Identifier
-
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
St000008: Integer compositions ⟶ ℤ
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [2,1] => [2,1] => [1,1] => 1
[1,1,0,0] => [1,2] => [1,2] => [2] => 0
[1,0,1,0,1,0] => [2,3,1] => [1,3,2] => [2,1] => 2
[1,0,1,1,0,0] => [2,1,3] => [2,1,3] => [1,2] => 1
[1,1,0,0,1,0] => [1,3,2] => [3,1,2] => [1,2] => 1
[1,1,0,1,0,0] => [3,1,2] => [2,3,1] => [2,1] => 2
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [3] => 0
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [1,2,4,3] => [3,1] => 3
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [1,3,2,4] => [2,2] => 2
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [1,4,2,3] => [2,2] => 2
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [1,3,4,2] => [3,1] => 3
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => [1,3] => 1
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [2,4,1,3] => [2,2] => 2
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [3,1,2,4] => [1,3] => 1
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [4,2,1,3] => [1,1,2] => 3
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [3,1,4,2] => [1,2,1] => 4
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [2,3,1,4] => [2,2] => 2
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [4,1,2,3] => [1,3] => 1
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [3,4,1,2] => [2,2] => 2
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [2,3,4,1] => [3,1] => 3
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [4] => 0
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => [1,2,3,5,4] => [4,1] => 4
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [1,2,4,3,5] => [3,2] => 3
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [1,2,5,3,4] => [3,2] => 3
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [1,2,4,5,3] => [4,1] => 4
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [1,3,2,4,5] => [2,3] => 2
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [1,3,5,2,4] => [3,2] => 3
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [1,4,2,3,5] => [2,3] => 2
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [5,1,3,2,4] => [1,2,2] => 4
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [4,1,2,5,3] => [1,3,1] => 5
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [1,3,4,2,5] => [3,2] => 3
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [1,5,2,3,4] => [2,3] => 2
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [1,4,5,2,3] => [3,2] => 3
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [1,3,4,5,2] => [4,1] => 4
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4,5] => [1,4] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [2,3,5,1,4] => [3,2] => 3
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [2,4,1,3,5] => [2,3] => 2
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [2,5,1,3,4] => [2,3] => 2
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [2,4,5,1,3] => [3,2] => 3
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [3,1,2,4,5] => [1,4] => 1
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [3,1,5,2,4] => [1,2,2] => 4
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,3] => 3
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [1,5,3,2,4] => [2,1,2] => 5
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [1,4,2,5,3] => [2,2,1] => 6
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [3,1,4,2,5] => [1,2,2] => 4
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [5,2,1,3,4] => [1,1,3] => 3
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [4,1,5,2,3] => [1,2,2] => 4
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [3,1,4,5,2] => [1,3,1] => 5
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3] => 2
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [3,5,1,2,4] => [2,3] => 2
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [4,1,2,3,5] => [1,4] => 1
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [5,3,1,2,4] => [1,1,3] => 3
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [4,2,5,1,3] => [1,2,2] => 4
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [3,4,1,2,5] => [2,3] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [5,2,3,1,4] => [1,2,2] => 4
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [4,5,2,1,3] => [2,1,2] => 5
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [3,4,1,5,2] => [2,2,1] => 6
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [2,3,4,1,5] => [3,2] => 3
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [5,1,2,3,4] => [1,4] => 1
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [4,5,1,2,3] => [2,3] => 2
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [3,4,5,1,2] => [3,2] => 3
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [2,3,4,5,1] => [4,1] => 4
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [5] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => [1,2,3,4,6,5] => [5,1] => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [1,2,3,5,4,6] => [4,2] => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [1,2,3,6,4,5] => [4,2] => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [1,2,3,5,6,4] => [5,1] => 5
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [1,2,4,3,5,6] => [3,3] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [1,2,4,6,3,5] => [4,2] => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [1,2,5,3,4,6] => [3,3] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [6,1,2,4,3,5] => [1,3,2] => 5
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [5,1,2,3,6,4] => [1,4,1] => 6
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [1,2,4,5,3,6] => [4,2] => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [1,2,6,3,4,5] => [3,3] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [1,2,5,6,3,4] => [4,2] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [1,2,4,5,6,3] => [5,1] => 5
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [1,3,2,4,5,6] => [2,4] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [1,3,4,6,2,5] => [4,2] => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [1,3,5,2,4,6] => [3,3] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [1,3,6,2,4,5] => [3,3] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => [1,3,5,6,2,4] => [4,2] => 4
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [1,4,2,3,5,6] => [2,4] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [4,1,2,6,3,5] => [1,3,2] => 5
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [5,1,3,2,4,6] => [1,2,3] => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [2,6,1,4,3,5] => [2,2,2] => 6
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [2,5,1,3,6,4] => [2,3,1] => 7
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [4,1,2,5,3,6] => [1,3,2] => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [6,1,3,2,4,5] => [1,2,3] => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [5,1,2,6,3,4] => [1,3,2] => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [4,1,2,5,6,3] => [1,4,1] => 6
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [1,3,4,2,5,6] => [3,3] => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [1,4,6,2,3,5] => [3,3] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [1,5,2,3,4,6] => [2,4] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [6,1,4,2,3,5] => [1,2,3] => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => [5,1,3,6,2,4] => [1,3,2] => 5
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [1,4,5,2,3,6] => [3,3] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [6,1,3,4,2,5] => [1,3,2] => 5
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [5,6,1,3,2,4] => [2,2,2] => 6
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [4,5,1,2,6,3] => [2,3,1] => 7
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [1,3,4,5,2,6] => [4,2] => 4
>>> Load all 1875 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [1,6,2,3,4,5] => [2,4] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [1,5,6,2,3,4] => [3,3] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [1,4,5,6,2,3] => [4,2] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [1,3,4,5,6,2] => [5,1] => 5
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,5] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [2,3,4,6,1,5] => [4,2] => 4
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [2,3,5,1,4,6] => [3,3] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [2,3,6,1,4,5] => [3,3] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [2,3,5,6,1,4] => [4,2] => 4
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => [2,4] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [2,4,6,1,3,5] => [3,3] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [2,5,1,3,4,6] => [2,4] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [6,2,4,1,3,5] => [1,2,3] => 4
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [5,2,3,6,1,4] => [1,3,2] => 5
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [2,4,5,1,3,6] => [3,3] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [2,6,1,3,4,5] => [2,4] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [2,5,6,1,3,4] => [3,3] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [2,4,5,6,1,3] => [4,2] => 4
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => [1,5] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [3,1,4,6,2,5] => [1,3,2] => 5
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [3,1,5,2,4,6] => [1,2,3] => 4
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [3,1,6,2,4,5] => [1,2,3] => 4
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => [3,1,5,6,2,4] => [1,3,2] => 5
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [4,2,1,3,5,6] => [1,1,4] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [1,4,2,6,3,5] => [2,2,2] => 6
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [1,5,3,2,4,6] => [2,1,3] => 5
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [1,2,6,4,3,5] => [3,1,2] => 7
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [1,2,5,3,6,4] => [3,2,1] => 8
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [1,4,2,5,3,6] => [2,2,2] => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [1,6,3,2,4,5] => [2,1,3] => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [1,5,2,6,3,4] => [2,2,2] => 6
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [1,4,2,5,6,3] => [2,3,1] => 7
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [1,2,3] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [4,1,6,2,3,5] => [1,2,3] => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [5,2,1,3,4,6] => [1,1,4] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [1,6,4,2,3,5] => [2,1,3] => 5
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => [1,5,3,6,2,4] => [2,2,2] => 6
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [4,1,5,2,3,6] => [1,2,3] => 4
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [1,6,3,4,2,5] => [2,2,2] => 6
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [1,5,6,3,2,4] => [3,1,2] => 7
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [1,4,5,2,6,3] => [3,2,1] => 8
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [3,1,4,5,2,6] => [1,3,2] => 5
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [6,2,1,3,4,5] => [1,1,4] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [5,1,6,2,3,4] => [1,2,3] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => [4,1,5,6,2,3] => [1,3,2] => 5
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [3,1,4,5,6,2] => [1,4,1] => 6
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,4] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [3,4,6,1,2,5] => [3,3] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => [3,5,1,2,4,6] => [2,4] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [3,6,1,2,4,5] => [2,4] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [3,5,6,1,2,4] => [3,3] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => [1,5] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [4,2,6,1,3,5] => [1,2,3] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [5,3,1,2,4,6] => [1,1,4] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [2,6,4,1,3,5] => [2,1,3] => 5
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [2,5,3,6,1,4] => [2,2,2] => 6
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [4,2,5,1,3,6] => [1,2,3] => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [6,3,1,2,4,5] => [1,1,4] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [5,2,6,1,3,4] => [1,2,3] => 4
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [4,2,5,6,1,3] => [1,3,2] => 5
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [3,4,1,2,5,6] => [2,4] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => [4,6,2,1,3,5] => [2,1,3] => 5
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => [5,2,3,1,4,6] => [1,2,3] => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [6,4,2,1,3,5] => [1,1,1,3] => 6
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => [5,3,1,6,2,4] => [1,1,2,2] => 7
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => [4,5,2,1,3,6] => [2,1,3] => 5
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => [6,3,1,4,2,5] => [1,1,2,2] => 7
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => [5,1,6,3,2,4] => [1,2,1,2] => 8
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [1,2,2,1] => 9
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [2,2,2] => 6
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => [6,2,3,1,4,5] => [1,2,3] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => [5,6,2,1,3,4] => [2,1,3] => 5
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => [4,5,1,6,2,3] => [2,2,2] => 6
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [3,4,1,5,6,2] => [2,3,1] => 7
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [3,3] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [4,6,1,2,3,5] => [2,4] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => [1,5] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [6,4,1,2,3,5] => [1,1,4] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [5,3,6,1,2,4] => [1,2,3] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [4,5,1,2,3,6] => [2,4] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [6,3,4,1,2,5] => [1,2,3] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [5,6,3,1,2,4] => [2,1,3] => 5
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [4,5,2,6,1,3] => [2,2,2] => 6
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [3,4,5,1,2,6] => [3,3] => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => [6,2,3,4,1,5] => [1,3,2] => 5
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => [5,6,2,3,1,4] => [2,2,2] => 6
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => [4,5,6,2,1,3] => [3,1,2] => 7
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,2,1] => 8
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [4,2] => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => [1,5] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [5,6,1,2,3,4] => [2,4] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [4,5,6,1,2,3] => [3,3] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [3,4,5,6,1,2] => [4,2] => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [5,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [6] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1] => [1,2,3,4,5,7,6] => [6,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,6,5,7] => [5,2] => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6] => [1,2,3,4,7,5,6] => [5,2] => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => [1,2,3,4,6,7,5] => [6,1] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,5,4,6,7] => [4,3] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5] => [1,2,3,5,7,4,6] => [5,2] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7] => [1,2,3,6,4,5,7] => [4,3] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,6,1,7,5] => [7,1,2,3,5,4,6] => [1,4,2] => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => [6,1,2,3,4,7,5] => [1,5,1] => 7
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,6,1,5,7] => [1,2,3,5,6,4,7] => [5,2] => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6] => [1,2,3,7,4,5,6] => [4,3] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,6] => [1,2,3,6,7,4,5] => [5,2] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => [1,2,3,5,6,7,4] => [6,1] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,4,3,5,6,7] => [3,4] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4] => [1,2,4,5,7,3,6] => [5,2] => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7] => [1,2,4,6,3,5,7] => [4,3] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => [1,2,4,7,3,5,6] => [4,3] => 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,7,4,6] => [1,2,4,6,7,3,5] => [5,2] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7] => [1,2,5,3,4,6,7] => [3,4] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,5,1,6,7,4] => [5,1,2,3,7,4,6] => [1,4,2] => 6
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,7] => [6,1,2,4,3,5,7] => [1,3,3] => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,5,6,1,7,4] => [3,7,1,2,5,4,6] => [2,3,2] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,1,4] => [3,6,1,2,4,7,5] => [2,4,1] => 8
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,6,1,4,7] => [5,1,2,3,6,4,7] => [1,4,2] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,7,6] => [7,1,2,4,3,5,6] => [1,3,3] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,6] => [6,1,2,3,7,4,5] => [1,4,2] => 6
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,7,1,4,6] => [5,1,2,3,6,7,4] => [1,5,1] => 7
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => [1,2,4,5,3,6,7] => [4,3] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5] => [1,2,5,7,3,4,6] => [4,3] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7] => [1,2,6,3,4,5,7] => [3,4] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => [7,1,2,5,3,4,6] => [1,3,3] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => [6,1,2,4,7,3,5] => [1,4,2] => 6
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,5,7] => [1,2,5,6,3,4,7] => [4,3] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,6,1,4,7,5] => [7,1,2,4,5,3,6] => [1,4,2] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,6,1,7,4,5] => [6,7,1,2,4,3,5] => [2,3,2] => 7
