 1111000 => 10
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,4,7,1,3,5,6,8] => [7,2,1,4,3,5,6,8] => 1101000 => 7
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,4,7,1,3,5,8,6] => [7,2,1,4,8,3,5,6] => 1100100 => 8
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,4,7,1,3,8,5,6] => [7,2,4,1,8,3,5,6] => 1010100 => 9
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,4,7,1,8,3,5,6] => [7,8,2,1,4,3,5,6] => 0110100 => 10
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,1,3,5,6] => [2,7,1,8,4,3,5,6] => 0101100 => 11
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,1,3,5,6,7] => [4,2,1,3,8,5,6,7] => 1100100 => 8
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,1,3,4,6,7,8] => [2,1,5,3,4,6,7,8] => 1010000 => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,1,3,4,7,6,8] => [2,1,5,7,3,4,6,8] => 1001000 => 5
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,1,3,4,7,8,6] => [2,1,5,7,8,3,4,6] => 1000100 => 6
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,1,3,4,8,6,7] => [2,5,1,8,3,4,6,7] => 0101000 => 6
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,5,1,3,6,4,7,8] => [2,1,5,6,3,4,7,8] => 1001000 => 5
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,1,3,6,4,8,7] => [2,1,5,6,8,3,4,7] => 1000100 => 6
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,1,3,6,7,4,8] => [2,1,5,6,7,3,4,8] => 1000100 => 6
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,1,3,6,7,8,4] => [2,1,5,6,7,8,3,4] => 1000010 => 7
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,1,3,6,8,4,7] => [2,8,1,5,6,3,4,7] => 0100100 => 7
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,1,3,7,4,8,6] => [2,5,1,7,8,3,4,6] => 0100100 => 7
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,1,3,7,8,4,6] => [2,5,7,1,8,3,4,6] => 0010100 => 8
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,1,3,8,4,6,7] => [5,2,1,8,3,4,6,7] => 1101000 => 7
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,5,1,6,3,4,7,8] => [2,5,1,6,3,4,7,8] => 0101000 => 6
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,5,1,6,3,4,8,7] => [2,5,1,6,8,3,4,7] => 0100100 => 7
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4,8] => [2,5,1,6,7,3,4,8] => 0100100 => 7
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,1,6,3,7,8,4] => [2,5,1,6,7,8,3,4] => 0100010 => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,1,6,7,3,4,8] => [2,5,6,1,7,3,4,8] => 0010100 => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,1,6,7,3,8,4] => [2,5,6,1,7,8,3,4] => 0010010 => 9
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,1,6,7,8,3,4] => [2,5,6,7,1,8,3,4] => 0001010 => 10
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,1,7,3,4,8,6] => [5,2,1,7,8,3,4,6] => 1100100 => 8
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,8,4,6] => [5,2,7,1,8,3,4,6] => 1010100 => 9
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,1,7,8,3,4,6] => [5,7,2,1,8,3,4,6] => 0110100 => 10
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,1,8,3,4,6,7] => [2,1,8,5,3,4,6,7] => 1011000 => 8
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,5,6,1,3,4,7,8] => [5,2,1,6,3,4,7,8] => 1101000 => 7
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,1,3,4,8,7] => [5,2,1,6,8,3,4,7] => 1100100 => 8
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,5,6,1,3,7,8,4] => [5,2,1,6,7,8,3,4] => 1100010 => 9
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,5,6,1,3,8,4,7] => [5,2,6,1,8,3,4,7] => 1010100 => 9
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,1,7,3,4,8] => [5,2,6,1,7,3,4,8] => 1010100 => 9
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,1,8,3,4,7] => [5,6,2,1,8,3,4,7] => 0110100 => 10
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,1,3,8,4] => [5,6,2,1,7,8,3,4] => 0110010 => 11
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,1,8,3,4] => [5,6,2,7,1,8,3,4] => 0101010 => 12
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,1,3,4] => [5,6,7,2,1,8,3,4] => 0011010 => 13
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,5,6,8,1,3,4,7] => [8,5,2,1,6,3,4,7] => 1110100 => 11
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,5,7,1,3,4,8,6] => [2,1,7,5,8,3,4,6] => 1010100 => 9
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,5,7,1,3,8,4,6] => [2,7,5,1,8,3,4,6] => 0110100 => 10
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,5,7,1,8,3,4,6] => [7,5,2,1,8,3,4,6] => 1110100 => 11
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,5,7,8,1,3,4,6] => [7,2,1,8,5,3,4,6] => 1101100 => 12
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,6,1,3,4,5,7,8] => [2,1,3,6,4,5,7,8] => 1001000 => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,1,3,4,7,8,5] => [2,1,3,6,7,8,4,5] => 1000010 => 7
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,1,3,4,8,5,7] => [2,6,1,3,8,4,5,7] => 0100100 => 7
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,6,1,3,7,4,8,5] => [2,6,1,3,7,8,4,5] => 0100010 => 8
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,1,3,8,4,5,7] => [6,2,1,3,8,4,5,7] => 1100100 => 8
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,1,7,3,4,8,5] => [6,2,1,3,7,8,4,5] => 1100010 => 9
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,6,1,7,8,3,4,5] => [6,7,2,1,3,8,4,5] => 0110010 => 11
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,6,1,8,3,4,5,7] => [2,1,6,3,8,4,5,7] => 1010100 => 9
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,1,3,4,5,8] => [2,1,6,3,7,4,5,8] => 1010100 => 9
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,6,7,1,3,4,8,5] => [2,1,6,3,7,8,4,5] => 1010010 => 10
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,6,7,1,3,8,4,5] => [2,1,6,7,3,8,4,5] => 1001010 => 11
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,1,8,3,4,5] => [2,6,1,7,3,8,4,5] => 0101010 => 12
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,1,3,4,5] => [6,2,1,7,3,8,4,5] => 1101010 => 13
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => [2,1,3,8,6,4,5,7] => 1001100 => 10
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,1,3,4,5,6,8] => [2,1,3,4,7,5,6,8] => 1000100 => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,1,3,4,5,8,6] => [2,1,3,4,7,8,5,6] => 1000010 => 7
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,1,3,4,8,5,6] => [2,7,1,3,4,8,5,6] => 0100010 => 8
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,7,1,3,8,4,5,6] => [7,2,1,3,4,8,5,6] => 1100010 => 9
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,1,8,3,4,5,6] => [2,1,7,3,4,8,5,6] => 1010010 => 10
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [2,1,3,7,4,8,5,6] => 1001010 => 11
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [2,1,3,4,5,8,6,7] => 1000010 => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 0100000 => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,6,8,7] => [1,3,8,2,4,5,6,7] => 0010000 => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,2,4,5,7,6,8] => [1,3,7,2,4,5,6,8] => 0010000 => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,2,4,5,7,8,6] => [1,3,7,8,2,4,5,6] => 0001000 => 4
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,8,6,7] => [3,1,8,2,4,5,6,7] => 1010000 => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,4,6,7,8,5] => [1,3,6,7,8,2,4,5] => 0000100 => 5
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,2,4,6,8,5,7] => [8,1,3,6,2,4,5,7] => 1001000 => 5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => [3,1,7,2,4,5,6,8] => 1010000 => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,2,4,7,5,8,6] => [3,1,7,8,2,4,5,6] => 1001000 => 5
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,2,4,7,8,5,6] => [3,7,1,8,2,4,5,6] => 0101000 => 6
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,2,4,8,5,6,7] => [1,8,3,2,4,5,6,7] => 0110000 => 5
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,2,5,4,6,7,8] => [1,3,5,2,4,6,7,8] => 0010000 => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => [1,3,5,7,2,4,6,8] => 0001000 => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,2,5,6,4,7,8] => [1,3,5,6,2,4,7,8] => 0001000 => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,6,7,4,8] => [1,3,5,6,7,2,4,8] => 0000100 => 5
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,5,6,7,8,4] => [1,3,5,6,7,8,2,4] => 0000010 => 6
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,8] => [7,1,3,5,2,4,6,8] => 1001000 => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,2,5,7,4,8,6] => [7,1,3,5,8,2,4,6] => 1000100 => 6
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,2,5,7,8,4,6] => [7,8,1,3,5,2,4,6] => 0100100 => 7
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,2,5,8,4,6,7] => [3,8,1,5,2,4,6,7] => 0101000 => 6
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,2,6,4,5,7,8] => [3,1,6,2,4,5,7,8] => 1010000 => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5,8] => [3,1,6,7,2,4,5,8] => 1001000 => 5
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,1,2,6,4,8,5,7] => [3,6,1,8,2,4,5,7] => 0101000 => 6
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,2,6,7,4,8,5] => [3,6,1,7,8,2,4,5] => 0100100 => 7
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,1,2,6,8,4,5,7] => [8,3,1,6,2,4,5,7] => 1101000 => 7
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => [1,7,3,2,4,5,6,8] => 0110000 => 5
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,2,7,4,8,5,6] => [7,3,1,8,2,4,5,6] => 1101000 => 7
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => [1,3,2,8,4,5,6,7] => 0101000 => 6
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7,8] => [1,3,4,2,5,6,7,8] => 0010000 => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,4,2,5,6,8,7] => [1,3,4,8,2,5,6,7] => 0001000 => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,2,5,7,6,8] => [1,3,4,7,2,5,6,8] => 0001000 => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,2,5,7,8,6] => [1,3,4,7,8,2,5,6] => 0000100 => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,5,7,8] => [1,3,4,6,2,5,7,8] => 0001000 => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7] => [1,3,4,6,8,2,5,7] => 0000100 => 5
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,2,6,7,5,8] => [1,3,4,6,7,2,5,8] => 0000100 => 5
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,2,6,7,8,5] => [1,3,4,6,7,8,2,5] => 0000010 => 6
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,2,6,8,5,7] => [8,1,3,4,6,2,5,7] => 1000100 => 6
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,8,6] => [7,1,3,4,8,2,5,6] => 1000100 => 6
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,2,6,7,8] => [1,3,4,5,2,6,7,8] => 0001000 => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6,8] => [1,3,4,5,7,2,6,8] => 0000100 => 5
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,5,2,7,8,6] => [1,3,4,5,7,8,2,6] => 0000010 => 6
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,6,2,7,8] => [1,3,4,5,6,2,7,8] => 0000100 => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,6,2,8,7] => [1,3,4,5,6,8,2,7] => 0000010 => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,7,2,8] => [1,3,4,5,6,7,2,8] => 0000010 => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,2] => [1,3,4,5,6,7,8,2] => 0000001 => 7