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,6,7,1,4,5] => [5,6,1,2,3,7,4] => [2,4,1] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => [1,2,4,5,6,3,7] => [5,2] => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6] => [1,2,7,3,4,5,6] => [3,4] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,7,5,6] => [1,2,6,7,3,4,5] => [4,3] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,5,6] => [1,2,5,6,7,3,4] => [5,2] => 5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => [1,2,4,5,6,7,3] => [6,1] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,3,2,4,5,6,7] => [2,5] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3] => [1,3,4,5,7,2,6] => [5,2] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7] => [1,3,4,6,2,5,7] => [4,3] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => [1,3,4,7,2,5,6] => [4,3] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,5,7,3,6] => [1,3,4,6,7,2,5] => [5,2] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7] => [1,3,5,2,4,6,7] => [3,4] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,3,5,7,2,4,6] => [4,3] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => [1,3,6,2,4,5,7] => [3,4] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [7,1,3,5,2,4,6] => [1,3,3] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,6,7,3,5] => [6,1,3,4,7,2,5] => [1,4,2] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5,7] => [1,3,5,6,2,4,7] => [4,3] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => [1,3,7,2,4,5,6] => [3,4] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => [1,3,6,7,2,4,5] => [4,3] => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,7,3,5,6] => [1,3,5,6,7,2,4] => [5,2] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7] => [1,4,2,3,5,6,7] => [2,5] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,6,7,3] => [4,1,2,5,7,3,6] => [1,4,2] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,6,3,7] => [4,1,2,6,3,5,7] => [1,3,3] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6] => [4,1,2,7,3,5,6] => [1,3,3] => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,7,3,6] => [4,1,2,6,7,3,5] => [1,4,2] => 6
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,6,7] => [5,1,3,2,4,6,7] => [1,2,4] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => [2,5,1,3,7,4,6] => [2,3,2] => 7
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,7] => [2,6,1,4,3,5,7] => [2,2,3] => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,1,7,3] => [2,3,7,1,5,4,6] => [3,2,2] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,1,3] => [2,3,6,1,4,7,5] => [3,3,1] => 9
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,1,3,7] => [2,5,1,3,6,4,7] => [2,3,2] => 7
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,1,3,7,6] => [2,7,1,4,3,5,6] => [2,2,3] => 6
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,6] => [2,6,1,3,7,4,5] => [2,3,2] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,7,1,3,6] => [2,5,1,3,6,7,4] => [2,4,1] => 8
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,1,3,6,7] => [4,1,2,5,3,6,7] => [1,3,3] => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,6,7,5] => [5,1,2,7,3,4,6] => [1,3,3] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5,7] => [6,1,3,2,4,5,7] => [1,2,4] => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5] => [2,7,1,5,3,4,6] => [2,2,3] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,7,3,5] => [2,6,1,4,7,3,5] => [2,3,2] => 7
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5,7] => [5,1,2,6,3,4,7] => [1,3,3] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,6,1,3,7,5] => [2,7,1,4,5,3,6] => [2,3,2] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,6,1,7,3,5] => [2,6,7,1,4,3,5] => [3,2,2] => 8
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,6,7,1,3,5] => [2,5,6,1,3,7,4] => [3,3,1] => 9
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,7] => [4,1,2,5,6,3,7] => [1,4,2] => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,4,1,3,5,7,6] => [7,1,3,2,4,5,6] => [1,2,4] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,4,1,3,7,5,6] => [6,1,2,7,3,4,5] => [1,3,3] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,5,6] => [5,1,2,6,7,3,4] => [1,4,2] => 6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,7,1,3,5,6] => [4,1,2,5,6,7,3] => [1,5,1] => 7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => [1,3,4,2,5,6,7] => [3,4] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4] => [1,4,5,7,2,3,6] => [4,3] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7] => [1,4,6,2,3,5,7] => [3,4] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => [1,4,7,2,3,5,6] => [3,4] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,3,5,7,4,6] => [1,4,6,7,2,3,5] => [4,3] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7] => [1,5,2,3,4,6,7] => [2,5] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [5,1,3,7,2,4,6] => [1,3,3] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => [6,1,4,2,3,5,7] => [1,2,4] => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [3,7,1,5,2,4,6] => [2,2,3] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,6,7,3,4] => [3,6,1,4,7,2,5] => [2,3,2] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,6,3,4,7] => [5,1,3,6,2,4,7] => [1,3,3] => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => [7,1,4,2,3,5,6] => [1,2,4] => 4
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => [6,1,3,7,2,4,5] => [1,3,3] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,7,3,4,6] => [5,1,3,6,7,2,4] => [1,4,2] => 6
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,4,6,7] => [1,4,5,2,3,6,7] => [3,4] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,5,1,3,6,7,4] => [5,7,1,3,2,4,6] => [2,2,3] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,5,1,3,6,4,7] => [6,1,3,4,2,5,7] => [1,3,3] => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4] => [7,5,1,3,2,4,6] => [1,1,2,3] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,5,1,6,7,3,4] => [6,4,1,2,7,3,5] => [1,1,3,2] => 8
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,4,7] => [5,6,1,3,2,4,7] => [2,2,3] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,6,1,3,7,4] => [7,4,1,2,5,3,6] => [1,1,3,2] => 8
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,5,6,1,7,3,4] => [6,2,7,1,4,3,5] => [1,2,2,2] => 9
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,1,3,4] => [5,2,6,1,3,7,4] => [1,2,3,1] => 10
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,5,6,1,3,4,7] => [4,5,1,2,6,3,7] => [2,3,2] => 7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1,3,4,7,6] => [7,1,3,4,2,5,6] => [1,3,3] => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,5,1,3,7,4,6] => [6,7,1,3,2,4,5] => [2,2,3] => 6
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,4,6] => [5,6,1,2,7,3,4] => [2,3,2] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => [4,5,1,2,6,7,3] => [2,4,1] => 8
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => [1,3,4,5,2,6,7] => [4,3] => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5] => [1,5,7,2,3,4,6] => [3,4] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7] => [1,6,2,3,4,5,7] => [2,5] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [7,1,5,2,3,4,6] => [1,2,4] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => [6,1,4,7,2,3,5] => [1,3,3] => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,6,4,5,7] => [1,5,6,2,3,4,7] => [3,4] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => [7,1,4,5,2,3,6] => [1,3,3] => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => [6,7,1,4,2,3,5] => [2,2,3] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,7,3,4,5] => [5,6,1,3,7,2,4] => [2,3,2] => 7
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => [1,4,5,6,2,3,7] => [4,3] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,6,1,3,4,7,5] => [7,1,3,4,5,2,6] => [1,4,2] => 6
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6,1,3,7,4,5] => [6,7,1,3,4,2,5] => [2,3,2] => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => [5,6,7,1,3,2,4] => [3,2,2] => 8
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => [4,5,6,1,2,7,3] => [3,3,1] => 9
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => [1,3,4,5,6,2,7] => [5,2] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [1,7,2,3,4,5,6] => [2,5] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => [1,6,7,2,3,4,5] => [3,4] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => [1,5,6,7,2,3,4] => [4,3] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => [1,4,5,6,7,2,3] => [5,2] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => [1,3,4,5,6,7,2] => [6,1] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,6] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => [2,3,4,5,7,1,6] => [5,2] => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => [2,3,4,6,1,5,7] => [4,3] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => [2,3,4,7,1,5,6] => [4,3] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => [2,3,4,6,7,1,5] => [5,2] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => [2,3,5,1,4,6,7] => [3,4] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [2,3,5,7,1,4,6] => [4,3] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [2,3,6,1,4,5,7] => [3,4] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => [7,2,3,5,1,4,6] => [1,3,3] => 5
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => [6,2,3,4,7,1,5] => [1,4,2] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => [2,3,5,6,1,4,7] => [4,3] => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [2,3,7,1,4,5,6] => [3,4] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [2,3,6,7,1,4,5] => [4,3] => 4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => [2,3,5,6,7,1,4] => [5,2] => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => [2,5] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [2,4,5,7,1,3,6] => [4,3] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [2,4,6,1,3,5,7] => [3,4] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [2,4,7,1,3,5,6] => [3,4] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [2,4,6,7,1,3,5] => [4,3] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [2,5,1,3,4,6,7] => [2,5] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => [5,2,3,7,1,4,6] => [1,3,3] => 5
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => [6,2,4,1,3,5,7] => [1,2,4] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => [3,7,2,5,1,4,6] => [2,2,3] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => [3,6,2,4,7,1,5] => [2,3,2] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => [5,2,3,6,1,4,7] => [1,3,3] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => [7,2,4,1,3,5,6] => [1,2,4] => 4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => [6,2,3,7,1,4,5] => [1,3,3] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => [5,2,3,6,7,1,4] => [1,4,2] => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => [2,4,5,1,3,6,7] => [3,4] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [2,5,7,1,3,4,6] => [3,4] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [2,6,1,3,4,5,7] => [2,5] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [7,2,5,1,3,4,6] => [1,2,4] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [6,2,4,7,1,3,5] => [1,3,3] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [2,5,6,1,3,4,7] => [3,4] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => [7,2,4,5,1,3,6] => [1,3,3] => 5
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => [6,7,2,4,1,3,5] => [2,2,3] => 6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => [5,6,2,3,7,1,4] => [2,3,2] => 7
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => [2,4,5,6,1,3,7] => [4,3] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [2,7,1,3,4,5,6] => [2,5] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [2,6,7,1,3,4,5] => [3,4] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [2,5,6,7,1,3,4] => [4,3] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => [2,4,5,6,7,1,3] => [5,2] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => [1,6] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,2] => [3,1,4,5,7,2,6] => [1,4,2] => 6
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,2,7] => [3,1,4,6,2,5,7] => [1,3,3] => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6] => [3,1,4,7,2,5,6] => [1,3,3] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,5,7,2,6] => [3,1,4,6,7,2,5] => [1,4,2] => 6
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,5,2,6,7] => [3,1,5,2,4,6,7] => [1,2,4] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [3,1,5,7,2,4,6] => [1,3,3] => 5
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => [3,1,6,2,4,5,7] => [1,2,4] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [1,7,3,5,2,4,6] => [2,2,3] => 6
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,6,7,2,5] => [1,6,3,4,7,2,5] => [2,3,2] => 7
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,6,2,5,7] => [3,1,5,6,2,4,7] => [1,3,3] => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => [3,1,7,2,4,5,6] => [1,2,4] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => [3,1,6,7,2,4,5] => [1,3,3] => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,7,2,5,6] => [3,1,5,6,7,2,4] => [1,4,2] => 6
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,5,6,7] => [4,2,1,3,5,6,7] => [1,1,5] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,6,7,2] => [1,4,2,5,7,3,6] => [2,3,2] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,6,2,7] => [1,4,2,6,3,5,7] => [2,2,3] => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6] => [1,4,2,7,3,5,6] => [2,2,3] => 6
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,7,2,6] => [1,4,2,6,7,3,5] => [2,3,2] => 7
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,6,7] => [1,5,3,2,4,6,7] => [2,1,4] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,1,6,7,2] => [1,2,5,3,7,4,6] => [3,2,2] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,7] => [1,2,6,4,3,5,7] => [3,1,3] => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,1,7,2] => [1,2,3,7,5,4,6] => [4,1,2] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,2] => [1,2,3,6,4,7,5] => [4,2,1] => 10
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,1,2,7] => [1,2,5,3,6,4,7] => [3,2,2] => 8
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,1,2,7,6] => [1,2,7,4,3,5,6] => [3,1,3] => 7
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,6] => [1,2,6,3,7,4,5] => [3,2,2] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,7,1,2,6] => [1,2,5,3,6,7,4] => [3,3,1] => 9
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6,7] => [1,4,2,5,3,6,7] => [2,2,3] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,1,2,6,7,5] => [1,5,2,7,3,4,6] => [2,2,3] => 6
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5,7] => [1,6,3,2,4,5,7] => [2,1,4] => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5] => [1,2,7,5,3,4,6] => [3,1,3] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,7,2,5] => [1,2,6,4,7,3,5] => [3,2,2] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5,7] => [1,5,2,6,3,4,7] => [2,2,3] => 6
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,6,1,2,7,5] => [1,2,7,4,5,3,6] => [3,2,2] => 8
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,6,1,7,2,5] => [1,2,6,7,4,3,5] => [4,1,2] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,6,7,1,2,5] => [1,2,5,6,3,7,4] => [4,2,1] => 10
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5,7] => [1,4,2,5,6,3,7] => [2,3,2] => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,1,2,5,7,6] => [1,7,3,2,4,5,6] => [2,1,4] => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,2,7,5,6] => [1,6,2,7,3,4,5] => [2,2,3] => 6
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,5,6] => [1,5,2,6,7,3,4] => [2,3,2] => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,7,1,2,5,6] => [1,4,2,5,6,7,3] => [2,4,1] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [3,1,4,2,5,6,7] => [1,2,4] => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,5,6,7,4] => [4,1,5,7,2,3,6] => [1,3,3] => 5
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,5,6,4,7] => [4,1,6,2,3,5,7] => [1,2,4] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => [4,1,7,2,3,5,6] => [1,2,4] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,7,4,6] => [4,1,6,7,2,3,5] => [1,3,3] => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,5,4,6,7] => [5,2,1,3,4,6,7] => [1,1,5] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [1,5,3,7,2,4,6] => [2,2,3] => 6
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,7] => [1,6,4,2,3,5,7] => [2,1,4] => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [1,3,7,5,2,4,6] => [3,1,3] => 7
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,6,7,2,4] => [1,3,6,4,7,2,5] => [3,2,2] => 8
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,6,2,4,7] => [1,5,3,6,2,4,7] => [2,2,3] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,7,6] => [1,7,4,2,3,5,6] => [2,1,4] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,6] => [1,6,3,7,2,4,5] => [2,2,3] => 6
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,7,2,4,6] => [1,5,3,6,7,2,4] => [2,3,2] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,4,6,7] => [4,1,5,2,3,6,7] => [1,2,4] => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,5,1,2,6,7,4] => [1,5,7,3,2,4,6] => [3,1,3] => 7
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,6,4,7] => [1,6,3,4,2,5,7] => [2,2,3] => 6
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => [7,1,5,3,2,4,6] => [1,2,1,3] => 8
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,5,1,6,7,2,4] => [6,1,4,2,7,3,5] => [1,2,2,2] => 9
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,4,7] => [1,5,6,3,2,4,7] => [3,1,3] => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,5,6,1,2,7,4] => [7,1,4,2,5,3,6] => [1,2,2,2] => 9
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,5,6,1,7,2,4] => [6,1,2,7,4,3,5] => [1,3,1,2] => 10
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,1,2,4] => [5,1,2,6,3,7,4] => [1,3,2,1] => 11
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => [1,4,5,2,6,3,7] => [3,2,2] => 8
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,7,6] => [1,7,3,4,2,5,6] => [2,2,3] => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,7,4,6] => [1,6,7,3,2,4,5] => [3,1,3] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,4,6] => [1,5,6,2,7,3,4] => [3,2,2] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,5,7,1,2,4,6] => [1,4,5,2,6,7,3] => [3,3,1] => 9