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,4,5,7,2,8,6] => [7,1,3,4,5,8,2,6] => 1000010 => 7
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,4,5,7,8,2,6] => [7,8,1,3,4,5,2,6] => 0100010 => 8
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,4,5,8,2,6,7] => [1,8,3,4,5,2,6,7] => 0100100 => 7
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,4,6,2,5,7,8] => [6,1,3,4,2,5,7,8] => 1001000 => 5
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,5,8,7] => [6,1,3,4,8,2,5,7] => 1000100 => 6
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,4,6,2,7,5,8] => [6,1,3,4,7,2,5,8] => 1000100 => 6
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,4,6,2,8,5,7] => [6,8,1,3,4,2,5,7] => 0100100 => 7
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,4,6,7,2,8,5] => [6,7,1,3,4,8,2,5] => 0100010 => 8
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,4,6,7,8,2,5] => [6,7,8,1,3,4,2,5] => 0010010 => 9
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,4,6,8,2,5,7] => [8,6,1,3,4,2,5,7] => 1100100 => 8
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,4,8,2,5,6,7] => [1,3,8,4,2,5,6,7] => 0011000 => 7
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,5,2,4,6,7,8] => [3,1,5,2,4,6,7,8] => 1010000 => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,5,2,4,6,8,7] => [3,1,5,8,2,4,6,7] => 1001000 => 5
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,2,4,7,6,8] => [3,1,5,7,2,4,6,8] => 1001000 => 5
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,5,2,4,7,8,6] => [3,1,5,7,8,2,4,6] => 1000100 => 6
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,5,2,4,8,6,7] => [3,5,1,8,2,4,6,7] => 0101000 => 6
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,4,7,8] => [3,1,5,6,2,4,7,8] => 1001000 => 5
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7] => [3,1,5,6,8,2,4,7] => 1000100 => 6
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,2,6,7,8,4] => [3,1,5,6,7,8,2,4] => 1000010 => 7
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,2,6,8,4,7] => [3,8,1,5,6,2,4,7] => 0100100 => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,7,4,6,8] => [3,5,1,7,2,4,6,8] => 0101000 => 6
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,8,6] => [3,5,1,7,8,2,4,6] => 0100100 => 7
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,8,4,6,7] => [8,3,1,5,2,4,6,7] => 1101000 => 7
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,5,6,2,4,7,8] => [3,5,1,6,2,4,7,8] => 0101000 => 6
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,1,5,6,2,4,8,7] => [3,5,1,6,8,2,4,7] => 0100100 => 7
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,5,6,2,7,4,8] => [3,5,1,6,7,2,4,8] => 0100100 => 7
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,1,5,6,2,7,8,4] => [3,5,1,6,7,8,2,4] => 0100010 => 8
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,1,5,6,2,8,4,7] => [3,5,6,1,8,2,4,7] => 0010100 => 8
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,5,6,7,2,4,8] => [3,5,6,1,7,2,4,8] => 0010100 => 8
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,1,5,6,7,2,8,4] => [3,5,6,1,7,8,2,4] => 0010010 => 9
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,1,5,6,7,8,2,4] => [3,5,6,7,1,8,2,4] => 0001010 => 10
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,1,5,6,8,2,4,7] => [8,3,5,1,6,2,4,7] => 1010100 => 9
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,5,7,2,4,6,8] => [7,3,1,5,2,4,6,8] => 1101000 => 7
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,1,5,7,2,4,8,6] => [7,3,1,5,8,2,4,6] => 1100100 => 8
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,1,5,7,2,8,4,6] => [7,3,5,1,8,2,4,6] => 1010100 => 9
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,1,5,7,8,2,4,6] => [7,8,3,1,5,2,4,6] => 0110100 => 10
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,1,5,8,2,4,6,7] => [3,1,8,5,2,4,6,7] => 1011000 => 8
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7,8] => [1,6,3,2,4,5,7,8] => 0110000 => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,6,2,4,7,5,8] => [1,6,3,7,2,4,5,8] => 0101000 => 6
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,6,2,4,7,8,5] => [1,6,3,7,8,2,4,5] => 0100100 => 7
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,6,2,4,8,5,7] => [6,3,1,8,2,4,5,7] => 1101000 => 7
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,8,5] => [6,3,1,7,8,2,4,5] => 1100100 => 8
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,2,7,8,4,5] => [6,3,7,1,8,2,4,5] => 1010100 => 9
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,8,4,5,7] => [6,1,8,3,2,4,5,7] => 1011000 => 8
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,6,7,2,4,5,8] => [6,1,7,3,2,4,5,8] => 1011000 => 8
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,1,6,7,2,8,4,5] => [6,7,3,1,8,2,4,5] => 0110100 => 10
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [3,1,6,7,8,2,4,5] => [6,7,1,8,3,2,4,5] => 0101100 => 11
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,1,6,8,2,4,5,7] => [1,8,6,3,2,4,5,7] => 0111000 => 9
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,7,2,4,5,6,8] => [1,3,2,7,4,5,6,8] => 0101000 => 6
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,7,2,4,8,5,6] => [1,3,7,2,8,4,5,6] => 0010100 => 8
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,8,4,5,6] => [3,1,7,2,8,4,5,6] => 1010100 => 9
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,7,8,2,4,5,6] => [1,7,3,2,8,4,5,6] => 0110100 => 10
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [1,3,2,4,8,5,6,7] => 0100100 => 7
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8] => [3,1,4,2,5,6,7,8] => 1010000 => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,5,6,8,7] => [3,1,4,8,2,5,6,7] => 1001000 => 5
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,4,1,2,5,8,6,7] => [3,4,1,8,2,5,6,7] => 0101000 => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [3,1,4,6,8,2,5,7] => 1000100 => 6
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,1,2,6,7,8,5] => [3,1,4,6,7,8,2,5] => 1000010 => 7
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,1,2,6,8,5,7] => [3,8,1,4,6,2,5,7] => 0100100 => 7
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,1,2,7,8,5,6] => [3,4,7,1,8,2,5,6] => 0010100 => 8
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,2,6,7,8] => [3,1,4,5,2,6,7,8] => 1001000 => 5
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,2,6,8,7] => [3,1,4,5,8,2,6,7] => 1000100 => 6
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2,7,8,6] => [3,1,4,5,7,8,2,6] => 1000010 => 7
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2,7,8] => [3,1,4,5,6,2,7,8] => 1000100 => 6
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,6,2,8,7] => [3,1,4,5,6,8,2,7] => 1000010 => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,1,5,6,7,2,8] => [3,1,4,5,6,7,2,8] => 1000010 => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,8,2] => [3,1,4,5,6,7,8,2] => 1000001 => 8
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,1,5,6,8,2,7] => [3,8,1,4,5,6,2,7] => 0100010 => 8
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,1,5,7,2,6,8] => [3,7,1,4,5,2,6,8] => 0100100 => 7
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,1,5,7,8,2,6] => [3,7,8,1,4,5,2,6] => 0010010 => 9
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,1,5,8,2,6,7] => [3,4,8,1,5,2,6,7] => 0010100 => 8
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,1,6,2,5,8,7] => [3,4,1,6,8,2,5,7] => 0100100 => 7
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5,8] => [3,4,1,6,7,2,5,8] => 0100100 => 7
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,2,7,8,5] => [3,4,1,6,7,8,2,5] => 0100010 => 8
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,1,6,7,2,8,5] => [3,4,6,1,7,8,2,5] => 0010010 => 9
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,4,1,6,7,8,2,5] => [3,4,6,7,1,8,2,5] => 0001010 => 10
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,4,1,6,8,2,5,7] => [8,3,4,1,6,2,5,7] => 1010100 => 9
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,4,1,7,2,5,8,6] => [7,3,1,4,8,2,5,6] => 1100100 => 8
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,8,5,6] => [7,3,4,1,8,2,5,6] => 1010100 => 9
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,4,1,7,8,2,5,6] => [7,8,3,1,4,2,5,6] => 0110100 => 10
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,1,8,2,5,6,7] => [3,1,8,4,2,5,6,7] => 1011000 => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,1,2,6,7,8] => [3,4,1,5,2,6,7,8] => 0101000 => 6
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,1,2,6,8,7] => [3,4,1,5,8,2,6,7] => 0100100 => 7
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,5,1,2,7,6,8] => [3,4,1,5,7,2,6,8] => 0100100 => 7
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,5,1,2,7,8,6] => [3,4,1,5,7,8,2,6] => 0100010 => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,1,6,2,7,8] => [3,4,1,5,6,2,7,8] => 0100100 => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,8,7] => [3,4,1,5,6,8,2,7] => 0100010 => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,1,6,7,2,8] => [3,4,1,5,6,7,2,8] => 0100010 => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,1,6,7,8,2] => [3,4,1,5,6,7,8,2] => 0100001 => 9
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,8,6] => [3,4,5,1,7,8,2,6] => 0010010 => 9
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,1,7,8,2,6] => [3,4,5,7,1,8,2,6] => 0001010 => 10
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,1,2,7,8] => [3,4,5,1,6,2,7,8] => 0010100 => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,1,7,2,8] => [3,4,5,1,6,7,2,8] => 0010010 => 9
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,1,7,8,2] => [3,4,5,1,6,7,8,2] => 0010001 => 10
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,1,8,2,7] => [3,4,5,6,1,8,2,7] => 0001010 => 10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,1,2,8] => [3,4,5,6,1,7,2,8] => 0001010 => 10
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,1,8,2] => [3,4,5,6,1,7,8,2] => 0001001 => 11
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,1,2] => [3,4,5,6,7,1,8,2] => 0000101 => 12
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,5,7,1,2,6,8] => [7,3,4,1,5,2,6,8] => 1010100 => 9
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,1,2,6] => [7,8,3,4,1,5,2,6] => 0101010 => 12
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,1,2,6,7] => [3,8,4,1,5,2,6,7] => 0110100 => 10
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,1,2,5,8,7] => [6,3,1,4,8,2,5,7] => 1100100 => 8
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,1,2,7,5,8] => [6,3,1,4,7,2,5,8] => 1100100 => 8
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,1,2,7,8,5] => [6,3,1,4,7,8,2,5] => 1100010 => 9
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,1,7,8,2,5] => [6,3,4,7,1,8,2,5] => 1001010 => 11
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,4,6,1,8,2,5,7] => [6,8,3,1,4,2,5,7] => 0110100 => 10
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,4,6,7,1,2,5,8] => [6,7,3,1,4,2,5,8] => 0110100 => 10