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,5,1,2,4,6,7] => [3,1,4,5,2,6,7] => [1,3,3] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,2,4,6,7,5] => [5,1,7,2,3,4,6] => [1,2,4] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,2,4,6,5,7] => [6,2,1,3,4,5,7] => [1,1,5] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [1,7,5,2,3,4,6] => [2,1,4] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,2,6,7,4,5] => [1,6,4,7,2,3,5] => [2,2,3] => 6
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,2,6,4,5,7] => [5,1,6,2,3,4,7] => [1,2,4] => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,4,7,5] => [1,7,4,5,2,3,6] => [2,2,3] => 6
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,5] => [1,6,7,4,2,3,5] => [3,1,3] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,7,2,4,5] => [1,5,6,3,7,2,4] => [3,2,2] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,4,5,7] => [4,1,5,6,2,3,7] => [1,3,3] => 5
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1,2,4,7,5] => [1,7,3,4,5,2,6] => [2,3,2] => 7
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [3,6,1,2,7,4,5] => [1,6,7,3,4,2,5] => [3,2,2] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,6,1,7,2,4,5] => [1,5,6,7,3,2,4] => [4,1,2] => 9
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => [1,4,5,6,2,7,3] => [4,2,1] => 10
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,6,1,2,4,5,7] => [3,1,4,5,6,2,7] => [1,4,2] => 6
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [7,2,1,3,4,5,6] => [1,1,5] => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,2,4,7,5,6] => [6,1,7,2,3,4,5] => [1,2,4] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,2,7,4,5,6] => [5,1,6,7,2,3,4] => [1,3,3] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,4,5,6] => [4,1,5,6,7,2,3] => [1,4,2] => 6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,7,1,2,4,5,6] => [3,1,4,5,6,7,2] => [1,5,1] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [2,5] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [3,4,5,7,1,2,6] => [4,3] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [3,4,6,1,2,5,7] => [3,4] => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [3,4,7,1,2,5,6] => [3,4] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [3,4,6,7,1,2,5] => [4,3] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [3,5,1,2,4,6,7] => [2,5] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [3,5,7,1,2,4,6] => [3,4] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [3,6,1,2,4,5,7] => [2,5] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [7,3,5,1,2,4,6] => [1,2,4] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [6,3,4,7,1,2,5] => [1,3,3] => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [3,5,6,1,2,4,7] => [3,4] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [3,7,1,2,4,5,6] => [2,5] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [3,6,7,1,2,4,5] => [3,4] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [3,5,6,7,1,2,4] => [4,3] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => [1,6] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => [4,2,5,7,1,3,6] => [1,3,3] => 5
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => [4,2,6,1,3,5,7] => [1,2,4] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => [4,2,7,1,3,5,6] => [1,2,4] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => [4,2,6,7,1,3,5] => [1,3,3] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => [5,3,1,2,4,6,7] => [1,1,5] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => [2,5,3,7,1,4,6] => [2,2,3] => 6
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => [2,6,4,1,3,5,7] => [2,1,4] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => [2,3,7,5,1,4,6] => [3,1,3] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => [2,3,6,4,7,1,5] => [3,2,2] => 8
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => [2,5,3,6,1,4,7] => [2,2,3] => 6
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => [2,7,4,1,3,5,6] => [2,1,4] => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => [2,6,3,7,1,4,5] => [2,2,3] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => [2,5,3,6,7,1,4] => [2,3,2] => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => [4,2,5,1,3,6,7] => [1,2,4] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [5,2,7,1,3,4,6] => [1,2,4] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [6,3,1,2,4,5,7] => [1,1,5] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => [2,7,5,1,3,4,6] => [2,1,4] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => [2,6,4,7,1,3,5] => [2,2,3] => 6
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => [5,2,6,1,3,4,7] => [1,2,4] => 4
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => [2,7,4,5,1,3,6] => [2,2,3] => 6
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => [2,6,7,4,1,3,5] => [3,1,3] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => [2,5,6,3,7,1,4] => [3,2,2] => 8
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => [4,2,5,6,1,3,7] => [1,3,3] => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [7,3,1,2,4,5,6] => [1,1,5] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [6,2,7,1,3,4,5] => [1,2,4] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => [5,2,6,7,1,3,4] => [1,3,3] => 5
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => [4,2,5,6,7,1,3] => [1,4,2] => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [3,4,1,2,5,6,7] => [2,5] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,6,7,3] => [4,5,1,7,2,3,6] => [2,2,3] => 6
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2,5,6,3,7] => [4,6,2,1,3,5,7] => [2,1,4] => 5
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6] => [4,7,2,1,3,5,6] => [2,1,4] => 5
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,5,7,3,6] => [4,6,1,7,2,3,5] => [2,2,3] => 6
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,3,6,7] => [5,2,3,1,4,6,7] => [1,2,4] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [5,3,1,7,2,4,6] => [1,1,2,3] => 7
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,7] => [6,4,2,1,3,5,7] => [1,1,1,4] => 6
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [3,1,7,5,2,4,6] => [1,2,1,3] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,6,7,2,3] => [3,1,6,4,7,2,5] => [1,2,2,2] => 9
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,6,2,3,7] => [5,3,1,6,2,4,7] => [1,1,2,3] => 7
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,3,7,6] => [7,4,2,1,3,5,6] => [1,1,1,4] => 6
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,6] => [6,3,1,7,2,4,5] => [1,1,2,3] => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,7,2,3,6] => [5,3,1,6,7,2,4] => [1,1,3,2] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,3,6,7] => [4,5,2,1,3,6,7] => [2,1,4] => 5
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,1,2,6,7,3] => [5,1,7,3,2,4,6] => [1,2,1,3] => 8
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,6,3,7] => [6,3,1,4,2,5,7] => [1,1,2,3] => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => [1,7,5,3,2,4,6] => [2,1,1,3] => 9
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,1,6,7,2,3] => [1,6,4,2,7,3,5] => [2,1,2,2] => 10
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,3,7] => [5,1,6,3,2,4,7] => [1,2,1,3] => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,1,2,7,3] => [1,7,4,2,5,3,6] => [2,1,2,2] => 10
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,1,7,2,3] => [1,6,2,7,4,3,5] => [2,2,1,2] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,1,2,3] => [1,5,2,6,3,7,4] => [2,2,2,1] => 12
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [4,1,5,2,6,3,7] => [1,2,2,2] => 9
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,1,2,3,7,6] => [7,3,1,4,2,5,6] => [1,1,2,3] => 7
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,1,2,7,3,6] => [6,1,7,3,2,4,5] => [1,2,1,3] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,3,6] => [5,1,6,2,7,3,4] => [1,2,2,2] => 9
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => [4,1,5,2,6,7,3] => [1,2,3,1] => 10
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7] => [3,4,1,5,2,6,7] => [2,2,3] => 6
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,6,7,5] => [5,7,2,1,3,4,6] => [2,1,4] => 5
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5,7] => [6,2,3,1,4,5,7] => [1,2,4] => 4
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [7,5,2,1,3,4,6] => [1,1,1,4] => 6
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [4,1,2,6,7,3,5] => [6,4,1,7,2,3,5] => [1,1,2,3] => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5,7] => [5,6,2,1,3,4,7] => [2,1,4] => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,3,7,5] => [7,4,1,5,2,3,6] => [1,1,2,3] => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => [6,1,7,4,2,3,5] => [1,2,1,3] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,7,2,3,5] => [5,1,6,3,7,2,4] => [1,2,2,2] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5,7] => [4,5,1,6,2,3,7] => [2,2,3] => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => [7,3,1,4,5,2,6] => [1,1,3,2] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,6,1,2,7,3,5] => [6,1,7,3,4,2,5] => [1,2,2,2] => 9
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,6,1,7,2,3,5] => [5,1,6,7,3,2,4] => [1,3,1,2] => 10
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => [4,1,5,6,2,7,3] => [1,3,2,1] => 11
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5,7] => [3,4,1,5,6,2,7] => [2,3,2] => 7
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [7,2,3,1,4,5,6] => [1,2,4] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [4,1,2,3,7,5,6] => [6,7,2,1,3,4,5] => [2,1,4] => 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,2,7,3,5,6] => [5,6,1,7,2,3,4] => [2,2,3] => 6
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,3,5,6] => [4,5,1,6,7,2,3] => [2,3,2] => 7
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,7,1,2,3,5,6] => [3,4,1,5,6,7,2] => [2,4,1] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [3,4] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [4,5,7,1,2,3,6] => [3,4] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [4,6,1,2,3,5,7] => [2,5] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [4,7,1,2,3,5,6] => [2,5] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [4,6,7,1,2,3,5] => [3,4] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => [1,6] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [5,3,7,1,2,4,6] => [1,2,4] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [6,4,1,2,3,5,7] => [1,1,5] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [3,7,5,1,2,4,6] => [2,1,4] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [3,6,4,7,1,2,5] => [2,2,3] => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [5,3,6,1,2,4,7] => [1,2,4] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [7,4,1,2,3,5,6] => [1,1,5] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [6,3,7,1,2,4,5] => [1,2,4] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [5,3,6,7,1,2,4] => [1,3,3] => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [4,5,1,2,3,6,7] => [2,5] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => [5,7,3,1,2,4,6] => [2,1,4] => 5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => [6,3,4,1,2,5,7] => [1,2,4] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => [7,5,3,1,2,4,6] => [1,1,1,4] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => [6,4,2,7,1,3,5] => [1,1,2,3] => 7
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => [5,6,3,1,2,4,7] => [2,1,4] => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => [7,4,2,5,1,3,6] => [1,1,2,3] => 7
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => [6,2,7,4,1,3,5] => [1,2,1,3] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => [5,2,6,3,7,1,4] => [1,2,2,2] => 9
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => [4,5,2,6,1,3,7] => [2,2,3] => 6
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => [7,3,4,1,2,5,6] => [1,2,4] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => [6,7,3,1,2,4,5] => [2,1,4] => 5
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => [5,6,2,7,1,3,4] => [2,2,3] => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => [4,5,2,6,7,1,3] => [2,3,2] => 7
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => [3,4,5,1,2,6,7] => [3,4] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,2,3,6,7,4] => [5,7,2,3,1,4,6] => [2,2,3] => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,1,2,3,6,4,7] => [6,2,3,4,1,5,7] => [1,3,3] => 5
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [7,5,2,3,1,4,6] => [1,1,2,3] => 7
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,1,2,6,7,3,4] => [6,4,7,2,1,3,5] => [1,2,1,3] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,1,2,6,3,4,7] => [5,6,2,3,1,4,7] => [2,2,3] => 6
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => [7,4,5,2,1,3,6] => [1,2,1,3] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => [6,7,4,2,1,3,5] => [2,1,1,3] => 9
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,1,6,7,2,3,4] => [5,6,3,1,7,2,4] => [2,1,2,2] => 10
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,3,4,7] => [4,5,6,2,1,3,7] => [3,1,3] => 7
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => [7,3,4,1,5,2,6] => [1,2,2,2] => 9
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,6,1,2,7,3,4] => [6,7,3,1,4,2,5] => [2,1,2,2] => 10
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,6,1,7,2,3,4] => [5,6,1,7,3,2,4] => [2,2,1,2] => 11
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,1,2,3,4] => [4,5,1,6,2,7,3] => [2,2,2,1] => 12
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => [3,4,5,1,6,2,7] => [3,2,2] => 8
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [7,2,3,4,1,5,6] => [1,3,3] => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,2,3,7,4,6] => [6,7,2,3,1,4,5] => [2,2,3] => 6
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,1,2,7,3,4,6] => [5,6,7,2,1,3,4] => [3,1,3] => 7
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,3,4,6] => [4,5,6,1,7,2,3] => [3,2,2] => 8
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => [3,4,5,1,6,7,2] => [3,3,1] => 9
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [4,3] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [5,7,1,2,3,4,6] => [2,5] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => [1,6] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [7,5,1,2,3,4,6] => [1,1,5] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [6,4,7,1,2,3,5] => [1,2,4] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [5,6,1,2,3,4,7] => [2,5] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [7,4,5,1,2,3,6] => [1,2,4] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [6,7,4,1,2,3,5] => [2,1,4] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [5,6,3,7,1,2,4] => [2,2,3] => 6
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [4,5,6,1,2,3,7] => [3,4] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => [7,3,4,5,1,2,6] => [1,3,3] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => [6,7,3,4,1,2,5] => [2,2,3] => 6
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => [5,6,7,3,1,2,4] => [3,1,3] => 7
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => [4,5,6,2,7,1,3] => [3,2,2] => 8
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => [3,4,5,6,1,2,7] => [4,3] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [7,2,3,4,5,1,6] => [1,4,2] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,1,2,3,7,4,5] => [6,7,2,3,4,1,5] => [2,3,2] => 7
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,1,2,7,3,4,5] => [5,6,7,2,3,1,4] => [3,2,2] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [6,1,7,2,3,4,5] => [4,5,6,7,2,1,3] => [4,1,2] => 9
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [6,7,1,2,3,4,5] => [3,4,5,6,1,7,2] => [4,2,1] => 10
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [5,2] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => [1,6] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [6,7,1,2,3,4,5] => [2,5] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [5,6,7,1,2,3,4] => [3,4] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [4,5,6,7,1,2,3] => [4,3] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => [3,4,5,6,7,1,2] => [5,2] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [6,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [7] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,8,7] => [7,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,1,8] => [1,2,3,4,5,7,6,8] => [6,2] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7] => [1,2,3,4,5,8,6,7] => [6,2] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,8,1,7] => [1,2,3,4,5,7,8,6] => [7,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,1,7,8] => [1,2,3,4,6,5,7,8] => [5,3] => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,8,6] => [1,2,3,4,6,8,5,7] => [6,2] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,8] => [1,2,3,4,7,5,6,8] => [5,3] => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,7,1,8,6] => [8,1,2,3,4,6,5,7] => [1,5,2] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,7,8,1,6] => [7,1,2,3,4,5,8,6] => [1,6,1] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6,8] => [1,2,3,4,6,7,5,8] => [6,2] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,5,1,6,8,7] => [1,2,3,4,8,5,6,7] => [5,3] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,1,8,6,7] => [1,2,3,4,7,8,5,6] => [6,2] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,8,1,6,7] => [1,2,3,4,6,7,8,5] => [7,1] => 7
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [1,2,3,5,4,6,7,8] => [4,4] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,5] => [1,2,3,5,6,8,4,7] => [6,2] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,4,1,6,7,5,8] => [1,2,3,5,7,4,6,8] => [5,3] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7] => [1,2,3,5,8,4,6,7] => [5,3] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,8,5,7] => [1,2,3,5,7,8,4,6] => [6,2] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,1,6,5,7,8] => [1,2,3,6,4,5,7,8] => [4,4] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,4,6,1,7,8,5] => [6,1,2,3,4,8,5,7] => [1,5,2] => 7
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,4,6,1,7,5,8] => [7,1,2,3,5,4,6,8] => [1,4,3] => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,1,5] => [4,7,1,2,3,5,8,6] => [2,5,1] => 9
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,4,6,7,1,5,8] => [6,1,2,3,4,7,5,8] => [1,5,2] => 7
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,8,5,7] => [7,1,2,3,4,8,5,6] => [1,5,2] => 7
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,4,6,8,1,5,7] => [6,1,2,3,4,7,8,5] => [1,6,1] => 8
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8] => [1,2,3,5,6,4,7,8] => [5,3] => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,4,1,5,7,8,6] => [1,2,3,6,8,4,5,7] => [5,3] => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,4,1,5,7,6,8] => [1,2,3,7,4,5,6,8] => [4,4] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,1,7,5,8,6] => [8,1,2,3,6,4,5,7] => [1,4,3] => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,1,7,8,5,6] => [7,1,2,3,5,8,4,6] => [1,5,2] => 7
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,4,1,7,5,6,8] => [1,2,3,6,7,4,5,8] => [5,3] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,4,7,1,5,8,6] => [8,1,2,3,5,6,4,7] => [1,5,2] => 7
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,4,7,1,8,5,6] => [7,8,1,2,3,5,4,6] => [2,4,2] => 8
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,7,8,1,5,6] => [6,7,1,2,3,4,8,5] => [2,5,1] => 9
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => [1,2,3,5,6,7,4,8] => [6,2] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,4,1,5,6,8,7] => [1,2,3,8,4,5,6,7] => [4,4] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,4,1,5,8,6,7] => [1,2,3,7,8,4,5,6] => [5,3] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [1,2,3,6,7,8,4,5] => [6,2] => 6
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [1,2,3,5,6,7,8,4] => [7,1] => 7
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [1,2,4,3,5,6,7,8] => [3,5] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,4] => [1,2,4,5,6,8,3,7] => [6,2] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,5,6,7,4,8] => [1,2,4,5,7,3,6,8] => [5,3] => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,5,6,8,4,7] => [1,2,4,5,7,8,3,6] => [6,2] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,5,6,4,7,8] => [1,2,4,6,3,5,7,8] => [4,4] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8] => [1,2,4,7,3,5,6,8] => [4,4] => 4
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,5,4,6,7,8] => [1,2,5,3,4,6,7,8] => [3,5] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,4] => [5,1,2,3,6,8,4,7] => [1,5,2] => 7
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,5,1,6,4,8,7] => [5,1,2,3,8,4,6,7] => [1,4,3] => 6
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,5,1,6,8,4,7] => [5,1,2,3,7,8,4,6] => [1,5,2] => 7
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,5,1,6,4,7,8] => [6,1,2,4,3,5,7,8] => [1,3,4] => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,5,6,1,7,8,4] => [3,6,1,2,4,8,5,7] => [2,4,2] => 8
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,5,6,1,7,4,8] => [3,7,1,2,5,4,6,8] => [2,3,3] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,5,6,7,1,8,4] => [3,4,8,1,2,6,5,7] => [3,3,2] => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,1,4] => [3,4,7,1,2,5,8,6] => [3,4,1] => 10
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,6,7,1,4,8] => [3,6,1,2,4,7,5,8] => [2,4,2] => 8
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,6,1,8,4,7] => [3,7,1,2,4,8,5,6] => [2,4,2] => 8
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,8,1,4,7] => [3,6,1,2,4,7,8,5] => [2,5,1] => 9
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => [5,1,2,3,6,4,7,8] => [1,4,3] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6,8] => [7,1,2,4,3,5,6,8] => [1,3,4] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,7,4,8,6] => [3,8,1,2,6,4,5,7] => [2,3,3] => 7
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,7,1,4,8,6] => [3,8,1,2,5,6,4,7] => [2,4,2] => 8
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,7,1,8,4,6] => [3,7,8,1,2,5,4,6] => [3,3,2] => 9
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,7,8,1,4,6] => [3,6,7,1,2,4,8,5] => [3,4,1] => 10
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6,8] => [5,1,2,3,6,7,4,8] => [1,5,2] => 7
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,5,1,4,8,6,7] => [7,1,2,3,8,4,5,6] => [1,4,3] => 6
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,8,4,6,7] => [6,1,2,3,7,8,4,5] => [1,5,2] => 7
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,8,1,4,6,7] => [5,1,2,3,6,7,8,4] => [1,6,1] => 8
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,1,4,6,7,8] => [1,2,4,5,3,6,7,8] => [4,4] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,5] => [1,2,5,6,8,3,4,7] => [5,3] => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,4,6,7,5,8] => [1,2,5,7,3,4,6,8] => [4,4] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,1,4,6,5,8,7] => [1,2,5,8,3,4,6,7] => [4,4] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,8] => [7,1,2,5,3,4,6,8] => [1,3,4] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,4,5] => [4,7,1,2,5,8,3,6] => [2,4,2] => 8
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,4,8,5,7] => [7,1,2,4,8,3,5,6] => [1,4,3] => 6
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,1,6,8,4,5,7] => [6,1,2,4,7,8,3,5] => [1,5,2] => 7
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,1,6,4,5,7,8] => [1,2,5,6,3,4,7,8] => [4,4] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,1,4,7,8,5] => [6,8,1,2,4,3,5,7] => [2,3,3] => 7
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,1,4,7,5,8] => [7,1,2,4,5,3,6,8] => [1,4,3] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,1,7,8,4,5] => [7,5,1,2,3,8,4,6] => [1,1,4,2] => 9
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,6,7,1,8,4,5] => [7,3,8,1,2,5,4,6] => [1,2,3,2] => 10
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,6,7,8,1,4,5] => [6,3,7,1,2,4,8,5] => [1,2,4,1] => 11
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,6,7,1,4,5,8] => [5,6,1,2,3,7,4,8] => [2,4,2] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,8,7] => [8,1,2,4,5,3,6,7] => [1,4,3] => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,6,1,4,8,5,7] => [7,8,1,2,4,3,5,6] => [2,3,3] => 7
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,6,1,8,4,5,7] => [6,7,1,2,3,8,4,5] => [2,4,2] => 8
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,6,8,1,4,5,7] => [5,6,1,2,3,7,8,4] => [2,5,1] => 9
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,6,1,4,5,7,8] => [1,2,4,5,6,3,7,8] => [5,3] => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,4,5,7,8,6] => [1,2,6,8,3,4,5,7] => [4,4] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,1,4,5,7,6,8] => [1,2,7,3,4,5,6,8] => [3,5] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,4,7,8,5,6] => [7,1,2,5,8,3,4,6] => [1,4,3] => 6
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,1,4,7,5,6,8] => [1,2,6,7,3,4,5,8] => [4,4] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,7,4,5,8,6] => [8,1,2,5,6,3,4,7] => [1,4,3] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,7,4,8,5,6] => [7,8,1,2,5,3,4,6] => [2,3,3] => 7
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,7,8,4,5,6] => [6,7,1,2,4,8,3,5] => [2,4,2] => 8
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,1,4,5,8,6] => [8,1,2,4,5,6,3,7] => [1,5,2] => 7
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,1,4,8,5,6] => [7,8,1,2,4,5,3,6] => [2,4,2] => 8
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [5,6,7,1,2,3,8,4] => [3,4,1] => 10
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6,8] => [1,2,4,5,6,7,3,8] => [6,2] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,1,4,5,6,8,7] => [1,2,8,3,4,5,6,7] => [3,5] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => [1,2,7,8,3,4,5,6] => [4,4] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,1,4,8,5,6,7] => [1,2,6,7,8,3,4,5] => [5,3] => 5
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,1,8,4,5,6,7] => [1,2,5,6,7,8,3,4] => [6,2] => 6
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [1,2,4,5,6,7,8,3] => [7,1] => 7
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [2,6] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,3] => [1,3,4,5,6,8,2,7] => [6,2] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,7,3,8] => [1,3,4,5,7,2,6,8] => [5,3] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,3,8,7] => [1,3,4,5,8,2,6,7] => [5,3] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,4,5,6,8,3,7] => [1,3,4,5,7,8,2,6] => [6,2] => 6
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,7,3,8,6] => [8,1,3,4,6,2,5,7] => [1,4,3] => 6
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4,5,7,8,3,6] => [7,1,3,4,5,8,2,6] => [1,5,2] => 7
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,3,6,8,7] => [1,3,4,8,2,5,6,7] => [4,4] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4,5,8,3,6,7] => [1,3,4,6,7,8,2,5] => [6,2] => 6
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4,5,3,6,7,8] => [1,3,5,2,4,6,7,8] => [3,5] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [1,3,5,6,8,2,4,7] => [5,3] => 5
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,6,7,5,8] => [1,3,5,7,2,4,6,8] => [4,4] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7] => [1,3,5,8,2,4,6,7] => [4,4] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,8,5,7] => [1,3,5,7,8,2,4,6] => [5,3] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,7,8] => [1,3,6,2,4,5,7,8] => [3,5] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,6,3,7,8,5] => [6,1,3,4,8,2,5,7] => [1,4,3] => 6
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,6,3,7,5,8] => [7,1,3,5,2,4,6,8] => [1,3,4] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,6,7,3,8,5] => [4,8,1,3,6,2,5,7] => [2,3,3] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,6,7,8,3,5] => [4,7,1,3,5,8,2,6] => [2,4,2] => 8
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,6,7,3,5,8] => [6,1,3,4,7,2,5,8] => [1,4,3] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,8,7] => [8,1,3,5,2,4,6,7] => [1,3,4] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,8,5,7] => [7,1,3,4,8,2,5,6] => [1,4,3] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,8,3,5,7] => [6,1,3,4,7,8,2,5] => [1,5,2] => 7
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,6,3,5,7,8] => [1,3,5,6,2,4,7,8] => [4,4] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => [1,3,6,8,2,4,5,7] => [4,4] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,3,7,5,8,6] => [8,1,3,6,2,4,5,7] => [1,3,4] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => [7,1,3,5,8,2,4,6] => [1,4,3] => 6
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,7,3,5,8,6] => [8,1,3,5,6,2,4,7] => [1,4,3] => 6
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,4,7,8,3,5,6] => [6,7,1,3,4,8,2,5] => [2,4,2] => 8
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,3,5,6,8,7] => [1,3,8,2,4,5,6,7] => [3,5] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,3,5,8,6,7] => [1,3,7,8,2,4,5,6] => [4,4] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,3,8,5,6,7] => [1,3,6,7,8,2,4,5] => [5,3] => 5
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,8,3,5,6,7] => [1,3,5,6,7,8,2,4] => [6,2] => 6
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => [2,6] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,3] => [4,1,2,5,6,8,3,7] => [1,5,2] => 7
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,5,6,7,3,8] => [4,1,2,5,7,3,6,8] => [1,4,3] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,4,1,5,6,3,8,7] => [4,1,2,5,8,3,6,7] => [1,4,3] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,5,6,8,3,7] => [4,1,2,5,7,8,3,6] => [1,5,2] => 7
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,4,1,5,6,3,7,8] => [4,1,2,6,3,5,7,8] => [1,3,4] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,5,3,7,8,6] => [4,1,2,6,8,3,5,7] => [1,4,3] => 6
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,8] => [4,1,2,7,3,5,6,8] => [1,3,4] => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,4,1,5,7,3,8,6] => [2,8,1,4,6,3,5,7] => [2,3,3] => 7
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,3,6,8,7] => [4,1,2,8,3,5,6,7] => [1,3,4] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,5,3,8,6,7] => [4,1,2,7,8,3,5,6] => [1,4,3] => 6
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,3,6,7,8] => [5,1,3,2,4,6,7,8] => [1,2,5] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,4,5,1,6,7,8,3] => [2,5,1,3,6,8,4,7] => [2,4,2] => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,4,5,1,6,7,3,8] => [2,5,1,3,7,4,6,8] => [2,3,3] => 7
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,4,5,1,6,3,8,7] => [2,5,1,3,8,4,6,7] => [2,3,3] => 7
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,4,5,1,6,8,3,7] => [2,5,1,3,7,8,4,6] => [2,4,2] => 8
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,4,5,1,6,3,7,8] => [2,6,1,4,3,5,7,8] => [2,2,4] => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,6,1,7,8,3] => [2,3,6,1,4,8,5,7] => [3,3,2] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,1,8,3] => [2,3,4,8,1,6,5,7] => [4,2,2] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,1,3] => [2,3,4,7,1,5,8,6] => [4,3,1] => 11
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,7,1,3,8] => [2,3,6,1,4,7,5,8] => [3,3,2] => 9
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,6,1,8,3,7] => [2,3,7,1,4,8,5,6] => [3,3,2] => 9
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,6,8,1,3,7] => [2,3,6,1,4,7,8,5] => [3,4,1] => 10
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => [2,5,1,3,6,4,7,8] => [2,3,3] => 7
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,4,5,1,3,7,8,6] => [2,6,1,3,8,4,5,7] => [2,3,3] => 7
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,4,5,1,7,3,8,6] => [2,3,8,1,6,4,5,7] => [3,2,3] => 8
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6,8] => [2,6,1,3,7,4,5,8] => [2,3,3] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,7,1,3,8,6] => [2,3,8,1,5,6,4,7] => [3,3,2] => 9
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,7,1,8,3,6] => [2,3,7,8,1,5,4,6] => [4,2,2] => 10
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,7,8,1,3,6] => [2,3,6,7,1,4,8,5] => [4,3,1] => 11
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => [2,6,1,3,7,8,4,5] => [2,4,2] => 8
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,4,5,8,1,3,6,7] => [2,5,1,3,6,7,8,4] => [2,5,1] => 9
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,1,3,6,7,8] => [4,1,2,5,3,6,7,8] => [1,3,4] => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,6,7,8,5] => [5,1,2,6,8,3,4,7] => [1,4,3] => 6
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7] => [5,1,2,8,3,4,6,7] => [1,3,4] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,8,5,7] => [5,1,2,7,8,3,4,6] => [1,4,3] => 6
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,8,5] => [2,6,1,4,8,3,5,7] => [2,3,3] => 7
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5,8] => [2,7,1,5,3,4,6,8] => [2,2,4] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,6,7,3,8,5] => [2,4,8,1,6,3,5,7] => [3,2,3] => 8
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,6,7,8,3,5] => [2,4,7,1,5,8,3,6] => [3,3,2] => 9
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,1,6,7,3,5,8] => [2,6,1,4,7,3,5,8] => [2,3,3] => 7
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,8,7] => [2,8,1,5,3,4,6,7] => [2,2,4] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,7] => [2,7,1,4,8,3,5,6] => [2,3,3] => 7
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,8,3,5,7] => [2,6,1,4,7,8,3,5] => [2,4,2] => 8
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,6,3,5,7,8] => [5,1,2,6,3,4,7,8] => [1,3,4] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,6,1,3,7,8,5] => [2,6,8,1,4,3,5,7] => [3,2,3] => 8
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,6,1,3,7,5,8] => [2,7,1,4,5,3,6,8] => [2,3,3] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,6,1,7,3,8,5] => [8,2,6,1,4,3,5,7] => [1,2,2,3] => 9
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,6,7,1,3,8,5] => [8,2,5,1,3,6,4,7] => [1,2,3,2] => 10
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => [2,5,6,1,3,7,4,8] => [3,3,2] => 9
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,8,7] => [2,8,1,4,5,3,6,7] => [2,3,3] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [2,6,7,1,3,8,4,5] => [3,3,2] => 9
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [2,5,6,1,3,7,8,4] => [3,4,1] => 10
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,6,1,3,5,7,8] => [4,1,2,5,6,3,7,8] => [1,4,3] => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,3,5,7,8,6] => [6,1,2,8,3,4,5,7] => [1,3,4] => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,3,7,5,8,6] => [2,8,1,6,3,4,5,7] => [2,2,4] => 6
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,3,7,8,5,6] => [2,7,1,5,8,3,4,6] => [2,3,3] => 7
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,7,3,5,8,6] => [2,8,1,5,6,3,4,7] => [2,3,3] => 7
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,7,3,8,5,6] => [2,7,8,1,5,3,4,6] => [3,2,3] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,7,8,3,5,6] => [2,6,7,1,4,8,3,5] => [3,3,2] => 9
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,4,7,1,3,5,8,6] => [2,8,1,4,5,6,3,7] => [2,4,2] => 8
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,4,7,1,3,8,5,6] => [2,7,8,1,4,5,3,6] => [3,3,2] => 9
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,4,7,1,8,3,5,6] => [2,6,7,8,1,4,3,5] => [4,2,2] => 10
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => [2,5,6,7,1,3,8,4] => [4,3,1] => 11
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1,3,8,5,6,7] => [6,1,2,7,8,3,4,5] => [1,4,3] => 6
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1,8,3,5,6,7] => [5,1,2,6,7,8,3,4] => [1,5,2] => 7
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,8,1,3,5,6,7] => [4,1,2,5,6,7,8,3] => [1,6,1] => 8
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8] => [1,3,4,2,5,6,7,8] => [3,5] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,4] => [1,4,5,6,8,2,3,7] => [5,3] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,6,4,8,7] => [1,4,5,8,2,3,6,7] => [4,4] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,8,4,7] => [1,4,5,7,8,2,3,6] => [5,3] => 5
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,7,8,6] => [1,4,6,8,2,3,5,7] => [4,4] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4,6,8,7] => [1,4,8,2,3,5,6,7] => [3,5] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,1,3,5,8,4,6,7] => [1,4,6,7,8,2,3,5] => [5,3] => 5
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,3,5,4,6,7,8] => [1,5,2,3,4,6,7,8] => [2,6] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => [5,1,3,6,8,2,4,7] => [1,4,3] => 6
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,1,5,3,6,7,4,8] => [5,1,3,7,2,4,6,8] => [1,3,4] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7] => [5,1,3,8,2,4,6,7] => [1,3,4] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,1,5,3,6,8,4,7] => [5,1,3,7,8,2,4,6] => [1,4,3] => 6