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,1,2,8,5] => [6,7,3,1,4,8,2,5] => 0110010 => 11
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,4,6,7,1,8,2,5] => [6,7,3,4,1,8,2,5] => 0101010 => 12
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,1,2,5] => [6,7,8,3,1,4,2,5] => 0011010 => 13
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,6,8,1,2,5,7] => [8,6,3,1,4,2,5,7] => 1110100 => 11
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,1,2,5,8,6] => [3,1,7,4,8,2,5,6] => 1010100 => 9
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,4,7,1,2,8,5,6] => [3,7,4,1,8,2,5,6] => 0110100 => 10
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,4,7,1,8,2,5,6] => [3,7,1,8,4,2,5,6] => 0101100 => 11
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,7,8,1,2,5,6] => [7,3,1,8,4,2,5,6] => 1101100 => 12
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,1,2,5,6,7] => [3,1,4,2,8,5,6,7] => 1010100 => 9
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,1,2,4,6,7,8] => [1,5,3,2,4,6,7,8] => 0110000 => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,1,2,4,6,8,7] => [1,5,3,8,2,4,6,7] => 0101000 => 6
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,1,2,4,7,6,8] => [1,5,3,7,2,4,6,8] => 0101000 => 6
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,1,2,4,8,6,7] => [5,3,1,8,2,4,6,7] => 1101000 => 7
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,5,1,2,6,4,7,8] => [1,5,3,6,2,4,7,8] => 0101000 => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,1,2,6,4,8,7] => [1,5,3,6,8,2,4,7] => 0100100 => 7
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,1,2,6,7,8,4] => [1,5,3,6,7,8,2,4] => 0100010 => 8
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,1,2,7,4,6,8] => [5,3,1,7,2,4,6,8] => 1101000 => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,1,2,7,4,8,6] => [5,3,1,7,8,2,4,6] => 1100100 => 8
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,1,2,7,8,4,6] => [5,3,7,1,8,2,4,6] => 1010100 => 9
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [3,5,1,2,8,4,6,7] => [5,1,8,3,2,4,6,7] => 1011000 => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,5,1,6,2,4,7,8] => [5,3,1,6,2,4,7,8] => 1101000 => 7
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,1,6,2,4,8,7] => [5,3,1,6,8,2,4,7] => 1100100 => 8
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4,8] => [5,3,1,6,7,2,4,8] => 1100100 => 8
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,1,6,2,7,8,4] => [5,3,1,6,7,8,2,4] => 1100010 => 9
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,8,4,7] => [5,3,6,1,8,2,4,7] => 1010100 => 9
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [3,5,1,6,7,2,4,8] => [5,3,6,1,7,2,4,8] => 1010100 => 9
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,1,6,7,2,8,4] => [5,3,6,1,7,8,2,4] => 1010010 => 10
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,1,6,7,8,2,4] => [5,3,6,7,1,8,2,4] => 1001010 => 11
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,5,1,7,2,4,6,8] => [5,1,7,3,2,4,6,8] => 1011000 => 8
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,8,4,6] => [5,7,3,1,8,2,4,6] => 0110100 => 10
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,5,1,8,2,4,6,7] => [1,8,5,3,2,4,6,7] => 0111000 => 9
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,5,6,1,2,4,7,8] => [5,1,6,3,2,4,7,8] => 1011000 => 8
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,1,2,4,8,7] => [5,1,6,3,8,2,4,7] => 1010100 => 9
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,1,2,7,8,4] => [5,1,6,3,7,8,2,4] => 1010010 => 10
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,5,6,1,2,8,4,7] => [5,6,3,1,8,2,4,7] => 0110100 => 10
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,1,7,2,8,4] => [5,6,3,1,7,8,2,4] => 0110010 => 11
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,1,7,8,2,4] => [5,6,3,7,1,8,2,4] => 0101010 => 12
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,1,2,8,4] => [5,6,1,7,3,8,2,4] => 0101010 => 12
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,1,8,2,4] => [5,6,7,3,1,8,2,4] => 0011010 => 13
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,1,2,4] => [5,6,7,1,8,3,2,4] => 0010110 => 14
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,1,2,4,7] => [8,5,1,6,3,2,4,7] => 1101100 => 12
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,1,2,4,6,8] => [1,7,5,3,2,4,6,8] => 0111000 => 9
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,1,2,4,8,6] => [1,7,5,3,8,2,4,6] => 0110100 => 10
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,1,2,8,4,6] => [7,5,3,1,8,2,4,6] => 1110100 => 11
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,1,2,4,6] => [7,1,8,5,3,2,4,6] => 1011100 => 13
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,1,2,4,6,7] => [1,8,3,2,5,4,6,7] => 0110100 => 10
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,1,2,4,5,7,8] => [1,3,2,6,4,5,7,8] => 0101000 => 6
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,1,2,4,5,8,7] => [1,3,2,6,8,4,5,7] => 0100100 => 7
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,6,1,2,4,7,5,8] => [1,3,2,6,7,4,5,8] => 0100100 => 7
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,1,2,4,7,8,5] => [1,3,2,6,7,8,4,5] => 0100010 => 8
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,6,1,2,7,4,5,8] => [1,3,6,2,7,4,5,8] => 0010100 => 8
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,1,2,7,4,8,5] => [1,3,6,2,7,8,4,5] => 0010010 => 9
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,1,2,8,4,5,7] => [3,1,6,2,8,4,5,7] => 1010100 => 9
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [3,6,1,7,2,4,5,8] => [3,1,6,2,7,4,5,8] => 1010100 => 9
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,6,1,7,2,8,4,5] => [3,1,6,7,2,8,4,5] => 1001010 => 11
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,1,7,8,2,4,5] => [3,6,1,7,2,8,4,5] => 0101010 => 12
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,6,1,8,2,4,5,7] => [1,6,3,2,8,4,5,7] => 0110100 => 10
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [3,6,7,1,2,4,5,8] => [1,6,3,2,7,4,5,8] => 0110100 => 10
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,6,7,1,2,4,8,5] => [1,6,3,2,7,8,4,5] => 0110010 => 11
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,6,7,1,2,8,4,5] => [1,6,3,7,2,8,4,5] => 0101010 => 12
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,6,7,8,1,2,4,5] => [6,1,7,3,2,8,4,5] => 1011010 => 14
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,1,2,4,5,7] => [1,3,2,8,6,4,5,7] => 0101100 => 11
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,7,1,2,4,5,8,6] => [1,3,2,4,7,8,5,6] => 0100010 => 8
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,1,2,4,8,5,6] => [1,3,7,2,4,8,5,6] => 0010010 => 9
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,1,8,2,4,5,6] => [1,7,3,2,4,8,5,6] => 0110010 => 11
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,1,2,4,5,6] => [1,3,2,7,4,8,5,6] => 0101010 => 12
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [1,3,2,4,5,8,6,7] => 0100010 => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => 0010000 => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,2,3,5,6,8,7] => [1,2,4,8,3,5,6,7] => 0001000 => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,3,5,7,6,8] => [1,2,4,7,3,5,6,8] => 0001000 => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,3,5,7,8,6] => [1,2,4,7,8,3,5,6] => 0000100 => 5
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,3,5,8,6,7] => [4,1,2,8,3,5,6,7] => 1001000 => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,3,6,5,7,8] => [1,2,4,6,3,5,7,8] => 0001000 => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => [1,2,4,6,8,3,5,7] => 0000100 => 5
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,3,6,7,5,8] => [1,2,4,6,7,3,5,8] => 0000100 => 5
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,3,6,7,8,5] => [1,2,4,6,7,8,3,5] => 0000010 => 6
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,1,2,3,6,8,5,7] => [8,1,2,4,6,3,5,7] => 1000100 => 6
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => [4,1,2,7,3,5,6,8] => 1001000 => 5
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,1,2,3,7,5,8,6] => [4,1,2,7,8,3,5,6] => 1000100 => 6
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,1,2,3,7,8,5,6] => [4,7,1,2,8,3,5,6] => 0100100 => 7
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => [1,4,2,8,3,5,6,7] => 0101000 => 6
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6,8] => [1,2,4,5,7,3,6,8] => 0000100 => 5
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,5,3,7,8,6] => [1,2,4,5,7,8,3,6] => 0000010 => 6
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,1,2,5,3,8,6,7] => [8,1,2,4,5,3,6,7] => 1000100 => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,2,5,6,3,7,8] => [1,2,4,5,6,3,7,8] => 0000100 => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,1,2,5,6,3,8,7] => [1,2,4,5,6,8,3,7] => 0000010 => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,6,7,3,8] => [1,2,4,5,6,7,3,8] => 0000010 => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,8,3] => [1,2,4,5,6,7,8,3] => 0000001 => 7
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,1,2,5,6,8,3,7] => [8,1,2,4,5,6,3,7] => 1000010 => 7
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,1,2,5,8,3,6,7] => [4,8,1,2,5,3,6,7] => 0100100 => 7
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5,8] => [4,1,2,6,7,3,5,8] => 1000100 => 6
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,1,2,6,3,8,5,7] => [4,6,1,2,8,3,5,7] => 0100100 => 7
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,6,7,3,5,8] => [4,6,1,2,7,3,5,8] => 0100100 => 7
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,1,2,6,7,3,8,5] => [4,6,1,2,7,8,3,5] => 0100010 => 8
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,1,2,6,8,3,5,7] => [8,4,1,2,6,3,5,7] => 1100100 => 8
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,7,3,5,6,8] => [1,4,2,7,3,5,6,8] => 0101000 => 6
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,1,2,7,3,5,8,6] => [1,4,2,7,8,3,5,6] => 0100100 => 7
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [4,1,2,7,3,8,5,6] => [1,4,7,2,8,3,5,6] => 0010100 => 8
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,1,2,7,8,3,5,6] => [4,1,7,2,8,3,5,6] => 1010100 => 9
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,1,2,8,3,5,6,7] => [1,2,8,4,3,5,6,7] => 0011000 => 7
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,3,6,7,8] => [4,1,2,5,3,6,7,8] => 1001000 => 5
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,1,5,2,3,6,8,7] => [4,1,2,5,8,3,6,7] => 1000100 => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,1,5,2,3,7,6,8] => [4,1,2,5,7,3,6,8] => 1000100 => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,5,2,3,7,8,6] => [4,1,2,5,7,8,3,6] => 1000010 => 7
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,5,2,3,8,6,7] => [4,5,1,2,8,3,6,7] => 0100100 => 7
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,3,7,8] => [4,1,2,5,6,3,7,8] => 1000100 => 6