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,1,5,6,3,7,8,4] => [3,6,1,4,8,2,5,7] => [2,3,3] => 7
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,1,5,6,3,7,4,8] => [3,7,1,5,2,4,6,8] => [2,2,4] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,1,5,6,7,3,8,4] => [3,4,8,1,6,2,5,7] => [3,2,3] => 8
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,3,4] => [3,4,7,1,5,8,2,6] => [3,3,2] => 9
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,1,5,6,7,3,4,8] => [3,6,1,4,7,2,5,8] => [2,3,3] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,8,7] => [3,8,1,5,2,4,6,7] => [2,2,4] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,1,5,6,8,3,4,7] => [3,6,1,4,7,8,2,5] => [2,4,2] => 8
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,1,5,6,3,4,7,8] => [5,1,3,6,2,4,7,8] => [1,3,4] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,1,5,3,7,4,8,6] => [3,8,1,6,2,4,5,7] => [2,2,4] => 6
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,1,5,3,7,8,4,6] => [3,7,1,5,8,2,4,6] => [2,3,3] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,5,7,3,4,8,6] => [3,8,1,5,6,2,4,7] => [2,3,3] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,5,7,3,8,4,6] => [3,7,8,1,5,2,4,6] => [3,2,3] => 8
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,5,7,8,3,4,6] => [3,6,7,1,4,8,2,5] => [3,3,2] => 9
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6,8] => [5,1,3,6,7,2,4,8] => [1,4,3] => 6
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,5,3,4,6,8,7] => [8,1,4,2,3,5,6,7] => [1,2,5] => 4
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,1,5,3,8,4,6,7] => [6,1,3,7,8,2,4,5] => [1,4,3] => 6
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,1,5,8,3,4,6,7] => [5,1,3,6,7,8,2,4] => [1,5,2] => 7
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,1,5,3,4,6,7,8] => [1,4,5,2,3,6,7,8] => [3,5] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,1,3,6,7,8,4] => [5,6,1,2,8,3,4,7] => [2,3,3] => 7
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,5,1,3,6,4,8,7] => [5,8,1,3,2,4,6,7] => [2,2,4] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,5,1,3,6,8,4,7] => [5,7,1,2,8,3,4,6] => [2,3,3] => 7
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,1,3,6,4,7,8] => [6,1,3,4,2,5,7,8] => [1,3,4] => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,5,1,6,3,7,8,4] => [6,4,1,2,8,3,5,7] => [1,1,3,3] => 8
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,5,1,6,3,7,4,8] => [7,5,1,3,2,4,6,8] => [1,1,2,4] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,1,6,7,3,8,4] => [4,2,8,1,6,3,5,7] => [1,2,2,3] => 9
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,1,6,7,8,3,4] => [4,2,7,1,5,8,3,6] => [1,2,3,2] => 10
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,1,6,7,3,4,8] => [6,4,1,2,7,3,5,8] => [1,1,3,3] => 8
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,5,1,6,3,4,8,7] => [8,5,1,3,2,4,6,7] => [1,1,2,4] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,1,6,3,8,4,7] => [7,4,1,2,8,3,5,6] => [1,1,3,3] => 8
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,1,6,8,3,4,7] => [6,4,1,2,7,8,3,5] => [1,1,4,2] => 9
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,1,6,3,4,7,8] => [5,6,1,3,2,4,7,8] => [2,2,4] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,5,6,1,3,7,8,4] => [6,2,8,1,4,3,5,7] => [1,2,2,3] => 9
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,5,6,1,3,7,4,8] => [7,4,1,2,5,3,6,8] => [1,1,3,3] => 8
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,5,6,1,7,8,3,4] => [2,7,5,1,3,8,4,6] => [2,1,3,2] => 11
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,5,6,1,7,3,4,8] => [6,2,7,1,4,3,5,8] => [1,2,2,3] => 9
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,5,6,7,1,8,3,4] => [2,7,3,8,1,5,4,6] => [2,2,2,2] => 12
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,1,3,4] => [2,6,3,7,1,4,8,5] => [2,2,3,1] => 13
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,5,6,1,3,4,8,7] => [8,4,1,2,5,3,6,7] => [1,1,3,3] => 8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,5,6,8,1,3,4,7] => [5,2,6,1,3,7,8,4] => [1,2,4,1] => 11
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,7,4,8,6] => [8,6,1,3,2,4,5,7] => [1,1,2,4] => 7
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,7,8,4,6] => [7,5,1,2,8,3,4,6] => [1,1,3,3] => 8
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,5,1,7,3,4,8,6] => [8,5,1,2,6,3,4,7] => [1,1,3,3] => 8
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,5,1,7,3,8,4,6] => [7,2,8,1,5,3,4,6] => [1,2,2,3] => 9
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,5,1,7,8,3,4,6] => [6,2,7,1,4,8,3,5] => [1,2,3,2] => 10
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,5,7,1,3,4,8,6] => [8,4,1,2,5,6,3,7] => [1,1,4,2] => 9
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,5,7,1,3,8,4,6] => [7,2,8,1,4,5,3,6] => [1,2,3,2] => 10
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,5,7,1,8,3,4,6] => [6,2,7,8,1,4,3,5] => [1,3,2,2] => 11
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [5,2,6,7,1,3,8,4] => [1,3,3,1] => 12
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,5,1,3,8,4,6,7] => [6,7,1,2,8,3,4,5] => [2,3,3] => 7
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,5,1,8,3,4,6,7] => [5,6,1,2,7,8,3,4] => [2,4,2] => 8
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,5,8,1,3,4,6,7] => [4,5,1,2,6,7,8,3] => [2,5,1] => 9
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,4,6,7,8] => [1,3,4,5,2,6,7,8] => [4,4] => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,5] => [1,5,6,8,2,3,4,7] => [4,4] => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,1,3,4,6,7,5,8] => [1,5,7,2,3,4,6,8] => [3,5] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,3,4,6,5,8,7] => [1,5,8,2,3,4,6,7] => [3,5] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,6,5,7,8] => [1,6,2,3,4,5,7,8] => [2,6] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,1,3,6,7,4,8,5] => [4,8,1,6,2,3,5,7] => [2,2,4] => 6
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,6,7,8,4,5] => [4,7,1,5,8,2,3,6] => [2,3,3] => 7
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,1,3,6,4,5,8,7] => [8,1,5,2,3,4,6,7] => [1,2,5] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,1,3,6,4,8,5,7] => [7,1,4,8,2,3,5,6] => [1,3,4] => 5
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,1,3,6,4,5,7,8] => [1,5,6,2,3,4,7,8] => [3,5] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [6,8,1,4,2,3,5,7] => [2,2,4] => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,1,6,3,7,4,8,5] => [8,6,1,4,2,3,5,7] => [1,1,2,4] => 7
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,1,6,3,7,8,4,5] => [7,5,1,3,8,2,4,6] => [1,1,3,3] => 8
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,1,6,3,7,4,5,8] => [6,7,1,4,2,3,5,8] => [2,2,4] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,6,7,3,4,8,5] => [8,5,1,3,6,2,4,7] => [1,1,3,3] => 8
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,1,6,7,3,8,4,5] => [7,3,8,1,5,2,4,6] => [1,2,2,3] => 9
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,3,4,5] => [6,3,7,1,4,8,2,5] => [1,2,3,2] => 10
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,8,7] => [8,1,4,5,2,3,6,7] => [1,3,4] => 5
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,1,6,3,4,8,5,7] => [7,8,1,4,2,3,5,6] => [2,2,4] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,1,6,3,8,4,5,7] => [6,7,1,3,8,2,4,5] => [2,3,3] => 7
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,1,6,8,3,4,5,7] => [5,6,1,3,7,8,2,4] => [2,4,2] => 8
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,1,3,4,7,8,5] => [6,8,1,3,4,2,5,7] => [2,3,3] => 7
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,1,3,4,7,5,8] => [7,1,3,4,5,2,6,8] => [1,4,3] => 6
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,6,1,3,7,4,8,5] => [8,6,1,3,4,2,5,7] => [1,1,3,3] => 8
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,1,3,7,8,4,5] => [7,5,8,1,3,2,4,6] => [1,2,2,3] => 9
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,6,1,7,3,4,8,5] => [8,5,6,1,3,2,4,7] => [1,2,2,3] => 9
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,6,1,7,3,8,4,5] => [7,8,5,1,3,2,4,6] => [2,1,2,3] => 10
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,6,1,7,8,3,4,5] => [6,7,4,1,2,8,3,5] => [2,1,3,2] => 11
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,6,1,7,3,4,5,8] => [5,6,7,1,3,2,4,8] => [3,2,3] => 8
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,6,7,1,3,4,8,5] => [8,4,5,1,2,6,3,7] => [1,2,3,2] => 10
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,6,7,1,3,8,4,5] => [7,8,4,1,2,5,3,6] => [2,1,3,2] => 11
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,6,7,1,8,3,4,5] => [6,7,2,8,1,4,3,5] => [2,2,2,2] => 12
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,6,7,8,1,3,4,5] => [5,6,2,7,1,3,8,4] => [2,2,3,1] => 13
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,6,7,1,3,4,5,8] => [4,5,6,1,2,7,3,8] => [3,3,2] => 9
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,8,7] => [8,1,3,4,5,2,6,7] => [1,4,3] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,8,5,7] => [7,8,1,3,4,2,5,6] => [2,3,3] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,6,1,3,8,4,5,7] => [6,7,8,1,3,2,4,5] => [3,2,3] => 8
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,6,1,8,3,4,5,7] => [5,6,7,1,2,8,3,4] => [3,3,2] => 9
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => [4,5,6,1,2,7,8,3] => [3,4,1] => 10
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,6,1,3,4,5,7,8] => [1,3,4,5,6,2,7,8] => [5,3] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,7,8,6] => [1,6,8,2,3,4,5,7] => [3,5] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,7,6,8] => [1,7,2,3,4,5,6,8] => [2,6] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,4,7,5,8,6] => [8,1,6,2,3,4,5,7] => [1,2,5] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,1,3,4,7,8,5,6] => [7,1,5,8,2,3,4,6] => [1,3,4] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,3,4,7,5,6,8] => [1,6,7,2,3,4,5,8] => [3,5] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,1,3,7,8,4,5,6] => [6,7,1,4,8,2,3,5] => [2,3,3] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,7,3,4,5,8,6] => [8,1,4,5,6,2,3,7] => [1,4,3] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,1,7,3,4,8,5,6] => [7,8,1,4,5,2,3,6] => [2,3,3] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,1,7,3,8,4,5,6] => [6,7,8,1,4,2,3,5] => [3,2,3] => 8
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,1,7,8,3,4,5,6] => [5,6,7,1,3,8,2,4] => [3,3,2] => 9
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6,8] => [1,4,5,6,7,2,3,8] => [5,3] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,1,3,4,8,5,6] => [7,8,1,3,4,5,2,6] => [2,4,2] => 8
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,7,1,3,8,4,5,6] => [6,7,8,1,3,4,2,5] => [3,3,2] => 9
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,7,1,8,3,4,5,6] => [5,6,7,8,1,3,2,4] => [4,2,2] => 10
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [4,5,6,7,1,2,8,3] => [4,3,1] => 11
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6,8] => [1,3,4,5,6,7,2,8] => [6,2] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [1,8,2,3,4,5,6,7] => [2,6] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,3,4,5,8,6,7] => [1,7,8,2,3,4,5,6] => [3,5] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,1,3,4,8,5,6,7] => [1,6,7,8,2,3,4,5] => [4,4] => 4
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => [1,5,6,7,8,2,3,4] => [5,3] => 5
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [1,4,5,6,7,8,2,3] => [6,2] => 6
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [1,3,4,5,6,7,8,2] => [7,1] => 7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [1,7] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,2] => [2,3,4,5,6,8,1,7] => [6,2] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,2,8] => [2,3,4,5,7,1,6,8] => [5,3] => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,6,2,8,7] => [2,3,4,5,8,1,6,7] => [5,3] => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,8,2,7] => [2,3,4,5,7,8,1,6] => [6,2] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,2,7,8] => [2,3,4,6,1,5,7,8] => [4,4] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,5,2,7,8,6] => [2,3,4,6,8,1,5,7] => [5,3] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,8] => [2,3,4,7,1,5,6,8] => [4,4] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,5,7,2,8,6] => [8,2,3,4,6,1,5,7] => [1,4,3] => 6
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,7,8,2,6] => [7,2,3,4,5,8,1,6] => [1,5,2] => 7
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6,8] => [2,3,4,6,7,1,5,8] => [5,3] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,5,2,6,8,7] => [2,3,4,8,1,5,6,7] => [4,4] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,5,2,8,6,7] => [2,3,4,7,8,1,5,6] => [5,3] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,5,8,2,6,7] => [2,3,4,6,7,8,1,5] => [6,2] => 6
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [2,3,5,1,4,6,7,8] => [3,5] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,4,2,6,7,8,5] => [2,3,5,6,8,1,4,7] => [5,3] => 5
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,6,7,5,8] => [2,3,5,7,1,4,6,8] => [4,4] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7] => [2,3,5,8,1,4,6,7] => [4,4] => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,6,2,7,5,8] => [7,2,3,5,1,4,6,8] => [1,3,4] => 5
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,6,7,2,8,5] => [4,8,2,3,6,1,5,7] => [2,3,3] => 7
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,6,7,8,2,5] => [4,7,2,3,5,8,1,6] => [2,4,2] => 8
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,7,2,5,8] => [6,2,3,4,7,1,5,8] => [1,4,3] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,8,7] => [8,2,3,5,1,4,6,7] => [1,3,4] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,4,6,8,2,5,7] => [6,2,3,4,7,8,1,5] => [1,5,2] => 7
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,4,6,2,5,7,8] => [2,3,5,6,1,4,7,8] => [4,4] => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,4,2,5,7,8,6] => [2,3,6,8,1,4,5,7] => [4,4] => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,4,2,5,7,6,8] => [2,3,7,1,4,5,6,8] => [3,5] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,2,7,5,8,6] => [8,2,3,6,1,4,5,7] => [1,3,4] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,4,2,7,8,5,6] => [7,2,3,5,8,1,4,6] => [1,4,3] => 6
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,4,7,2,5,8,6] => [8,2,3,5,6,1,4,7] => [1,4,3] => 6
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,4,7,8,2,5,6] => [6,7,2,3,4,8,1,5] => [2,4,2] => 8
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => [2,3,5,6,7,1,4,8] => [5,3] => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,2,5,6,8,7] => [2,3,8,1,4,5,6,7] => [3,5] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,3,4,2,5,8,6,7] => [2,3,7,8,1,4,5,6] => [4,4] => 4
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [2,3,6,7,8,1,4,5] => [5,3] => 5
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [2,3,5,6,7,8,1,4] => [6,2] => 6
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,2,5,6,7,8] => [2,4,1,3,5,6,7,8] => [2,6] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,6,7,8,4] => [2,4,5,6,8,1,3,7] => [5,3] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,5,6,4,8,7] => [2,4,5,8,1,3,6,7] => [4,4] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,5,6,4,7,8] => [2,4,6,1,3,5,7,8] => [3,5] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,8,6] => [2,4,6,8,1,3,5,7] => [4,4] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8] => [2,4,7,1,3,5,6,8] => [3,5] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,7,4,8,6] => [8,2,4,6,1,3,5,7] => [1,3,4] => 5
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,7,8,4,6] => [7,2,4,5,8,1,3,6] => [1,4,3] => 6
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6,8] => [2,4,6,7,1,3,5,8] => [4,4] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => [2,4,7,8,1,3,5,6] => [4,4] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,5,8,4,6,7] => [2,4,6,7,8,1,3,5] => [5,3] => 5
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8] => [2,5,1,3,4,6,7,8] => [2,6] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,5,2,6,7,8,4] => [5,2,3,6,8,1,4,7] => [1,4,3] => 6
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,5,2,6,4,8,7] => [5,2,3,8,1,4,6,7] => [1,3,4] => 5
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,5,2,6,4,7,8] => [6,2,4,1,3,5,7,8] => [1,2,5] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,5,6,2,7,8,4] => [3,6,2,4,8,1,5,7] => [2,3,3] => 7
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,5,6,2,7,4,8] => [3,7,2,5,1,4,6,8] => [2,2,4] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,8,2,4] => [3,4,7,2,5,8,1,6] => [3,3,2] => 9
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,6,7,2,4,8] => [3,6,2,4,7,1,5,8] => [2,3,3] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,5,6,2,4,8,7] => [3,8,2,5,1,4,6,7] => [2,2,4] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,5,6,2,8,4,7] => [3,7,2,4,8,1,5,6] => [2,3,3] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,6,8,2,4,7] => [3,6,2,4,7,8,1,5] => [2,4,2] => 8
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [5,2,3,6,1,4,7,8] => [1,3,4] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,7,8,6] => [6,2,3,8,1,4,5,7] => [1,3,4] => 5
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,7,4,8,6] => [3,8,2,6,1,4,5,7] => [2,2,4] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,7,8,4,6] => [3,7,2,5,8,1,4,6] => [2,3,3] => 7
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6,8] => [6,2,3,7,1,4,5,8] => [1,3,4] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,7,2,4,8,6] => [3,8,2,5,6,1,4,7] => [2,3,3] => 7
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,7,2,8,4,6] => [3,7,8,2,5,1,4,6] => [3,2,3] => 8
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,7,8,2,4,6] => [3,6,7,2,4,8,1,5] => [3,3,2] => 9
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,5,2,4,6,8,7] => [8,2,4,1,3,5,6,7] => [1,2,5] => 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,5,2,4,8,6,7] => [7,2,3,8,1,4,5,6] => [1,3,4] => 5
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => [6,2,3,7,8,1,4,5] => [1,4,3] => 6
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [5,2,3,6,7,8,1,4] => [1,5,2] => 7
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,2,4,6,7,8] => [2,4,5,1,3,6,7,8] => [3,5] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,4,6,7,8,5] => [2,5,6,8,1,3,4,7] => [4,4] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,4,6,5,8,7] => [2,5,8,1,3,4,6,7] => [3,5] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,4,6,8,5,7] => [2,5,7,8,1,3,4,6] => [4,4] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,4,6,5,7,8] => [2,6,1,3,4,5,7,8] => [2,6] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,3,2,6,4,7,8,5] => [6,2,4,8,1,3,5,7] => [1,3,4] => 5
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,6,4,7,5,8] => [7,2,5,1,3,4,6,8] => [1,2,5] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,3,2,6,7,4,8,5] => [4,8,2,6,1,3,5,7] => [2,2,4] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,7,8,4,5] => [4,7,2,5,8,1,3,6] => [2,3,3] => 7
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,2,6,7,4,5,8] => [6,2,4,7,1,3,5,8] => [1,3,4] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,4,8,5,7] => [7,2,4,8,1,3,5,6] => [1,3,4] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,6,8,4,5,7] => [6,2,4,7,8,1,3,5] => [1,4,3] => 6
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,2,6,4,5,7,8] => [2,5,6,1,3,4,7,8] => [3,5] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,6,2,4,7,8,5] => [6,8,2,4,1,3,5,7] => [2,2,4] => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,2,4,7,5,8] => [7,2,4,5,1,3,6,8] => [1,3,4] => 5
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,2,7,4,8,5] => [8,6,2,4,1,3,5,7] => [1,1,2,4] => 7
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,2,7,8,4,5] => [7,5,2,3,8,1,4,6] => [1,1,3,3] => 8
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,7,4,5,8] => [6,7,2,4,1,3,5,8] => [2,2,4] => 6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,6,7,2,4,8,5] => [8,5,2,3,6,1,4,7] => [1,1,3,3] => 8
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,6,7,8,2,4,5] => [6,3,7,2,4,8,1,5] => [1,2,3,2] => 10
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,6,2,4,8,5,7] => [7,8,2,4,1,3,5,6] => [2,2,4] => 6
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,6,2,4,5,7,8] => [2,4,5,6,1,3,7,8] => [4,4] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,3,2,4,5,7,8,6] => [2,6,8,1,3,4,5,7] => [3,5] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,3,2,4,5,7,6,8] => [2,7,1,3,4,5,6,8] => [2,6] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,3,2,4,7,5,8,6] => [8,2,6,1,3,4,5,7] => [1,2,5] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,4,7,8,5,6] => [7,2,5,8,1,3,4,6] => [1,3,4] => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,7,4,8,5,6] => [7,8,2,5,1,3,4,6] => [2,2,4] => 6
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,3,2,7,4,5,6,8] => [2,5,6,7,1,3,4,8] => [4,4] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,3,7,2,4,8,5,6] => [7,8,2,4,5,1,3,6] => [2,3,3] => 7
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [6,7,8,2,4,1,3,5] => [3,2,3] => 8
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,3,7,8,2,4,5,6] => [5,6,7,2,3,8,1,4] => [3,3,2] => 9
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6,8] => [2,4,5,6,7,1,3,8] => [5,3] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,3,2,4,5,6,8,7] => [2,8,1,3,4,5,6,7] => [2,6] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [2,7,8,1,3,4,5,6] => [3,5] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,3,2,4,8,5,6,7] => [2,6,7,8,1,3,4,5] => [4,4] => 4
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,3,2,8,4,5,6,7] => [2,5,6,7,8,1,3,4] => [5,3] => 5
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [2,4,5,6,7,8,1,3] => [6,2] => 6
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [1,7] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,2] => [3,1,4,5,6,8,2,7] => [1,5,2] => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,2,8] => [3,1,4,5,7,2,6,8] => [1,4,3] => 6
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,5,6,2,8,7] => [3,1,4,5,8,2,6,7] => [1,4,3] => 6
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,4,5,6,8,2,7] => [3,1,4,5,7,8,2,6] => [1,5,2] => 7
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,4,5,6,2,7,8] => [3,1,4,6,2,5,7,8] => [1,3,4] => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6,8] => [3,1,4,7,2,5,6,8] => [1,3,4] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4,5,7,8,2,6] => [1,7,3,4,5,8,2,6] => [2,4,2] => 8
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4,5,8,2,6,7] => [3,1,4,6,7,8,2,5] => [1,5,2] => 7
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,2,6,7,8] => [3,1,5,2,4,6,7,8] => [1,2,5] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [3,1,5,6,8,2,4,7] => [1,4,3] => 6
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,4,2,6,7,5,8] => [3,1,5,7,2,4,6,8] => [1,3,4] => 5
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7] => [3,1,5,8,2,4,6,7] => [1,3,4] => 5
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,8,5,7] => [3,1,5,7,8,2,4,6] => [1,4,3] => 6
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,1,4,2,6,5,7,8] => [3,1,6,2,4,5,7,8] => [1,2,5] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,6,7,2,8,5] => [1,4,8,3,6,2,5,7] => [3,2,3] => 8
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,8,5,7] => [1,7,3,4,8,2,5,6] => [2,3,3] => 7
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,4,6,8,2,5,7] => [1,6,3,4,7,8,2,5] => [2,4,2] => 8
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,7,5,8,6] => [1,8,3,6,2,4,5,7] => [2,2,4] => 6
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,7,2,5,8,6] => [1,8,3,5,6,2,4,7] => [2,3,3] => 7
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,4,7,2,8,5,6] => [1,7,8,3,5,2,4,6] => [3,2,3] => 8
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,4,2,8,5,6,7] => [3,1,6,7,8,2,4,5] => [1,4,3] => 6
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,1,4,8,2,5,6,7] => [3,1,5,6,7,8,2,4] => [1,5,2] => 7
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,2,5,6,7,8] => [4,2,1,3,5,6,7,8] => [1,1,6] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,2] => [1,4,2,5,6,8,3,7] => [2,4,2] => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,5,6,7,2,8] => [1,4,2,5,7,3,6,8] => [2,3,3] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,4,1,5,6,2,8,7] => [1,4,2,5,8,3,6,7] => [2,3,3] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,5,6,8,2,7] => [1,4,2,5,7,8,3,6] => [2,4,2] => 8
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,4,1,5,6,2,7,8] => [1,4,2,6,3,5,7,8] => [2,2,4] => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6,8] => [1,4,2,7,3,5,6,8] => [2,2,4] => 6
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,4,1,5,7,2,8,6] => [1,2,8,4,6,3,5,7] => [3,2,3] => 8
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,7,8,2,6] => [1,2,7,4,5,8,3,6] => [3,3,2] => 9
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6,8] => [1,4,2,6,7,3,5,8] => [2,3,3] => 7
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,2,8,6,7] => [1,4,2,7,8,3,5,6] => [2,3,3] => 7
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4,1,5,8,2,6,7] => [1,4,2,6,7,8,3,5] => [2,4,2] => 8
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4,1,5,2,6,7,8] => [1,5,3,2,4,6,7,8] => [2,1,5] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,2] => [1,2,5,3,6,8,4,7] => [3,3,2] => 9
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,5,1,6,7,2,8] => [1,2,5,3,7,4,6,8] => [3,2,3] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,1,6,2,8,7] => [1,2,5,3,8,4,6,7] => [3,2,3] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,5,1,6,2,7,8] => [1,2,6,4,3,5,7,8] => [3,1,4] => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,1,7,8,2] => [1,2,3,6,4,8,5,7] => [4,2,2] => 10
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,6,1,7,2,8] => [1,2,3,7,5,4,6,8] => [4,1,3] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,1,8,2] => [1,2,3,4,8,6,5,7] => [5,1,2] => 11
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,1,2] => [1,2,3,4,7,5,8,6] => [5,2,1] => 12
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,1,2,8] => [1,2,3,6,4,7,5,8] => [4,2,2] => 10
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,6,1,2,8,7] => [1,2,3,8,5,4,6,7] => [4,1,3] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,6,1,8,2,7] => [1,2,3,7,4,8,5,6] => [4,2,2] => 10
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,6,8,1,2,7] => [1,2,3,6,4,7,8,5] => [4,3,1] => 11
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [1,2,5,3,6,4,7,8] => [3,2,3] => 8
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,5,1,2,7,8,6] => [1,2,6,3,8,4,5,7] => [3,2,3] => 8
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,5,1,7,8,2,6] => [1,2,3,7,5,8,4,6] => [4,2,2] => 10
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6,8] => [1,2,6,3,7,4,5,8] => [3,2,3] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,5,7,1,2,8,6] => [1,2,3,8,5,6,4,7] => [4,2,2] => 10
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,5,7,1,8,2,6] => [1,2,3,7,8,5,4,6] => [5,1,2] => 11
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,5,7,8,1,2,6] => [1,2,3,6,7,4,8,5] => [5,2,1] => 12
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6,8] => [1,2,5,3,6,7,4,8] => [3,3,2] => 9
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,5,1,2,6,8,7] => [1,2,8,4,3,5,6,7] => [3,1,4] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,5,1,2,8,6,7] => [1,2,7,3,8,4,5,6] => [3,2,3] => 8
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [1,2,5,3,6,7,8,4] => [3,4,1] => 10
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [1,4,2,5,3,6,7,8] => [2,2,4] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,6,7,8,5] => [1,5,2,6,8,3,4,7] => [2,3,3] => 7
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,6,7,5,8] => [1,5,2,7,3,4,6,8] => [2,2,4] => 6
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => [1,5,2,8,3,4,6,7] => [2,2,4] => 6
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,8,5,7] => [1,5,2,7,8,3,4,6] => [2,3,3] => 7
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,6,5,7,8] => [1,6,3,2,4,5,7,8] => [2,1,5] => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,4,1,6,2,7,8,5] => [1,2,6,4,8,3,5,7] => [3,2,3] => 8
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,4,1,6,2,7,5,8] => [1,2,7,5,3,4,6,8] => [3,1,4] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,4,1,6,7,2,8,5] => [1,2,4,8,6,3,5,7] => [4,1,3] => 9
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,4,1,6,7,8,2,5] => [1,2,4,7,5,8,3,6] => [4,2,2] => 10
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,4,1,6,7,2,5,8] => [1,2,6,4,7,3,5,8] => [3,2,3] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,8,7] => [1,2,8,5,3,4,6,7] => [3,1,4] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,8,5,7] => [1,2,7,4,8,3,5,6] => [3,2,3] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,8,2,5,7] => [1,2,6,4,7,8,3,5] => [3,3,2] => 9
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,4,6,1,2,7,8,5] => [1,2,6,8,4,3,5,7] => [4,1,3] => 9
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,4,6,1,2,7,5,8] => [1,2,7,4,5,3,6,8] => [3,2,3] => 8
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,4,6,1,7,8,2,5] => [7,1,2,5,3,8,4,6] => [1,3,2,2] => 11
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,4,6,7,1,2,8,5] => [8,1,2,5,3,6,4,7] => [1,3,2,2] => 11
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,4,6,7,1,8,2,5] => [7,1,2,3,8,5,4,6] => [1,4,1,2] => 12
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,6,7,8,1,2,5] => [6,1,2,3,7,4,8,5] => [1,4,2,1] => 13
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,7,1,2,5,8] => [1,2,5,6,3,7,4,8] => [4,2,2] => 10
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,8,7] => [1,2,8,4,5,3,6,7] => [3,2,3] => 8
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [1,2,5,6,3,7,8,4] => [4,3,1] => 11
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,4,1,2,5,7,8,6] => [1,6,2,8,3,4,5,7] => [2,2,4] => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,7,6,8] => [1,7,3,2,4,5,6,8] => [2,1,5] => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,4,1,2,7,5,8,6] => [1,2,8,6,3,4,5,7] => [3,1,4] => 7
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,2,7,8,5,6] => [1,2,7,5,8,3,4,6] => [3,2,3] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,4,1,2,7,5,6,8] => [1,6,2,7,3,4,5,8] => [2,2,4] => 6
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,4,1,7,2,5,8,6] => [1,2,8,5,6,3,4,7] => [3,2,3] => 8
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,4,7,1,2,5,8,6] => [1,2,8,4,5,6,3,7] => [3,3,2] => 9
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => [1,2,6,7,8,4,3,5] => [5,1,2] => 11
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => [1,2,5,6,7,3,8,4] => [5,2,1] => 12
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1,2,5,6,8,7] => [1,8,3,2,4,5,6,7] => [2,1,5] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1,2,5,8,6,7] => [1,7,2,8,3,4,5,6] => [2,2,4] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1,2,8,5,6,7] => [1,6,2,7,8,3,4,5] => [2,3,3] => 7
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1,8,2,5,6,7] => [1,5,2,6,7,8,3,4] => [2,4,2] => 8
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,8,1,2,5,6,7] => [1,4,2,5,6,7,8,3] => [2,5,1] => 9
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [3,1,4,2,5,6,7,8] => [1,2,5] => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,5,6,7,8,4] => [4,1,5,6,8,2,3,7] => [1,4,3] => 6
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,5,6,7,4,8] => [4,1,5,7,2,3,6,8] => [1,3,4] => 5
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,5,6,8,4,7] => [4,1,5,7,8,2,3,6] => [1,4,3] => 6
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,5,6,4,7,8] => [4,1,6,2,3,5,7,8] => [1,2,5] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,8] => [4,1,7,2,3,5,6,8] => [1,2,5] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,7,4,8,6] => [1,8,4,6,2,3,5,7] => [2,2,4] => 6
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,7,8,4,6] => [1,7,4,5,8,2,3,6] => [2,3,3] => 7
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6,8] => [4,1,6,7,2,3,5,8] => [1,3,4] => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,5,4,6,8,7] => [4,1,8,2,3,5,6,7] => [1,2,5] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,5,8,4,6,7] => [4,1,6,7,8,2,3,5] => [1,4,3] => 6
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,7,8,4] => [1,5,3,6,8,2,4,7] => [2,3,3] => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7] => [1,5,3,8,2,4,6,7] => [2,2,4] => 6
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,5,6,2,7,8,4] => [1,3,6,4,8,2,5,7] => [3,2,3] => 8
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,5,6,7,2,8,4] => [1,3,4,8,6,2,5,7] => [4,1,3] => 9
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,5,6,7,8,2,4] => [1,3,4,7,5,8,2,6] => [4,2,2] => 10
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,5,6,2,4,8,7] => [1,3,8,5,2,4,6,7] => [3,1,4] => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,5,6,2,8,4,7] => [1,3,7,4,8,2,5,6] => [3,2,3] => 8
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,5,6,8,2,4,7] => [1,3,6,4,7,8,2,5] => [3,3,2] => 9
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,5,6,2,4,7,8] => [1,5,3,6,2,4,7,8] => [2,2,4] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,7,8,6] => [1,6,3,8,2,4,5,7] => [2,2,4] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6,8] => [1,7,4,2,3,5,6,8] => [2,1,5] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,8,6] => [1,3,8,6,2,4,5,7] => [3,1,4] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,7,8,4,6] => [1,3,7,5,8,2,4,6] => [3,2,3] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6,8] => [1,6,3,7,2,4,5,8] => [2,2,4] => 6
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,7,2,4,8,6] => [1,3,8,5,6,2,4,7] => [3,2,3] => 8
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,7,2,8,4,6] => [1,3,7,8,5,2,4,6] => [4,1,3] => 9
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,7,8,2,4,6] => [1,3,6,7,4,8,2,5] => [4,2,2] => 10
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,5,2,4,6,8,7] => [1,8,4,2,3,5,6,7] => [2,1,5] => 5
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,5,2,4,8,6,7] => [1,7,3,8,2,4,5,6] => [2,2,4] => 6
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,5,2,8,4,6,7] => [1,6,3,7,8,2,4,5] => [2,3,3] => 7
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,5,8,2,4,6,7] => [1,5,3,6,7,8,2,4] => [2,4,2] => 8
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,5,2,4,6,7,8] => [4,1,5,2,3,6,7,8] => [1,2,5] => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,5,1,2,6,7,8,4] => [1,5,6,2,8,3,4,7] => [3,2,3] => 8
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => [1,5,7,3,2,4,6,8] => [3,1,4] => 7
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,5,1,2,6,4,8,7] => [1,5,8,3,2,4,6,7] => [3,1,4] => 7
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,5,1,2,6,8,4,7] => [1,5,7,2,8,3,4,6] => [3,2,3] => 8
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,5,1,6,2,7,8,4] => [6,1,4,2,8,3,5,7] => [1,2,2,3] => 9
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,5,1,6,2,7,4,8] => [7,1,5,3,2,4,6,8] => [1,2,1,4] => 8
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,5,1,6,7,2,8,4] => [4,1,2,8,6,3,5,7] => [1,3,1,3] => 10
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,5,1,6,7,8,2,4] => [4,1,2,7,5,8,3,6] => [1,3,2,2] => 11
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,5,1,6,7,2,4,8] => [6,1,4,2,7,3,5,8] => [1,2,2,3] => 9
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,5,1,6,2,4,8,7] => [8,1,5,3,2,4,6,7] => [1,2,1,4] => 8
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,5,1,6,8,2,4,7] => [6,1,4,2,7,8,3,5] => [1,2,3,2] => 10
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,5,1,6,2,4,7,8] => [1,5,6,3,2,4,7,8] => [3,1,4] => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,5,6,1,2,7,8,4] => [6,1,2,8,4,3,5,7] => [1,3,1,3] => 10
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,5,6,1,2,7,4,8] => [7,1,4,2,5,3,6,8] => [1,2,2,3] => 9
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,5,6,1,7,2,8,4] => [2,8,1,6,4,3,5,7] => [2,2,1,3] => 11
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,5,6,1,7,8,2,4] => [2,7,1,5,3,8,4,6] => [2,2,2,2] => 12
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,5,6,1,7,2,4,8] => [6,1,2,7,4,3,5,8] => [1,3,1,3] => 10
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,5,6,7,1,8,2,4] => [2,7,1,3,8,5,4,6] => [2,3,1,2] => 13