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7] => [4,1,2,5,6,8,3,7] => 1000010 => 7
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,2,6,7,3,8] => [4,1,2,5,6,7,3,8] => 1000010 => 7
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,2,6,7,8,3] => [4,1,2,5,6,7,8,3] => 1000001 => 8
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,2,6,8,3,7] => [4,8,1,2,5,6,3,7] => 0100010 => 8
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,7,3,6,8] => [4,5,1,2,7,3,6,8] => 0100100 => 7
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,8,6] => [4,5,1,2,7,8,3,6] => 0100010 => 8
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,2,7,8,3,6] => [4,5,7,1,2,8,3,6] => 0010010 => 9
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,8,3,6,7] => [8,4,1,2,5,3,6,7] => 1100100 => 8
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,1,5,6,2,3,8,7] => [4,5,1,2,6,8,3,7] => 0100010 => 8
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,1,5,6,2,7,3,8] => [4,5,1,2,6,7,3,8] => 0100010 => 8
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [4,1,5,6,2,8,3,7] => [4,5,6,1,2,8,3,7] => 0010010 => 9
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [4,1,5,6,7,2,3,8] => [4,5,6,1,2,7,3,8] => 0010010 => 9
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,5,6,7,2,8,3] => [4,5,6,1,2,7,8,3] => 0010001 => 10
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,8,2,3] => [4,5,6,7,1,2,8,3] => 0001001 => 11
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,5,6,8,2,3,7] => [8,4,5,1,2,6,3,7] => 1010010 => 10
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,1,5,7,2,3,8,6] => [7,4,1,2,5,8,3,6] => 1100010 => 9
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,5,7,2,8,3,6] => [7,4,5,1,2,8,3,6] => 1010010 => 10
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,1,5,7,8,2,3,6] => [7,8,4,1,2,5,3,6] => 0110010 => 11
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7,8] => [1,4,2,6,3,5,7,8] => 0101000 => 6
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,1,6,2,3,5,8,7] => [1,4,2,6,8,3,5,7] => 0100100 => 7
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,1,6,2,3,7,5,8] => [1,4,2,6,7,3,5,8] => 0100100 => 7
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,1,6,2,3,7,8,5] => [1,4,2,6,7,8,3,5] => 0100010 => 8
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,1,6,2,3,8,5,7] => [1,4,6,2,8,3,5,7] => 0010100 => 8
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,7,3,5,8] => [1,4,6,2,7,3,5,8] => 0010100 => 8
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,8,5] => [1,4,6,2,7,8,3,5] => 0010010 => 9
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,2,7,8,3,5] => [1,4,6,7,2,8,3,5] => 0001010 => 10
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,8,3,5,7] => [4,1,6,2,8,3,5,7] => 1010100 => 9
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [4,1,6,7,2,3,5,8] => [4,1,6,2,7,3,5,8] => 1010100 => 9
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,1,6,7,8,2,3,5] => [4,6,1,7,2,8,3,5] => 0101010 => 12
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,1,6,8,2,3,5,7] => [1,8,4,2,6,3,5,7] => 0110100 => 10
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,1,7,2,3,5,6,8] => [1,2,7,4,3,5,6,8] => 0011000 => 7
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,1,7,2,3,5,8,6] => [1,2,7,4,8,3,5,6] => 0010100 => 8
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,1,7,8,2,3,5,6] => [1,7,2,8,4,3,5,6] => 0101100 => 11
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [1,2,4,3,8,5,6,7] => 0010100 => 8
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,1,2,3,6,7,8] => [1,4,2,5,3,6,7,8] => 0101000 => 6
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,5,1,2,3,6,8,7] => [1,4,2,5,8,3,6,7] => 0100100 => 7
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,5,1,2,3,7,6,8] => [1,4,2,5,7,3,6,8] => 0100100 => 7
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,5,1,2,3,7,8,6] => [1,4,2,5,7,8,3,6] => 0100010 => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,1,2,3,8,6,7] => [1,4,5,2,8,3,6,7] => 0010100 => 8
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,1,2,6,3,8,7] => [1,4,2,5,6,8,3,7] => 0100010 => 8
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,5,1,2,6,7,3,8] => [1,4,2,5,6,7,3,8] => 0100010 => 8
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,1,2,6,7,8,3] => [1,4,2,5,6,7,8,3] => 0100001 => 9
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,5,1,2,6,8,3,7] => [1,4,8,2,5,6,3,7] => 0010010 => 9
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,1,2,7,3,6,8] => [1,4,5,2,7,3,6,8] => 0010100 => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,5,1,2,7,3,8,6] => [1,4,5,2,7,8,3,6] => 0010010 => 9
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,1,2,8,3,6,7] => [4,1,5,2,8,3,6,7] => 1010100 => 9
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,5,1,6,2,3,7,8] => [1,4,5,2,6,3,7,8] => 0010100 => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,1,6,2,3,8,7] => [1,4,5,2,6,8,3,7] => 0010010 => 9
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3,8] => [1,4,5,2,6,7,3,8] => 0010010 => 9
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,5,1,6,2,7,8,3] => [1,4,5,2,6,7,8,3] => 0010001 => 10
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,8,3,7] => [1,4,5,6,2,8,3,7] => 0001010 => 10
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,5,1,6,7,2,3,8] => [1,4,5,6,2,7,3,8] => 0001010 => 10
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,1,6,7,2,8,3] => [1,4,5,6,2,7,8,3] => 0001001 => 11
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,1,6,7,8,2,3] => [1,4,5,6,7,2,8,3] => 0000101 => 12
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,5,1,7,2,3,6,8] => [4,1,5,2,7,3,6,8] => 1010100 => 9
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,5,1,7,2,3,8,6] => [4,1,5,2,7,8,3,6] => 1010010 => 10
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,8,3,6] => [4,1,5,7,2,8,3,6] => 1001010 => 11
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,1,7,8,2,3,6] => [4,5,1,7,2,8,3,6] => 0101010 => 12
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,1,8,2,3,6,7] => [1,8,4,2,5,3,6,7] => 0110100 => 10
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,1,2,3,7,8] => [4,1,5,2,6,3,7,8] => 1010100 => 9
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,1,2,3,8,7] => [4,1,5,2,6,8,3,7] => 1010010 => 10
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,1,2,7,8,3] => [4,1,5,2,6,7,8,3] => 1010001 => 11
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,1,2,8,3,7] => [4,1,5,6,2,8,3,7] => 1001010 => 11
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,5,6,1,7,8,2,3] => [4,1,5,6,7,2,8,3] => 1000101 => 13
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,1,8,2,3,7] => [4,5,1,6,2,8,3,7] => 0101010 => 12
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,1,2,3,8] => [4,5,1,6,2,7,3,8] => 0101010 => 12
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,1,2,8,3] => [4,5,1,6,2,7,8,3] => 0101001 => 13
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,1,8,2,3] => [4,5,1,6,7,2,8,3] => 0100101 => 14
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,1,2,3] => [4,5,6,1,7,2,8,3] => 0010101 => 15
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,1,2,3,7] => [8,4,1,5,2,6,3,7] => 1101010 => 13
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,1,2,3,6,8] => [1,7,4,2,5,3,6,8] => 0110100 => 10
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,5,7,1,2,3,8,6] => [1,7,4,2,5,8,3,6] => 0110010 => 11
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,5,7,1,2,8,3,6] => [4,7,1,5,2,8,3,6] => 0101010 => 12
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,5,7,8,1,2,3,6] => [7,1,8,4,2,5,3,6] => 1011010 => 14
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => [1,4,2,8,5,3,6,7] => 0101100 => 11
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,6,1,2,3,5,7,8] => [1,2,6,4,3,5,7,8] => 0011000 => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,6,1,2,3,7,5,8] => [1,2,6,4,7,3,5,8] => 0010100 => 8
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,6,1,2,3,7,8,5] => [1,2,6,4,7,8,3,5] => 0010010 => 9
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,1,2,3,8,5,7] => [6,1,4,2,8,3,5,7] => 1010100 => 9
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,1,2,7,3,8,5] => [6,1,4,2,7,8,3,5] => 1010010 => 10
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,6,1,2,7,8,3,5] => [6,1,4,7,2,8,3,5] => 1001010 => 11
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,6,1,2,8,3,5,7] => [1,6,4,2,8,3,5,7] => 0110100 => 10
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,1,7,2,3,5,8] => [1,6,4,2,7,3,5,8] => 0110100 => 10
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,1,7,2,3,8,5] => [1,6,4,2,7,8,3,5] => 0110010 => 11
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,1,8,2,3,5,7] => [1,6,2,8,4,3,5,7] => 0101100 => 11
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,1,2,3,8,5] => [1,6,2,7,4,8,3,5] => 0101010 => 12
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,6,7,1,2,8,3,5] => [1,6,7,4,2,8,3,5] => 0011010 => 13
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,1,8,2,3,5] => [6,1,7,4,2,8,3,5] => 1011010 => 14
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,1,2,3,5] => [6,1,7,2,8,4,3,5] => 1010110 => 15
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,1,2,3,5,7] => [1,2,8,6,4,3,5,7] => 0011100 => 12
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,1,2,3,5,6,8] => [1,2,4,3,7,5,6,8] => 0010100 => 8
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,1,2,3,5,8,6] => [1,2,4,3,7,8,5,6] => 0010010 => 9
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,1,2,3,8,5,6] => [1,2,4,7,3,8,5,6] => 0001010 => 10
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,1,8,2,3,5,6] => [1,4,2,7,3,8,5,6] => 0101010 => 12
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [1,2,4,3,5,8,6,7] => 0010010 => 9
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8] => [1,2,3,5,4,6,7,8] => 0001000 => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,4,6,8,7] => [1,2,3,5,8,4,6,7] => 0000100 => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,1,2,3,4,7,6,8] => [1,2,3,5,7,4,6,8] => 0000100 => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,1,2,3,4,7,8,6] => [1,2,3,5,7,8,4,6] => 0000010 => 6
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => [5,1,2,3,8,4,6,7] => 1000100 => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,2,3,6,4,7,8] => [1,2,3,5,6,4,7,8] => 0000100 => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,1,2,3,6,4,8,7] => [1,2,3,5,6,8,4,7] => 0000010 => 6
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,2,3,6,7,4,8] => [1,2,3,5,6,7,4,8] => 0000010 => 6
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,2,3,6,7,8,4] => [1,2,3,5,6,7,8,4] => 0000001 => 7
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,2,3,6,8,4,7] => [8,1,2,3,5,6,4,7] => 1000010 => 7
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,1,2,3,7,4,8,6] => [5,1,2,3,7,8,4,6] => 1000010 => 7
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,1,2,3,7,8,4,6] => [5,7,1,2,3,8,4,6] => 0100010 => 8