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,8,1,2,4] => [2,6,1,3,7,4,8,5] => [2,3,2,1] => 14
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,5,6,7,1,2,4,8] => [5,1,2,6,3,7,4,8] => [1,3,2,2] => 11
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,5,6,1,2,4,8,7] => [8,1,4,2,5,3,6,7] => [1,2,2,3] => 9
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,5,6,1,2,8,4,7] => [7,1,2,8,4,3,5,6] => [1,3,1,3] => 10
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => [6,1,2,7,3,8,4,5] => [1,3,2,2] => 11
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [5,1,2,6,3,7,8,4] => [1,3,3,1] => 12
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,5,6,1,2,4,7,8] => [1,4,5,2,6,3,7,8] => [3,2,3] => 8
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,7,8,6] => [1,6,8,3,2,4,5,7] => [3,1,4] => 7
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [1,7,3,4,2,5,6,8] => [2,2,4] => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,7,4,8,6] => [8,1,6,3,2,4,5,7] => [1,2,1,4] => 8
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,7,8,4,6] => [7,1,5,2,8,3,4,6] => [1,2,2,3] => 9
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6,8] => [1,6,7,3,2,4,5,8] => [3,1,4] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,7,2,4,8,6] => [8,1,5,2,6,3,4,7] => [1,2,2,3] => 9
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => [7,1,2,8,5,3,4,6] => [1,3,1,3] => 10
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,7,8,2,4,6] => [6,1,2,7,4,8,3,5] => [1,3,2,2] => 11
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6,8] => [1,5,6,2,7,3,4,8] => [3,2,3] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,7,1,2,4,8,6] => [8,1,4,2,5,6,3,7] => [1,2,3,2] => 10
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,7,1,2,8,4,6] => [7,1,2,8,4,5,3,6] => [1,3,2,2] => 11
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [5,1,2,6,7,3,8,4] => [1,4,2,1] => 13
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6,8] => [1,4,5,2,6,7,3,8] => [3,3,2] => 9
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,5,1,2,4,6,8,7] => [1,8,3,4,2,5,6,7] => [2,2,4] => 6
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,5,1,2,4,8,6,7] => [1,7,8,3,2,4,5,6] => [3,1,4] => 7
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,5,1,2,8,4,6,7] => [1,6,7,2,8,3,4,5] => [3,2,3] => 8
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,5,1,8,2,4,6,7] => [1,5,6,2,7,8,3,4] => [3,3,2] => 9
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,5,1,2,4,6,7,8] => [3,1,4,5,2,6,7,8] => [1,3,4] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,2,4,6,7,8,5] => [5,1,6,8,2,3,4,7] => [1,3,4] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,7,5,8] => [5,1,7,2,3,4,6,8] => [1,2,5] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,2,4,6,5,8,7] => [5,1,8,2,3,4,6,7] => [1,2,5] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [3,1,2,4,6,8,5,7] => [5,1,7,8,2,3,4,6] => [1,3,4] => 5
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [3,1,2,6,4,7,8,5] => [1,6,4,8,2,3,5,7] => [2,2,4] => 6
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [3,1,2,6,4,7,5,8] => [1,7,5,2,3,4,6,8] => [2,1,5] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,6,7,4,8,5] => [1,4,8,6,2,3,5,7] => [3,1,4] => 7
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,2,6,7,8,4,5] => [1,4,7,5,8,2,3,6] => [3,2,3] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [3,1,2,6,4,5,8,7] => [1,8,5,2,3,4,6,7] => [2,1,5] => 5
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [3,1,2,6,8,4,5,7] => [1,6,4,7,8,2,3,5] => [2,3,3] => 7
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,7,8,5] => [1,6,8,4,2,3,5,7] => [3,1,4] => 7
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,1,6,2,4,7,5,8] => [1,7,4,5,2,3,6,8] => [2,2,4] => 6
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,6,2,7,4,8,5] => [8,1,6,4,2,3,5,7] => [1,2,1,4] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [3,1,6,2,7,4,5,8] => [1,6,7,4,2,3,5,8] => [3,1,4] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [3,1,6,7,2,8,4,5] => [7,1,3,8,5,2,4,6] => [1,3,1,3] => 10
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,1,6,7,2,4,5,8] => [1,5,6,3,7,2,4,8] => [3,2,3] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,8,7] => [1,8,4,5,2,3,6,7] => [2,2,4] => 6
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [3,1,6,2,4,8,5,7] => [1,7,8,4,2,3,5,6] => [3,1,4] => 7
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,1,6,8,2,4,5,7] => [1,5,6,3,7,8,2,4] => [3,3,2] => 9
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,1,6,2,4,5,7,8] => [4,1,5,6,2,3,7,8] => [1,3,4] => 5
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,6,1,2,4,7,8,5] => [1,6,8,3,4,2,5,7] => [3,2,3] => 8
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => [1,7,3,4,5,2,6,8] => [2,3,3] => 7
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,6,1,2,7,4,8,5] => [8,1,6,3,4,2,5,7] => [1,2,2,3] => 9
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [3,6,1,2,7,8,4,5] => [7,1,5,8,3,2,4,6] => [1,3,1,3] => 10
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,6,1,7,2,4,8,5] => [8,1,5,6,3,2,4,7] => [1,3,1,3] => 10
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => [7,8,1,5,3,2,4,6] => [2,2,1,3] => 11
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [3,6,1,7,8,2,4,5] => [6,7,1,4,2,8,3,5] => [2,2,2,2] => 12
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [3,6,7,1,2,8,4,5] => [7,8,1,4,2,5,3,6] => [2,2,2,2] => 12
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [5,6,1,2,7,3,8,4] => [2,3,2,1] => 14
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,6,7,1,2,4,5,8] => [1,4,5,6,2,7,3,8] => [4,2,2] => 10
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,8,7] => [1,8,3,4,5,2,6,7] => [2,3,3] => 7
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,8,5,7] => [1,7,8,3,4,2,5,6] => [3,2,3] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [3,6,1,2,8,4,5,7] => [1,6,7,8,3,2,4,5] => [4,1,3] => 9
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,6,1,8,2,4,5,7] => [1,5,6,7,2,8,3,4] => [4,2,2] => 10
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,6,8,1,2,4,5,7] => [1,4,5,6,2,7,8,3] => [4,3,1] => 11
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,6,1,2,4,5,7,8] => [3,1,4,5,6,2,7,8] => [1,4,3] => 6
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,2,4,5,7,8,6] => [6,1,8,2,3,4,5,7] => [1,2,5] => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,2,4,5,7,6,8] => [7,2,1,3,4,5,6,8] => [1,1,6] => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,4,7,5,8,6] => [1,8,6,2,3,4,5,7] => [2,1,5] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,2,4,7,8,5,6] => [1,7,5,8,2,3,4,6] => [2,2,4] => 6
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [3,1,2,4,7,5,6,8] => [6,1,7,2,3,4,5,8] => [1,2,5] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [3,1,2,7,4,8,5,6] => [1,7,8,5,2,3,4,6] => [3,1,4] => 7
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [3,1,2,7,8,4,5,6] => [1,6,7,4,8,2,3,5] => [3,2,3] => 8
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,1,2,7,4,5,6,8] => [5,1,6,7,2,3,4,8] => [1,3,4] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,7,2,4,5,8,6] => [1,8,4,5,6,2,3,7] => [2,3,3] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [3,1,7,2,8,4,5,6] => [1,6,7,8,4,2,3,5] => [4,1,3] => 9
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,7,8,2,4,5,6] => [1,5,6,7,3,8,2,4] => [4,2,2] => 10
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6,8] => [4,1,5,6,7,2,3,8] => [1,4,3] => 6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,7,1,2,4,5,8,6] => [1,8,3,4,5,6,2,7] => [2,4,2] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [3,7,1,2,4,8,5,6] => [1,7,8,3,4,5,2,6] => [3,3,2] => 9
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [3,7,1,2,8,4,5,6] => [1,6,7,8,3,4,2,5] => [4,2,2] => 10
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,7,1,8,2,4,5,6] => [1,5,6,7,8,3,2,4] => [5,1,2] => 11
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,7,8,1,2,4,5,6] => [1,4,5,6,7,2,8,3] => [5,2,1] => 12
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6,8] => [3,1,4,5,6,7,2,8] => [1,5,2] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [8,2,1,3,4,5,6,7] => [1,1,6] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,2,4,5,8,6,7] => [7,1,8,2,3,4,5,6] => [1,2,5] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,2,4,8,5,6,7] => [6,1,7,8,2,3,4,5] => [1,3,4] => 5
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,2,8,4,5,6,7] => [5,1,6,7,8,2,3,4] => [1,4,3] => 6
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [4,1,5,6,7,8,2,3] => [1,5,2] => 7
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [3,1,4,5,6,7,8,2] => [1,6,1] => 8
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [2,6] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,3] => [3,4,5,6,8,1,2,7] => [5,3] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,7,3,8] => [3,4,5,7,1,2,6,8] => [4,4] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,4,5,6,3,8,7] => [3,4,5,8,1,2,6,7] => [4,4] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,6,8,3,7] => [3,4,5,7,8,1,2,6] => [5,3] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,4,5,6,3,7,8] => [3,4,6,1,2,5,7,8] => [3,5] => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,5,3,7,8,6] => [3,4,6,8,1,2,5,7] => [4,4] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6,8] => [3,4,7,1,2,5,6,8] => [3,5] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,7,3,8,6] => [8,3,4,6,1,2,5,7] => [1,3,4] => 5
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,7,8,3,6] => [7,3,4,5,8,1,2,6] => [1,4,3] => 6
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6,8] => [3,4,6,7,1,2,5,8] => [4,4] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,4,5,3,8,6,7] => [3,4,7,8,1,2,5,6] => [4,4] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,4,5,8,3,6,7] => [3,4,6,7,8,1,2,5] => [5,3] => 5
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [3,5,1,2,4,6,7,8] => [2,6] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,5] => [3,5,6,8,1,2,4,7] => [4,4] => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,6,7,5,8] => [3,5,7,1,2,4,6,8] => [3,5] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7] => [3,5,8,1,2,4,6,7] => [3,5] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,8,5,7] => [3,5,7,8,1,2,4,6] => [4,4] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8] => [3,6,1,2,4,5,7,8] => [2,6] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,6,3,7,8,5] => [6,3,4,8,1,2,5,7] => [1,3,4] => 5
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,6,3,7,5,8] => [7,3,5,1,2,4,6,8] => [1,2,5] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,6,7,8,3,5] => [4,7,3,5,8,1,2,6] => [2,3,3] => 7
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,6,7,3,5,8] => [6,3,4,7,1,2,5,8] => [1,3,4] => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,8,7] => [8,3,5,1,2,4,6,7] => [1,2,5] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,8,5,7] => [7,3,4,8,1,2,5,6] => [1,3,4] => 5
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,8,3,5,7] => [6,3,4,7,8,1,2,5] => [1,4,3] => 6
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => [3,5,6,1,2,4,7,8] => [3,5] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,4,3,5,7,8,6] => [3,6,8,1,2,4,5,7] => [3,5] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5,7,6,8] => [3,7,1,2,4,5,6,8] => [2,6] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,3,7,5,8,6] => [8,3,6,1,2,4,5,7] => [1,2,5] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,4,3,7,8,5,6] => [7,3,5,8,1,2,4,6] => [1,3,4] => 5
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,4,3,7,5,6,8] => [3,6,7,1,2,4,5,8] => [3,5] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,7,3,5,8,6] => [8,3,5,6,1,2,4,7] => [1,3,4] => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,4,7,3,8,5,6] => [7,8,3,5,1,2,4,6] => [2,2,4] => 6
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,4,7,8,3,5,6] => [6,7,3,4,8,1,2,5] => [2,3,3] => 7
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => [3,5,6,7,1,2,4,8] => [4,4] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,3,5,6,8,7] => [3,8,1,2,4,5,6,7] => [2,6] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,3,5,8,6,7] => [3,7,8,1,2,4,5,6] => [3,5] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [3,6,7,8,1,2,4,5] => [4,4] => 4
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [3,5,6,7,8,1,2,4] => [5,3] => 5
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => [1,7] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,3] => [4,2,5,6,8,1,3,7] => [1,4,3] => 6
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,4,2,5,6,7,3,8] => [4,2,5,7,1,3,6,8] => [1,3,4] => 5
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,4,2,5,6,8,3,7] => [4,2,5,7,8,1,3,6] => [1,4,3] => 6
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,4,2,5,3,7,8,6] => [4,2,6,8,1,3,5,7] => [1,3,4] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,8] => [4,2,7,1,3,5,6,8] => [1,2,5] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,4,2,5,7,3,8,6] => [2,8,4,6,1,3,5,7] => [2,2,4] => 6
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,4,2,5,7,8,3,6] => [2,7,4,5,8,1,3,6] => [2,3,3] => 7
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6,8] => [4,2,6,7,1,3,5,8] => [1,3,4] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,4,2,5,3,6,8,7] => [4,2,8,1,3,5,6,7] => [1,2,5] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3,8,6,7] => [4,2,7,8,1,3,5,6] => [1,3,4] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,4,2,5,8,3,6,7] => [4,2,6,7,8,1,3,5] => [1,4,3] => 6
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,4,2,5,3,6,7,8] => [5,3,1,2,4,6,7,8] => [1,1,6] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,5,2,6,7,8,3] => [2,5,3,6,8,1,4,7] => [2,3,3] => 7
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,5,2,6,7,3,8] => [2,5,3,7,1,4,6,8] => [2,2,4] => 6
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,5,2,6,3,8,7] => [2,5,3,8,1,4,6,7] => [2,2,4] => 6
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,5,2,6,8,3,7] => [2,5,3,7,8,1,4,6] => [2,3,3] => 7
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,5,2,6,3,7,8] => [2,6,4,1,3,5,7,8] => [2,1,5] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,4,5,6,2,7,8,3] => [2,3,6,4,8,1,5,7] => [3,2,3] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,7,2,8,3] => [2,3,4,8,6,1,5,7] => [4,1,3] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,2,3] => [2,3,4,7,5,8,1,6] => [4,2,2] => 10
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,7,2,3,8] => [2,3,6,4,7,1,5,8] => [3,2,3] => 8
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,4,5,6,2,3,8,7] => [2,3,8,5,1,4,6,7] => [3,1,4] => 7
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,4,5,6,2,8,3,7] => [2,3,7,4,8,1,5,6] => [3,2,3] => 8
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,4,5,6,8,2,3,7] => [2,3,6,4,7,8,1,5] => [3,3,2] => 9
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3,7,8] => [2,5,3,6,1,4,7,8] => [2,2,4] => 6
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,4,5,2,3,7,8,6] => [2,6,3,8,1,4,5,7] => [2,2,4] => 6
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6,8] => [2,7,4,1,3,5,6,8] => [2,1,5] => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,4,5,2,7,3,8,6] => [2,3,8,6,1,4,5,7] => [3,1,4] => 7
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,4,5,2,7,8,3,6] => [2,3,7,5,8,1,4,6] => [3,2,3] => 8
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6,8] => [2,6,3,7,1,4,5,8] => [2,2,4] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,4,5,7,2,3,8,6] => [2,3,8,5,6,1,4,7] => [3,2,3] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,4,5,7,8,2,3,6] => [2,3,6,7,4,8,1,5] => [4,2,2] => 10
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6,8] => [2,5,3,6,7,1,4,8] => [2,3,3] => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,4,5,2,3,8,6,7] => [2,7,3,8,1,4,5,6] => [2,2,4] => 6
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,8,3,6,7] => [2,6,3,7,8,1,4,5] => [2,3,3] => 7
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,4,5,8,2,3,6,7] => [2,5,3,6,7,8,1,4] => [2,4,2] => 8
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,4,5,2,3,6,7,8] => [4,2,5,1,3,6,7,8] => [1,2,5] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,6,7,8,5] => [5,2,6,8,1,3,4,7] => [1,3,4] => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,6,7,5,8] => [5,2,7,1,3,4,6,8] => [1,2,5] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7] => [5,2,8,1,3,4,6,7] => [1,2,5] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,6,5,7,8] => [6,3,1,2,4,5,7,8] => [1,1,6] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,6,3,7,5,8] => [2,7,5,1,3,4,6,8] => [2,1,5] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,7,8,3,5] => [2,4,7,5,8,1,3,6] => [3,2,3] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,8,7] => [2,8,5,1,3,4,6,7] => [2,1,5] => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,7] => [2,7,4,8,1,3,5,6] => [2,2,4] => 6
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,8,3,5,7] => [2,6,4,7,8,1,3,5] => [2,3,3] => 7
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,6,3,5,7,8] => [5,2,6,1,3,4,7,8] => [1,2,5] => 4
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,4,6,2,3,7,8,5] => [2,6,8,4,1,3,5,7] => [3,1,4] => 7
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,4,6,2,7,3,8,5] => [8,2,6,4,1,3,5,7] => [1,2,1,4] => 8
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,4,6,2,7,8,3,5] => [7,2,5,3,8,1,4,6] => [1,2,2,3] => 9
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,7,3,5,8] => [2,6,7,4,1,3,5,8] => [3,1,4] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,4,6,7,2,3,8,5] => [8,2,5,3,6,1,4,7] => [1,2,2,3] => 9
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,4,6,7,2,8,3,5] => [7,2,3,8,5,1,4,6] => [1,3,1,3] => 10
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,4,6,7,8,2,3,5] => [6,2,3,7,4,8,1,5] => [1,3,2,2] => 11
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => [2,5,6,3,7,1,4,8] => [3,2,3] => 8
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,8,7] => [2,8,4,5,1,3,6,7] => [2,2,4] => 6
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,8,5,7] => [2,7,8,4,1,3,5,6] => [3,1,4] => 7
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,8,3,5,7] => [2,6,7,3,8,1,4,5] => [3,2,3] => 8
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => [2,5,6,3,7,8,1,4] => [3,3,2] => 9