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,1,2,3,8,4,6,7] => [1,5,2,3,8,4,6,7] => 0100100 => 7
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,2,6,3,4,7,8] => [5,1,2,3,6,4,7,8] => 1000100 => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,1,2,6,3,4,8,7] => [5,1,2,3,6,8,4,7] => 1000010 => 7
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4,8] => [5,1,2,3,6,7,4,8] => 1000010 => 7
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,2,6,3,7,8,4] => [5,1,2,3,6,7,8,4] => 1000001 => 8
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,1,2,6,3,8,4,7] => [5,6,1,2,3,8,4,7] => 0100010 => 8
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,1,2,6,7,3,8,4] => [5,6,1,2,3,7,8,4] => 0100001 => 9
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,2,6,7,8,3,4] => [5,6,7,1,2,3,8,4] => 0010001 => 10
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,1,2,7,3,4,6,8] => [1,5,2,3,7,4,6,8] => 0100100 => 7
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,1,2,7,3,4,8,6] => [1,5,2,3,7,8,4,6] => 0100010 => 8
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,1,2,7,3,8,4,6] => [1,5,7,2,3,8,4,6] => 0010010 => 9
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,1,2,7,8,3,4,6] => [5,1,7,2,3,8,4,6] => 1010010 => 10
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,1,2,8,3,4,6,7] => [1,2,5,3,8,4,6,7] => 0010100 => 8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7,8] => [1,5,2,3,6,4,7,8] => 0100100 => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,6,2,3,4,8,7] => [1,5,2,3,6,8,4,7] => 0100010 => 8
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,6,2,3,7,4,8] => [1,5,2,3,6,7,4,8] => 0100010 => 8
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,1,6,2,3,7,8,4] => [1,5,2,3,6,7,8,4] => 0100001 => 9
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,1,6,2,3,8,4,7] => [1,5,6,2,3,8,4,7] => 0010010 => 9
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,8,4] => [1,5,6,2,3,7,8,4] => 0010001 => 10
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,6,2,7,8,3,4] => [1,5,6,7,2,3,8,4] => 0001001 => 11
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,8,3,4,7] => [5,1,6,2,3,8,4,7] => 1010010 => 10
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,1,6,7,2,3,4,8] => [5,1,6,2,3,7,4,8] => 1010010 => 10
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,6,7,2,3,8,4] => [5,1,6,2,3,7,8,4] => 1010001 => 11
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,6,7,2,8,3,4] => [5,1,6,7,2,3,8,4] => 1001001 => 12
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,6,7,8,2,3,4] => [5,6,1,7,2,3,8,4] => 0101001 => 13
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [5,1,6,8,2,3,4,7] => [1,8,5,2,3,6,4,7] => 0110010 => 11
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,1,7,2,3,4,6,8] => [1,2,5,3,7,4,6,8] => 0010100 => 8
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,1,7,2,3,8,4,6] => [1,2,5,7,3,8,4,6] => 0001010 => 10
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,8,3,4,6] => [5,1,2,7,3,8,4,6] => 1001010 => 11
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,1,7,8,2,3,4,6] => [1,5,2,7,3,8,4,6] => 0101010 => 12
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,1,8,2,3,4,6,7] => [1,2,3,8,5,4,6,7] => 0001100 => 9
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,1,2,3,4,7,8] => [1,2,5,3,6,4,7,8] => 0010100 => 8
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,6,1,2,3,7,4,8] => [1,2,5,3,6,7,4,8] => 0010010 => 9
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [5,6,1,2,3,7,8,4] => [1,2,5,3,6,7,8,4] => 0010001 => 10
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,8,4,7] => [1,2,5,6,3,8,4,7] => 0001010 => 10
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,1,2,7,3,4,8] => [1,2,5,6,3,7,4,8] => 0001010 => 10
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,6,1,2,7,3,8,4] => [1,2,5,6,3,7,8,4] => 0001001 => 11
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,6,1,2,7,8,3,4] => [1,2,5,6,7,3,8,4] => 0000101 => 12
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,1,2,8,3,4,7] => [5,1,2,6,3,8,4,7] => 1001010 => 11
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,1,7,2,3,4,8] => [5,1,2,6,3,7,4,8] => 1001010 => 11
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,6,1,7,2,3,8,4] => [5,1,2,6,3,7,8,4] => 1001001 => 12
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,6,1,7,2,8,3,4] => [5,1,2,6,7,3,8,4] => 1000101 => 13
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,1,7,8,2,3,4] => [5,6,1,2,7,3,8,4] => 0100101 => 14
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,1,8,2,3,4,7] => [1,5,2,6,3,8,4,7] => 0101010 => 12
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,1,2,3,4,8] => [1,5,2,6,3,7,4,8] => 0101010 => 12
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,1,2,3,8,4] => [1,5,2,6,3,7,8,4] => 0101001 => 13
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4] => [5,1,6,2,7,3,8,4] => 1010101 => 16
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => [1,2,8,5,3,6,4,7] => 0011010 => 13
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,1,2,3,4,6,8] => [1,2,3,7,5,4,6,8] => 0001100 => 9
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,1,2,3,4,8,6] => [1,2,3,7,5,8,4,6] => 0001010 => 10
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,1,2,3,8,4,6] => [7,1,2,5,3,8,4,6] => 1001010 => 11
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,1,2,8,3,4,6] => [1,7,2,5,3,8,4,6] => 0101010 => 12
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,1,8,2,3,4,6] => [1,2,7,5,3,8,4,6] => 0011010 => 13
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => [1,2,7,3,8,5,4,6] => 0010110 => 14
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [1,2,3,5,4,8,6,7] => 0001010 => 10
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,7,8] => [1,2,3,4,6,5,7,8] => 0000100 => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => [1,2,3,4,6,8,5,7] => 0000010 => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,2,3,4,7,5,8] => [1,2,3,4,6,7,5,8] => 0000010 => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,1,2,3,4,7,8,5] => [1,2,3,4,6,7,8,5] => 0000001 => 7
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,1,2,3,4,8,5,7] => [6,1,2,3,4,8,5,7] => 1000010 => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5,8] => [6,1,2,3,4,7,5,8] => 1000010 => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,1,2,3,7,4,8,5] => [6,1,2,3,4,7,8,5] => 1000001 => 8
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,1,2,3,7,8,4,5] => [6,7,1,2,3,4,8,5] => 0100001 => 9
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,1,2,3,8,4,5,7] => [1,6,2,3,4,8,5,7] => 0100010 => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,2,7,3,4,5,8] => [1,6,2,3,4,7,5,8] => 0100010 => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,1,2,7,3,4,8,5] => [1,6,2,3,4,7,8,5] => 0100001 => 9
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,1,2,7,3,8,4,5] => [1,6,7,2,3,4,8,5] => 0010001 => 10
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,1,2,7,8,3,4,5] => [6,1,7,2,3,4,8,5] => 1010001 => 11
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,1,2,8,3,4,5,7] => [1,2,6,3,4,8,5,7] => 0010010 => 9
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,7,2,3,4,5,8] => [1,2,6,3,4,7,5,8] => 0010010 => 9
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,1,7,2,3,4,8,5] => [1,2,6,3,4,7,8,5] => 0010001 => 10
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,1,7,2,8,3,4,5] => [6,1,2,7,3,4,8,5] => 1001001 => 12
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,1,7,8,2,3,4,5] => [1,6,2,7,3,4,8,5] => 0101001 => 13
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [1,2,3,6,4,8,5,7] => 0001010 => 10
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,1,2,3,4,5,8] => [1,2,3,6,4,7,5,8] => 0001010 => 10
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,1,2,3,4,8,5] => [1,2,3,6,4,7,8,5] => 0001001 => 11
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,1,2,3,8,4,5] => [1,2,3,6,7,4,8,5] => 0000101 => 12
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,1,2,8,3,4,5] => [6,1,2,3,7,4,8,5] => 1000101 => 13
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,1,8,2,3,4,5] => [1,6,2,3,7,4,8,5] => 0100101 => 14
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => [1,2,6,3,7,4,8,5] => 0010101 => 15
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => [1,2,3,4,8,6,5,7] => 0000110 => 11
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => [1,2,3,4,5,7,6,8] => 0000010 => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,8,6] => [1,2,3,4,5,7,8,6] => 0000001 => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,8,5,6] => [7,1,2,3,4,5,8,6] => 1000001 => 8
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1,2,3,8,4,5,6] => [1,7,2,3,4,5,8,6] => 0100001 => 9
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1,2,8,3,4,5,6] => [1,2,7,3,4,5,8,6] => 0010001 => 10
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [1,2,3,7,4,5,8,6] => 0001001 => 11
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [1,2,3,4,7,5,8,6] => 0000101 => 12
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,7] => 0000001 => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9] => [1,2,3,4,5,6,8,7,9] => 00000010 => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => [1,2,3,4,5,6,9,7,8] => 00000010 => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,10] => [1,2,3,4,5,6,7,9,8,10] => 000000010 => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,1,2,3,4,5,6,9] => [1,2,3,4,7,5,8,6,9] => 00001010 => 12
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7] => [1,2,3,4,8,5,9,6,7] => 00001010 => 12
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,10,8,9] => 000000010 => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => 0000000010 => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,1,2,3,4,5,6,7,10] => [1,2,3,4,5,8,6,9,7,10] => 000001010 => 14
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,1,8,2,3,4,5,6,9] => [1,2,3,7,4,5,8,6,9] => 00010010 => 11
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,1,2,3,4,5,7,9] => [1,2,3,4,8,6,5,7,9] => 00001100 => 11
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,9,3,4,5,6,7] => [1,2,3,8,4,5,9,6,7] => 00010010 => 11
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,2,3,4,5,6,8] => [1,2,3,4,9,7,5,6,8] => 00001100 => 11
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => [1,2,3,4,5,9,6,10,7,8] => 000001010 => 14
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,11,9,10] => 0000000010 => 9
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,8,2,3,4,5,9,6,7] => [8,1,2,3,4,5,9,6,7] => 10000010 => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,1,2,3,4,5,8,6,9] => [1,2,3,4,5,7,8,6,9] => 00000010 => 7
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,8,1,2,3,4,9] => [5,1,6,2,7,3,8,4,9] => 10101010 => 16
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,1,3,4,5,6,7,9] => [2,1,3,4,5,8,6,7,9] => 10000100 => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,6,9,8] => [1,2,3,4,5,7,9,6,8] => 00000010 => 7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,9,7] => [1,2,3,4,5,8,9,6,7] => 00000010 => 7
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,9,2,3,4,5] => [6,1,7,2,8,3,9,4,5] => 10101010 => 16
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => [2,1,3,4,5,9,6,7,8] => 10000100 => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,6,8,9] => [1,2,3,4,5,7,6,8,9] => 00000100 => 6
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,9,2,3,4,5,6,10,7,8] => [9,1,2,3,4,5,6,10,7,8] => 100000010 => 9
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,7,8,9,10,2,3,4,5,6] => [1,7,2,8,3,9,4,10,5,6] => 010101010 => 20
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => [1,2,3,4,5,9,6,7,8] => 00000100 => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,1,2,3,4,5,6,9,7,10] => [1,2,3,4,5,6,8,9,7,10] => 000000010 => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,1,2,3,4,5,6,7,10,9] => [1,2,3,4,5,6,8,10,7,9] => 000000010 => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,10,8] => [1,2,3,4,5,6,9,10,7,8] => 000000010 => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,1,2,3,4,5,6,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => 000000100 => 7
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [1,2,3,4,5,6,10,7,8,9] => 000000100 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1] => 00000001 => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,1,8] => [9,2,3,4,5,6,7,1,8] => 10000010 => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,1,9,7] => [8,2,3,4,5,6,9,1,7] => 10000010 => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,8,9,1,7] => [8,9,2,3,4,5,6,1,7] => 01000010 => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,1,7,8] => [2,9,3,4,5,6,1,7,8] => 01000100 => 8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,7,8,9,1,6] => [7,8,9,2,3,4,5,1,6] => 00100010 => 10
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,9,1,5] => [6,7,8,9,2,3,4,1,5] => 00010010 => 11
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,9,1,4] => [5,6,7,8,9,2,3,1,4] => 00001010 => 12
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,8,9,3] => [4,2,5,6,7,8,9,1,3] => 10000010 => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,9,7] => [4,6,8,2,9,1,3,5,7] => 00101000 => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,3,8,9,5,7] => [4,6,8,9,2,1,3,5,7] => 00011000 => 9
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,1,3] => [4,5,6,7,8,9,2,1,3] => 00000110 => 13
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [2,5,1,3,6,7,8,9,4] => [2,1,5,6,7,8,9,3,4] => 10000010 => 8
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,5,1,6,7,8,9,3,4] => [2,5,6,7,8,1,9,3,4] => 00001010 => 12
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => [2,1,3,4,5,6,9,7,8] => 10000010 => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,9,2] => [1,3,4,5,6,7,8,9,2] => 00000001 => 8
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,4,8,9,2,5,6,7] => [1,8,3,9,4,2,5,6,7] => 01011000 => 11
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,5,2,6,7,8,9,4] => [3,1,5,6,7,8,9,2,4] => 10000010 => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,8,9,2] => [3,1,4,5,6,7,8,9,2] => 10000001 => 9
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,1,6,7,8,9,2] => [3,4,1,5,6,7,8,9,2] => 01000001 => 10
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,6,1,7,8,9,2] => [3,4,5,1,6,7,8,9,2] => 00100001 => 11
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,7,1,8,9,2] => [3,4,5,6,1,7,8,9,2] => 00010001 => 12
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,1,9,2] => [3,4,5,6,7,1,8,9,2] => 00001001 => 13
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,1,2] => [3,4,5,6,7,8,1,9,2] => 00000101 => 14
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,9,1,2,4,5,6,7,8] => [1,3,2,4,5,6,9,7,8] => 01000010 => 9
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,8,9,3] => [1,2,4,5,6,7,8,9,3] => 00000001 => 8
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,1,2,8,9,3,5,6,7] => [1,8,2,9,4,3,5,6,7] => 01011000 => 11
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,8,9,2,3] => [4,5,6,7,8,1,2,9,3] => 00001001 => 13
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,5,1,2,6,7,8,9,3] => [1,4,2,5,6,7,8,9,3] => 01000001 => 10
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,5,1,6,7,8,9,2,3] => [1,4,5,6,7,8,2,9,3] => 00000101 => 14
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [4,5,6,7,1,8,2,9,3] => 00010101 => 18
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,1,2,3,6,7,8,9,4] => [1,2,3,5,6,7,8,9,4] => 00000001 => 8
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0] => [5,6,1,2,3,7,8,9,4] => [1,2,5,3,6,7,8,9,4] => 00100001 => 11
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [5,6,1,7,2,8,3,9,4] => 01010101 => 20
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,1,2,3,4,7,8,9,5] => [1,2,3,4,6,7,8,9,5] => 00000001 => 8
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,1,7,8,9,2,3,4,5] => [6,1,7,2,8,3,4,9,5] => 10101001 => 17
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [1,6,2,7,3,8,4,9,5] => 01010101 => 20
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,1,2,3,4,5,8,9,6] => [1,2,3,4,5,7,8,9,6] => 00000001 => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,1,2,3,4,5,9,6,8] => [7,1,2,3,4,5,9,6,8] => 10000010 => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,8,1,2,3,4,5,9,6] => [1,2,3,4,7,5,8,9,6] => 00001001 => 13
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [7,8,1,2,3,4,9,5,6] => [1,2,3,4,7,8,5,9,6] => 00000101 => 14
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => [1,2,3,7,4,8,5,9,6] => 00010101 => 18
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,1,2,3,4,5,6,8] => [1,2,3,4,5,9,7,6,8] => 00000110 => 13
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,9,7] => [1,2,3,4,5,6,8,9,7] => 00000001 => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,9,6,7] => [8,1,2,3,4,5,6,9,7] => 10000001 => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,1,2,3,4,9,5,6,7] => [1,8,2,3,4,5,6,9,7] => 01000001 => 10
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,1,2,3,9,4,5,6,7] => [1,2,8,3,4,5,6,9,7] => 00100001 => 11
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,1,9,2,3,4,5,6,7] => [1,2,3,4,8,5,6,9,7] => 00001001 => 13
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,8,6,9,7] => 00000101 => 14
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,9,8] => 00000001 => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 00000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [9,1,2,3,4,5,6,7,8] => 10000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [8,9,1,2,3,4,5,6,7] => 01000000 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [7,8,9,1,2,3,4,5,6] => 00100000 => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [6,7,8,9,1,2,3,4,5] => 00010000 => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [5,6,7,8,9,1,2,3,4] => 00001000 => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [4,5,6,7,8,9,1,2,3] => 00000100 => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [3,4,5,6,7,8,9,1,2] => 00000010 => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [10,1,2,3,4,5,6,7,8,9] => 100000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,7,8] => [1,9,2,3,4,5,6,7,8] => 01000000 => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [9,10,1,2,3,4,5,6,7,8] => 010000000 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,6,9,7] => [1,8,9,2,3,4,5,6,7] => 00100000 => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [8,9,10,1,2,3,4,5,6,7] => 001000000 => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,5,8,9,6] => [1,7,8,9,2,3,4,5,6] => 00010000 => 4
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [7,8,9,10,1,2,3,4,5,6] => 000100000 => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,4,7,8,9,5] => [1,6,7,8,9,2,3,4,5] => 00001000 => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [6,7,8,9,10,1,2,3,4,5] => 000010000 => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,3,6,7,8,9,4] => [1,5,6,7,8,9,2,3,4] => 00000100 => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [5,6,7,8,9,10,1,2,3,4] => 000001000 => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,8,9,3] => [1,4,5,6,7,8,9,2,3] => 00000010 => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [4,5,6,7,8,9,10,1,2,3] => 000000100 => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [3,4,5,6,7,8,9,10,1,2] => 000000010 => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,10,1] => 000000001 => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,8,9] => [1,10,2,3,4,5,6,7,8,9] => 010000000 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,8,9,6,7] => [8,1,9,2,3,4,5,6,7] => 10100000 => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,6,9,7,10,8] => [1,9,10,2,3,4,5,6,7,8] => 001000000 => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,4,7,8,5,9,6] => [7,1,8,9,2,3,4,5,6] => 10010000 => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,6,7,8] => [1,2,9,3,4,5,6,7,8] => 00100000 => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,2,5,6,3,7,8,9,4] => [5,1,6,7,8,9,2,3,4] => 10000100 => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,3,4,5,6,7,8,9,10,2] => 000000001 => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => [3,4,5,6,7,8,9,10,11,1,2] => 0000000010 => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000001 => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,6,9,10,7,8] => [9,1,10,2,3,4,5,6,7,8] => 101000000 => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,7,8,9,5,6] => [7,8,1,9,2,3,4,5,6] => 01010000 => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [1,2,10,3,4,5,6,7,8,9] => 001000000 => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,7,3,8,9,4] => [5,6,1,7,8,9,2,3,4] => 01000100 => 8
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,4,8,9,5,6,7] => [1,8,2,9,3,4,5,6,7] => 01010000 => 6
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,3,7,8,4,5,9,6] => [1,7,2,8,9,3,4,5,6] => 01001000 => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,8,9,10,2] => [3,1,4,5,6,7,8,9,10,2] => 100000001 => 10
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,8,9,10,3] => [1,2,4,5,6,7,8,9,10,3] => 000000001 => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => [1,3,4,5,6,7,8,9,10,11,2] => 0000000001 => 10
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [1,2,3,9,4,5,6,7,8] => 00010000 => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,4,5,9,10,6,7,8] => [1,9,2,10,3,4,5,6,7,8] => 010100000 => 6
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,1,6,7,8,9,10,2] => [3,4,1,5,6,7,8,9,10,2] => 010000001 => 11
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [1,2,3,10,4,5,6,7,8,9] => 000100000 => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,7,8,9,10,2] => [3,4,5,1,6,7,8,9,10,2] => 001000001 => 12
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [5,1,2,3,6,7,8,9,10,4] => [1,2,3,5,6,7,8,9,10,4] => 000000001 => 9
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,2,3] => [4,5,6,7,8,1,9,2,3] => 00001010 => 12
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,8,9,10,2] => [3,4,5,6,1,7,8,9,10,2] => 000100001 => 13
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [1,2,3,4,9,5,6,7,8] => 00001000 => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,7,8,1,9,10,2] => [3,4,5,6,7,1,8,9,10,2] => 000010001 => 14
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [1,2,3,4,10,5,6,7,8,9] => 000010000 => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [6,1,2,3,4,7,8,9,10,5] => [1,2,3,4,6,7,8,9,10,5] => 000000001 => 9
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,10,2,3] => [4,5,6,7,8,9,1,10,2,3] => 000001010 => 14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,9,1,10,2] => [3,4,5,6,7,8,1,9,10,2] => 000001001 => 15
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [8,1,2,3,4,5,6,7,9] => 10000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [7,1,2,3,4,5,6,8,9] => 10000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [7,9,1,2,3,4,5,6,8] => 01000000 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,5,8,6,7,9] => [1,8,2,3,4,5,6,7,9] => 01000000 => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [6,1,2,3,4,5,7,8,9] => 10000000 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,4,7,5,6,9,8] => [1,7,9,2,3,4,5,6,8] => 00100000 => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => 10000000 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => [5,7,9,1,2,3,4,6,8] => 00100000 => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => 10000000 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,7,9,8] => [4,9,1,2,3,5,6,7,8] => 01000000 => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => 10000000 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [3,9,1,2,4,5,6,7,8] => 01000000 => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [3,5,7,9,1,2,4,6,8] => 00010000 => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8,9] => [1,4,2,3,5,6,7,8,9] => 01000000 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2,3,4,5,6,9,8] => [1,2,3,4,7,9,5,6,8] => 00000100 => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => 10000000 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [2,9,1,3,4,5,6,7,8] => 01000000 => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [2,8,1,3,4,5,6,7,9] => 01000000 => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,9,7,8] => [9,2,1,3,4,5,6,7,8] => 11000000 => 3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5,8,6,7,9] => [8,2,1,3,4,5,6,7,9] => 11000000 => 3
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5,9,6,7,8] => [2,1,9,3,4,5,6,7,8] => 10100000 => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => 01000000 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9] => [2,4,6,1,3,5,7,8,9] => 00100000 => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,4,6,8,1,3,5,7,9] => 00010000 => 4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => 01000000 => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,6,7,9,8] => [1,3,9,2,4,5,6,7,8] => 00100000 => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,6,9,7,8] => [3,1,9,2,4,5,6,7,8] => 10100000 => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => 00100000 => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,2,3,5,6,7,9,8] => [1,2,4,9,3,5,6,7,8] => 00010000 => 4
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => [1,2,9,4,3,5,6,7,8] => 00110000 => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => 00010000 => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,2,3,4,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => 00001000 => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2,3,4,5,7,9,8] => [1,2,3,4,6,9,5,7,8] => 00000100 => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,1,2,3,4,5,8,7,9] => [1,2,3,4,6,8,5,7,9] => 00000100 => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,1,2,3,4,5,9,7,8] => [6,1,2,3,4,9,5,7,8] => 10000100 => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [9,1,2,3,4,5,6,7,8,10] => 100000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => 100000000 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => [8,10,1,2,3,4,5,6,7,9] => 010000000 => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,5,6,9,7,8,10] => [1,9,2,3,4,5,6,7,8,10] => 010000000 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => 100000000 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => 100000000 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7,10,9] => [6,8,10,1,2,3,4,5,7,9] => 001000000 => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => 100000000 => 1
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [1,2,3,4,5,10,6,7,8,9] => 000001000 => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => 100000000 => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => [4,6,8,10,1,2,3,5,7,9] => 000100000 => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => 100000000 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,7,10,8,9] => [10,3,1,2,4,5,6,7,8,9] => 110000000 => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [3,5,7,9,1,2,4,6,8,10] => 000100000 => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => 100000000 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [2,10,1,3,4,5,6,7,8,9] => 010000000 => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,7,10,8,9] => [10,2,1,3,4,5,6,7,8,9] => 110000000 => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => [2,4,1,3,5,6,7,8,9,10] => 010000000 => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9,10] => [2,4,6,1,3,5,7,8,9,10] => 001000000 => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9,10] => [2,4,6,8,1,3,5,7,9,10] => 000100000 => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,4,6,8,10,1,3,5,7,9] => 000010000 => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => 010000000 => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => 001000000 => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => 000100000 => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => 000010000 => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => 000001000 => 6
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,10,9] => 000000001 => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => 01000000 => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => 00100000 => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => 00010000 => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [2,3,4,5,6,1,7,8,9] => 00001000 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [2,3,4,5,6,7,1,8,9] => 00000100 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [2,3,4,5,6,7,8,1,9] => 00000010 => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => 010000000 => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => 001000000 => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => 000100000 => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => 000010000 => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => 000001000 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [2,3,4,5,6,7,8,1,9,10] => 000000100 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [2,3,4,5,6,7,8,9,1,10] => 000000010 => 8
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,8,10,1,2,3,4,9] => [10,5,1,6,2,7,3,8,4,9] => 110101010 => 21
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [2,8,9,1,3,4,5,6,7] => 00100000 => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,1,9] => [10,2,3,4,5,6,7,8,1,9] => 100000010 => 9
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,1,10,2,3,4,5,6,7,8] => [1,2,3,4,5,9,6,7,10,8] => 000001001 => 15
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,7,9,10,8] => [2,9,10,1,3,4,5,6,7,8] => 001000000 => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [2,3,9,1,4,5,6,7,8] => 00100000 => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,1,2,9] => [3,4,5,6,7,1,8,2,9] => 00001010 => 12
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,7,1,2,8,9] => [3,4,5,6,1,7,2,8,9] => 00010100 => 10
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,6,1,2,7,8,9] => [3,4,5,1,6,2,7,8,9] => 00101000 => 8
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8,9] => [3,1,4,2,5,6,7,8,9] => 10100000 => 4
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,10,8,9] => 100000010 => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => [1,2,3,4,5,6,7,9,10,8] => 000000001 => 9
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,11,9] => [1,2,3,4,5,6,7,8,10,11,9] => 0000000001 => 10
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,3,6,7,8,9] => [1,2,4,5,3,6,7,8,9] => 00010000 => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9] => [1,3,4,2,5,6,7,8,9] => 00100000 => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,9,7,10,8] => 000000101 => 16
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,9,3,4] => [5,6,7,8,9,2,1,3,4] => 00001100 => 11
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,10,1,3] => [4,5,6,7,8,9,10,2,1,3] => 000000110 => 15
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => [3,4,5,1,2,6,7,8,9] => 00100000 => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6,7,9,8] => [2,3,4,5,9,1,6,7,8] => 00001000 => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,7,8,2,9] => [1,3,4,5,6,7,8,2,9] => 00000010 => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,2,8] => [9,3,4,5,6,7,1,2,8] => 10000100 => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [2,3,4,5,6,7,9,1,8] => 00000010 => 7
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [2,4,5,6,7,8,9,1,3] => 00000010 => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,7,8] => [9,2,3,4,5,6,1,7,8] => 10000100 => 7
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,7,8,9,10,1,5,6] => [7,8,9,2,10,3,4,1,5,6] => 001010100 => 15
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [4,5,6,7,8,1,9,2,10,3] => 000010101 => 21
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,1,2,3,4,5,6,10,7,8] => [9,1,2,3,4,5,6,7,10,8] => 100000001 => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,1,2,3,4,10,5,6,7,8] => [1,2,9,3,4,5,6,7,10,8] => 001000001 => 12
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,4,6,7,8,5,9] => [6,7,8,1,2,3,4,5,9] => 00100000 => 3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,5,7,8,9,10,1,6] => [7,8,9,10,2,3,4,5,1,6] => 000100010 => 12
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,9] => [2,3,4,5,6,8,1,7,9] => 00000100 => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,6,8,9] => [2,3,4,5,7,1,6,8,9] => 00001000 => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,5,7,8,9] => [2,3,4,6,1,5,7,8,9] => 00010000 => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8,9] => [2,3,5,1,4,6,7,8,9] => 00100000 => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7,9] => [4,2,6,8,1,3,5,7,9] => 10010000 => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5,8,7,9] => [4,6,2,8,1,3,5,7,9] => 01010000 => 6
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,8,5,7,9] => [4,6,8,2,1,3,5,7,9] => 00110000 => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5,9,8] => [4,6,2,7,9,1,3,5,8] => 01001000 => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,9,8] => [4,2,5,7,9,1,3,6,8] => 10001000 => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [2,3,5,7,9,1,4,6,8] => 00001000 => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7,10,9] => [4,2,6,8,10,1,3,5,7,9] => 100010000 => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7,10,9] => [4,6,2,8,10,1,3,5,7,9] => 010010000 => 7
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,8,5,7,10,9] => [4,6,8,2,10,1,3,5,7,9] => 001010000 => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,10,7,9] => [4,6,8,10,2,1,3,5,7,9] => 000110000 => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,5,8,9] => [4,6,2,7,1,3,5,8,9] => 01010000 => 6
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,8,5,9,7,10] => [4,6,8,2,9,1,3,5,7,10] => 001010000 => 8
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,5,3,8,6,9,7] => [4,8,2,5,9,1,3,6,7] => 01001000 => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,7,5,9,8,10] => [4,6,2,7,9,1,3,5,8,10] => 010010000 => 7
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,9,8] => [6,2,3,7,9,1,4,5,8] => 10001000 => 6
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,9,8,10] => [4,2,5,7,9,1,3,6,8,10] => 100010000 => 6
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,9,8] => [1,4,5,7,9,2,3,6,8] => 00001000 => 5
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [2,3,5,7,9,1,4,6,8,10] => 000010000 => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,1,5,7,8,9,6] => [2,3,4,7,8,9,1,5,6] => 00000100 => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,7,9,10,1,8] => [9,10,2,3,4,5,6,7,1,8] => 010000010 => 10
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,8,9,10,1,7] => [8,9,10,2,3,4,5,6,1,7] => 001000010 => 11
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,9,10,1,5] => [6,7,8,9,10,2,3,4,1,5] => 000010010 => 13
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,9,10,1,4] => [5,6,7,8,9,10,2,3,1,4] => 000001010 => 14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [3,4,5,6,7,8,9,1,10,2] => 000000101 => 16
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,8,9,10,2,3] => [4,5,6,7,8,9,1,2,10,3] => 000001001 => 15
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,10,11,1,3] => [4,5,6,7,8,9,10,11,2,1,3] => 0000000110 => 17
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => [3,4,5,6,7,8,9,10,1,11,2] => 0000000101 => 18
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,7,8,4,9,5,10,6] => [7,2,8,9,3,10,1,4,5,6] => 100101000 => 11
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,11,10] => 0000000001 => 10
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,9,10,1,3,4,5,6,7,8] => [2,1,3,4,5,9,6,10,7,8] => 100001010 => 15
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,3,5,6,7,8] => [4,1,2,3,9,5,6,7,8] => 10001000 => 6
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => [9,1,2,5,3,4,6,7,8] => 10010000 => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,6,8] => [9,7,1,2,3,4,5,6,8] => 11000000 => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,1,2,5,6,7,8,9,4] => [1,3,5,6,7,8,9,2,4] => 00000010 => 7
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [5,6,7,1,8,2,9,3,10,4] => 001010101 => 24
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,7,8,9,10,1,3,4,5,6] => [7,2,1,8,3,9,4,10,5,6] => 110101010 => 21
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => 01000000 => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => [2,4,5,6,7,8,9,10,1,3] => 000000010 => 8
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => [2,3,5,6,7,8,9,1,4] => 00000010 => 7
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [1,2,3,4,8,5,9,6,10,7] => 000010101 => 21
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,1,8,9,10,7] => [2,3,4,5,6,8,9,10,1,7] => 000000010 => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [7,8,1,2,3,4,5,6,9] => 01000000 => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,6,8,9,7,10] => [8,9,1,2,3,4,5,6,7,10] => 010000000 => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,8,2,9,10] => [3,4,5,6,7,8,1,2,9,10] => 000001000 => 6
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [6,1,7,2,8,3,9,4,10,5] => 101010101 => 25
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [1,2,7,3,8,4,9,5,10,6] => 001010101 => 24
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => [2,3,4,5,6,7,8,9,10,1,11] => 0000000010 => 9
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [10,1,2,11,3,4,5,6,7,8,9] => [1,2,3,4,5,10,6,7,8,11,9] => 0000010001 => 16
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [3,4,5,6,7,8,1,2,9] => 00000100 => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,6,2,8,9,7] => [3,4,5,6,8,9,1,2,7] => 00000100 => 6
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,9,4] => [2,5,6,7,8,9,1,3,4] => 00000100 => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8,9,10] => [3,1,4,2,5,6,7,8,9,10] => 101000000 => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [2,3,4,5,6,7,8,10,1,9] => 000000010 => 8
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,7,8,9,10,1,2,3,5,6] => [7,1,8,2,9,4,3,10,5,6] => 101011010 => 23
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,9,2,5,6,7,8] => [3,4,1,2,9,5,6,7,8] => 01001000 => 7
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,5,2,4,6,7,8,9] => [5,3,1,2,4,6,7,8,9] => 11000000 => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [3,4,5,6,7,8,9,1,2,10] => 000000100 => 7
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,9,5] => [2,3,4,6,7,8,9,1,5] => 00000010 => 7
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,5,3,6,7,8,9] => [4,2,5,1,3,6,7,8,9] => 10100000 => 4
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [5,6,7,9,10,1,2,3,4,8] => [9,1,10,5,2,6,3,7,4,8] => 101101010 => 22
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [5,6,8,9,10,1,2,3,4,7] => [8,1,9,2,10,5,3,6,4,7] => 101011010 => 23
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,7,8,9,10,1,2,3,4,6] => [7,1,8,2,9,3,10,5,4,6] => 101010110 => 24
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,4,5,8,6,9,7,10] => [1,8,9,2,3,4,5,6,7,10] => 001000000 => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,7,9,1,10,8] => [9,2,3,4,5,6,7,10,1,8] => 100000010 => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,2,9] => [10,3,4,5,6,7,8,1,2,9] => 100000100 => 8
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,8,3,9] => [2,4,5,6,7,8,1,3,9] => 00000100 => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,1,2,3,4,5,6,9,10,7] => [1,2,3,4,5,6,8,9,10,7] => 000000001 => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,1,2,3,4,5,8,9,10,6] => [1,2,3,4,5,7,8,9,10,6] => 000000001 => 9
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [3,5,7,9,10,1,2,4,6,8] => 000010000 => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,4,8,5,9,6,7] => [8,1,2,9,3,4,5,6,7] => 10010000 => 5
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,5] => [2,4,6,7,8,9,1,3,5] => 00000100 => 6
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,9,4] => [3,5,6,7,8,9,1,2,4] => 00000100 => 6
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9,10] => [1,3,4,2,5,6,7,8,9,10] => 001000000 => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => [3,4,5,6,7,1,2,8,9] => 00001000 => 5
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,5,7,9,2,4,6,8] => [9,7,5,3,1,2,4,6,8] => 11110000 => 10
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,5,7,9,10,1,2,4,6,8] => [9,1,10,7,5,3,2,4,6,8] => 101111000 => 19
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,7,8,9,5,6] => [7,8,9,2,3,4,1,5,6] => 00100100 => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,10,2,11] => [3,4,5,6,7,8,9,10,1,2,11] => 0000000100 => 8
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,8,9,10,3] => [4,2,5,6,7,8,9,10,1,3] => 100000010 => 9
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [2,4,6,1,3,5,8,7,9] => [6,4,2,8,1,3,5,7,9] => 11010000 => 7
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,10,9] => [3,4,6,8,10,1,2,5,7,9] => 000010000 => 5
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,7,2,8,9,10,3,4,5,6] => [7,1,8,2,9,3,4,10,5,6] => 101010010 => 17
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,5,6,1,2,3,7,8,9,10] => [4,1,5,2,6,3,7,8,9,10] => 101010000 => 9
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,2,7,3,8,4,9,5,10,6] => [1,7,8,2,3,9,10,4,5,6] => 001000100 => 10
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,4,6,9,10,1,3,5,7,8] => [9,10,2,1,6,4,3,5,7,8] => 011011000 => 16
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,1,6,8,3,5,7,9] => [8,4,6,2,1,3,5,7,9] => 10110000 => 8
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [5,1,2,3,9,10,4,6,7,8] => [1,5,2,9,3,10,4,6,7,8] => 010101000 => 12
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => [10,8,6,4,2,1,3,5,7,9] => 111110000 => 15
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,6,1,2,3,7,8,9] => [4,1,5,2,6,3,7,8,9] => 10101000 => 9
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0] => [6,1,2,3,7,4,5,8,9] => [6,1,2,3,4,7,5,8,9] => 10000100 => 7
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,6,1,7,8,2,9] => [3,4,5,1,6,7,8,2,9] => 00100010 => 10
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,5,6,9,10,1,2,3,7,8] => [9,4,1,10,5,2,6,3,7,8] => 110110100 => 19
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,5,8,9,10,1,2,3,6,7] => [8,1,9,4,2,10,5,3,6,7] => 101101100 => 21
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,9,8] => [2,3,4,5,7,9,1,6,8] => 00000100 => 6
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,6,7,8,10,1,2,3,5,9] => [10,6,1,7,2,8,4,3,5,9] => 110101100 => 20
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,3,5,7,9,2,4,6,8,10] => [9,7,5,3,1,2,4,6,8,10] => 111100000 => 10
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,2,2 1,3,5,4,1 1,4,9,12,10,4,2 1,5,14,25,31,26,16,9,4,1 1,6,20,44,70,82,74,54,38,22,12,4,2
F2=1+q
F3=1+2 q+2 q2
F4=1+3 q+5 q2+4 q3+q4
F5=1+4 q+9 q2+12 q3+10 q4+4 q5+2 q6
F6=1+5 q+14 q2+25 q3+31 q4+26 q5+16 q6+9 q7+4 q8+q9
F7=1+6 q+20 q2+44 q3+70 q4+82 q5+74 q6+54 q7+38 q8+22 q9+12 q10+4 q11+2 q12
Description
The sum of the positions of the ones in a binary word.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation π of n letters and each 1≤i≤n−1 such that π(i)>π(i+1) we set wi=1, otherwise wi=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.
For a permutation π of n letters and each 1≤i≤n−1 such that π(i)>π(i+1) we set wi=1, otherwise wi=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
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength n in an n×n square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Draw the path of semilength n in an n×n square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
See Mp00067Foata bijection.
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