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,4,6,2,3,5,7,8] => [4,2,5,6,1,3,7,8] => [1,3,4] => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,4,2,3,5,7,8,6] => [6,2,8,1,3,4,5,7] => [1,2,5] => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2,3,5,7,6,8] => [7,3,1,2,4,5,6,8] => [1,1,6] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,4,2,3,7,5,8,6] => [2,8,6,1,3,4,5,7] => [2,1,5] => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,3,7,8,5,6] => [2,7,5,8,1,3,4,6] => [2,2,4] => 6
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2,3,7,5,6,8] => [6,2,7,1,3,4,5,8] => [1,2,5] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,4,2,7,3,5,8,6] => [2,8,5,6,1,3,4,7] => [2,2,4] => 6
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,7,3,8,5,6] => [2,7,8,5,1,3,4,6] => [3,1,4] => 7
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,2,7,8,3,5,6] => [2,6,7,4,8,1,3,5] => [3,2,3] => 8
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2,7,3,5,6,8] => [5,2,6,7,1,3,4,8] => [1,3,4] => 5
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,4,7,2,3,5,8,6] => [2,8,4,5,6,1,3,7] => [2,3,3] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,7,2,3,8,5,6] => [2,7,8,4,5,1,3,6] => [3,2,3] => 8
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,7,2,8,3,5,6] => [2,6,7,8,4,1,3,5] => [4,1,3] => 9
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,4,7,8,2,3,5,6] => [2,5,6,7,3,8,1,4] => [4,2,2] => 10
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6,8] => [4,2,5,6,7,1,3,8] => [1,4,3] => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,4,2,3,5,6,8,7] => [8,3,1,2,4,5,6,7] => [1,1,6] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [7,2,8,1,3,4,5,6] => [1,2,5] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,2,3,8,5,6,7] => [6,2,7,8,1,3,4,5] => [1,3,4] => 5
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,2,8,3,5,6,7] => [5,2,6,7,8,1,3,4] => [1,4,3] => 6
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => [4,2,5,6,7,8,1,3] => [1,5,2] => 7
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => [2,6] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,3] => [4,5,1,6,8,2,3,7] => [2,3,3] => 7
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,2,5,6,7,3,8] => [4,5,1,7,2,3,6,8] => [2,2,4] => 6
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,5,6,3,8,7] => [4,5,1,8,2,3,6,7] => [2,2,4] => 6
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,5,6,8,3,7] => [4,5,1,7,8,2,3,6] => [2,3,3] => 7
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3,7,8] => [4,6,2,1,3,5,7,8] => [2,1,5] => 5
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,5,3,7,8,6] => [4,6,1,8,2,3,5,7] => [2,2,4] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6,8] => [4,7,2,1,3,5,6,8] => [2,1,5] => 5
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,5,7,3,8,6] => [8,4,1,6,2,3,5,7] => [1,1,2,4] => 7
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,5,7,8,3,6] => [7,4,1,5,8,2,3,6] => [1,1,3,3] => 8
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6,8] => [4,6,1,7,2,3,5,8] => [2,2,4] => 6
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,1,2,5,8,3,6,7] => [4,6,1,7,8,2,3,5] => [2,3,3] => 7
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,5,3,6,7,8] => [5,2,3,1,4,6,7,8] => [1,2,5] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => [5,3,1,6,8,2,4,7] => [1,1,3,3] => 8
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => [5,3,1,8,2,4,6,7] => [1,1,2,4] => 7
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,5,2,6,8,3,7] => [5,3,1,7,8,2,4,6] => [1,1,3,3] => 8
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,1,5,2,6,3,7,8] => [6,4,2,1,3,5,7,8] => [1,1,1,5] => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,5,6,7,2,8,3] => [3,1,4,8,6,2,5,7] => [1,3,1,3] => 10
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,5,6,7,8,2,3] => [3,1,4,7,5,8,2,6] => [1,3,2,2] => 11
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,1,5,6,7,2,3,8] => [3,1,6,4,7,2,5,8] => [1,2,2,3] => 9
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,5,6,2,3,8,7] => [3,1,8,5,2,4,6,7] => [1,2,1,4] => 8
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [4,1,5,6,2,8,3,7] => [3,1,7,4,8,2,5,6] => [1,2,2,3] => 9
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [4,1,5,6,8,2,3,7] => [3,1,6,4,7,8,2,5] => [1,2,3,2] => 10
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,1,5,6,2,3,7,8] => [5,3,1,6,2,4,7,8] => [1,1,2,4] => 7
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => [6,3,1,8,2,4,5,7] => [1,1,2,4] => 7
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,5,2,7,3,8,6] => [3,1,8,6,2,4,5,7] => [1,2,1,4] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => [3,1,7,5,8,2,4,6] => [1,2,2,3] => 9
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6,8] => [6,3,1,7,2,4,5,8] => [1,1,2,4] => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,1,5,7,2,8,3,6] => [3,1,7,8,5,2,4,6] => [1,3,1,3] => 10
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6,8] => [5,3,1,6,7,2,4,8] => [1,1,3,3] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,1,5,2,3,8,6,7] => [7,3,1,8,2,4,5,6] => [1,1,2,4] => 7
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [4,1,5,2,8,3,6,7] => [6,3,1,7,8,2,4,5] => [1,1,3,3] => 8
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,1,5,8,2,3,6,7] => [5,3,1,6,7,8,2,4] => [1,1,4,2] => 9
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,5,1,2,6,7,8,3] => [5,1,6,2,8,3,4,7] => [1,2,2,3] => 9
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => [5,1,7,3,2,4,6,8] => [1,2,1,4] => 8
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,5,1,2,6,3,8,7] => [5,1,8,3,2,4,6,7] => [1,2,1,4] => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,5,1,6,2,7,8,3] => [1,6,4,2,8,3,5,7] => [2,1,2,3] => 10
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,5,1,6,2,7,3,8] => [1,7,5,3,2,4,6,8] => [2,1,1,4] => 9
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,5,1,6,7,2,8,3] => [1,4,2,8,6,3,5,7] => [2,2,1,3] => 11
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [4,5,1,6,7,8,2,3] => [1,4,2,7,5,8,3,6] => [2,2,2,2] => 12
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [4,5,1,6,7,2,3,8] => [1,6,4,2,7,3,5,8] => [2,1,2,3] => 10
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [4,5,1,6,2,3,8,7] => [1,8,5,3,2,4,6,7] => [2,1,1,4] => 9
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [4,5,1,6,2,8,3,7] => [1,7,4,2,8,3,5,6] => [2,1,2,3] => 10
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [4,5,1,6,8,2,3,7] => [1,6,4,2,7,8,3,5] => [2,1,3,2] => 11
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,1,6,2,3,7,8] => [5,1,6,3,2,4,7,8] => [1,2,1,4] => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,6,1,2,7,8,3] => [1,6,2,8,4,3,5,7] => [2,2,1,3] => 11
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,6,1,2,7,3,8] => [1,7,4,2,5,3,6,8] => [2,1,2,3] => 10
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,1,7,2,8,3] => [1,2,8,6,4,3,5,7] => [3,1,1,3] => 12
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,6,1,7,8,2,3] => [1,2,7,5,3,8,4,6] => [3,1,2,2] => 13
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,6,1,7,2,3,8] => [1,6,2,7,4,3,5,8] => [2,2,1,3] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,1,2,8,3] => [1,2,8,5,3,6,4,7] => [3,1,2,2] => 13
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,1,8,2,3] => [1,2,7,3,8,5,4,6] => [3,2,1,2] => 14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,1,2,3] => [1,2,6,3,7,4,8,5] => [3,2,2,1] => 15
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => [1,5,2,6,3,7,4,8] => [2,2,2,2] => 12
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => [1,8,4,2,5,3,6,7] => [2,1,2,3] => 10
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,6,1,2,8,3,7] => [1,7,2,8,4,3,5,6] => [2,2,1,3] => 11
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => [1,6,2,7,3,8,4,5] => [2,2,2,2] => 12
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [1,5,2,6,3,7,8,4] => [2,2,3,1] => 13
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [4,1,5,2,6,3,7,8] => [1,2,2,3] => 9
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [4,5,1,2,7,3,8,6] => [1,8,6,3,2,4,5,7] => [2,1,1,4] => 9
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [4,5,1,2,7,8,3,6] => [1,7,5,2,8,3,4,6] => [2,1,2,3] => 10
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6,8] => [6,1,7,3,2,4,5,8] => [1,2,1,4] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [4,5,1,7,2,3,8,6] => [1,8,5,2,6,3,4,7] => [2,1,2,3] => 10
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [4,5,1,7,2,8,3,6] => [1,7,2,8,5,3,4,6] => [2,2,1,3] => 11
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [4,5,1,7,8,2,3,6] => [1,6,2,7,4,8,3,5] => [2,2,2,2] => 12
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6,8] => [5,1,6,2,7,3,4,8] => [1,2,2,3] => 9
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [4,5,7,1,2,8,3,6] => [1,7,2,8,4,5,3,6] => [2,2,2,2] => 12
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [1,5,2,6,7,3,8,4] => [2,3,2,1] => 14
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,5,1,2,3,6,8,7] => [8,3,1,4,2,5,6,7] => [1,1,2,4] => 7
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [4,5,1,2,3,8,6,7] => [7,1,8,3,2,4,5,6] => [1,2,1,4] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,5,1,2,8,3,6,7] => [6,1,7,2,8,3,4,5] => [1,2,2,3] => 9
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,5,1,8,2,3,6,7] => [5,1,6,2,7,8,3,4] => [1,2,3,2] => 10
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => [4,1,5,2,6,7,8,3] => [1,2,4,1] => 11
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [3,4,1,5,2,6,7,8] => [2,2,4] => 6
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,6,7,8,5] => [5,6,1,8,2,3,4,7] => [2,2,4] => 6
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,6,7,5,8] => [5,7,2,1,3,4,6,8] => [2,1,5] => 5
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => [5,8,2,1,3,4,6,7] => [2,1,5] => 5
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,8,5,7] => [5,7,1,8,2,3,4,6] => [2,2,4] => 6
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,6,5,7,8] => [6,2,3,1,4,5,7,8] => [1,2,5] => 4
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,6,3,7,8,5] => [6,4,1,8,2,3,5,7] => [1,1,2,4] => 7
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5,8] => [7,5,2,1,3,4,6,8] => [1,1,1,5] => 6
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,6,7,3,8,5] => [4,1,8,6,2,3,5,7] => [1,2,1,4] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,8,7] => [8,5,2,1,3,4,6,7] => [1,1,1,5] => 6
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,8,5,7] => [7,4,1,8,2,3,5,6] => [1,1,2,4] => 7
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [6,1,8,4,2,3,5,7] => [1,2,1,4] => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,6,2,3,7,5,8] => [7,4,1,5,2,3,6,8] => [1,1,2,4] => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => [1,8,6,4,2,3,5,7] => [2,1,1,4] => 9
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,6,2,7,3,5,8] => [6,1,7,4,2,3,5,8] => [1,2,1,4] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,6,7,2,3,8,5] => [1,8,5,3,6,2,4,7] => [2,1,2,3] => 10
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,6,7,2,8,3,5] => [1,7,3,8,5,2,4,6] => [2,2,1,3] => 11
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,6,7,8,2,3,5] => [1,6,3,7,4,8,2,5] => [2,2,2,2] => 12
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,6,7,2,3,5,8] => [5,1,6,3,7,2,4,8] => [1,2,2,3] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,8,7] => [8,4,1,5,2,3,6,7] => [1,1,2,4] => 7
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,8,5,7] => [7,1,8,4,2,3,5,6] => [1,2,1,4] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,8,3,5,7] => [6,1,7,3,8,2,4,5] => [1,2,2,3] => 9
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,8,2,3,5,7] => [5,1,6,3,7,8,2,4] => [1,2,3,2] => 10
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,6,2,3,5,7,8] => [4,5,1,6,2,3,7,8] => [2,2,4] => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => [7,3,1,4,5,2,6,8] => [1,1,3,3] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [4,6,1,2,7,3,5,8] => [6,1,7,3,4,2,5,8] => [1,2,2,3] => 9
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [4,6,1,7,2,3,8,5] => [1,8,5,6,3,2,4,7] => [2,2,1,3] => 11
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [4,6,1,7,8,2,3,5] => [1,6,7,4,2,8,3,5] => [3,1,2,2] => 13
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,6,1,7,2,3,5,8] => [5,1,6,7,3,2,4,8] => [1,3,1,3] => 10
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [4,6,7,1,2,3,8,5] => [1,8,4,5,2,6,3,7] => [2,2,2,2] => 12
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [1,6,7,2,8,4,3,5] => [3,2,1,2] => 14
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => [1,5,6,2,7,3,8,4] => [3,2,2,1] => 15
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,6,7,1,2,3,5,8] => [4,1,5,6,2,7,3,8] => [1,3,2,2] => 11
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,8,5,7] => [7,1,8,3,4,2,5,6] => [1,2,2,3] => 9
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,8,3,5,7] => [6,1,7,8,3,2,4,5] => [1,3,1,3] => 10
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,8,2,3,5,7] => [5,1,6,7,2,8,3,4] => [1,3,2,2] => 11
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [4,6,1,2,3,5,7,8] => [3,4,1,5,6,2,7,8] => [2,3,3] => 7
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,2,3,5,7,8,6] => [6,8,2,1,3,4,5,7] => [2,1,5] => 5
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,7,6,8] => [7,2,3,1,4,5,6,8] => [1,2,5] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,3,7,8,5,6] => [7,5,1,8,2,3,4,6] => [1,1,2,4] => 7
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,3,7,5,6,8] => [6,7,2,1,3,4,5,8] => [2,1,5] => 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,7,3,5,8,6] => [8,5,1,6,2,3,4,7] => [1,1,2,4] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [4,1,2,7,8,3,5,6] => [6,1,7,4,8,2,3,5] => [1,2,2,3] => 9
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,1,2,7,3,5,6,8] => [5,6,1,7,2,3,4,8] => [2,2,4] => 6
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,7,2,3,5,8,6] => [8,4,1,5,6,2,3,7] => [1,1,3,3] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [4,1,7,2,3,8,5,6] => [7,1,8,4,5,2,3,6] => [1,2,2,3] => 9
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [4,1,7,2,8,3,5,6] => [6,1,7,8,4,2,3,5] => [1,3,1,3] => 10
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,1,7,8,2,3,5,6] => [5,1,6,7,3,8,2,4] => [1,3,2,2] => 11
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6,8] => [4,5,1,6,7,2,3,8] => [2,3,3] => 7
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [4,7,1,2,3,8,5,6] => [7,1,8,3,4,5,2,6] => [1,2,3,2] => 10
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [4,7,1,2,8,3,5,6] => [6,1,7,8,3,4,2,5] => [1,3,2,2] => 11
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,7,1,8,2,3,5,6] => [5,1,6,7,8,3,2,4] => [1,4,1,2] => 12
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,7,8,1,2,3,5,6] => [4,1,5,6,7,2,8,3] => [1,4,2,1] => 13
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6,8] => [3,4,1,5,6,7,2,8] => [2,4,2] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [8,2,3,1,4,5,6,7] => [1,2,5] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [4,1,2,3,5,8,6,7] => [7,8,2,1,3,4,5,6] => [2,1,5] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,1,2,3,8,5,6,7] => [6,7,1,8,2,3,4,5] => [2,2,4] => 6
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,8,3,5,6,7] => [5,6,1,7,8,2,3,4] => [2,3,3] => 7
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [4,5,1,6,7,8,2,3] => [2,4,2] => 8
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [3,4,1,5,6,7,8,2] => [2,5,1] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [2,3,4,1,5,6,7,8] => [3,5] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,4] => [4,5,6,8,1,2,3,7] => [4,4] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,5,6,7,4,8] => [4,5,7,1,2,3,6,8] => [3,5] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,2,3,5,6,4,8,7] => [4,5,8,1,2,3,6,7] => [3,5] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,8,4,7] => [4,5,7,8,1,2,3,6] => [4,4] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,5,6,4,7,8] => [4,6,1,2,3,5,7,8] => [2,6] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,7,8,6] => [4,6,8,1,2,3,5,7] => [3,5] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,8] => [4,7,1,2,3,5,6,8] => [2,6] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,2,3,5,7,4,8,6] => [8,4,6,1,2,3,5,7] => [1,2,5] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,2,3,5,7,8,4,6] => [7,4,5,8,1,2,3,6] => [1,3,4] => 5
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6,8] => [4,6,7,1,2,3,5,8] => [3,5] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,5,4,6,8,7] => [4,8,1,2,3,5,6,7] => [2,6] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => [4,7,8,1,2,3,5,6] => [3,5] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,5,8,4,6,7] => [4,6,7,8,1,2,3,5] => [4,4] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => [1,7] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,4] => [5,3,6,8,1,2,4,7] => [1,3,4] => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,2,5,3,6,7,4,8] => [5,3,7,1,2,4,6,8] => [1,2,5] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,2,5,3,6,4,8,7] => [5,3,8,1,2,4,6,7] => [1,2,5] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,2,5,3,6,4,7,8] => [6,4,1,2,3,5,7,8] => [1,1,6] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,2,5,6,3,7,8,4] => [3,6,4,8,1,2,5,7] => [2,2,4] => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,2,5,6,3,7,4,8] => [3,7,5,1,2,4,6,8] => [2,1,5] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,2,5,6,7,3,8,4] => [3,4,8,6,1,2,5,7] => [3,1,4] => 7
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,6,7,8,3,4] => [3,4,7,5,8,1,2,6] => [3,2,3] => 8
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,2,5,6,3,4,8,7] => [3,8,5,1,2,4,6,7] => [2,1,5] => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,2,5,6,3,8,4,7] => [3,7,4,8,1,2,5,6] => [2,2,4] => 6
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,2,5,6,8,3,4,7] => [3,6,4,7,8,1,2,5] => [2,3,3] => 7
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [5,3,6,1,2,4,7,8] => [1,2,5] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,7,8,6] => [6,3,8,1,2,4,5,7] => [1,2,5] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6,8] => [7,4,1,2,3,5,6,8] => [1,1,6] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,2,5,3,7,4,8,6] => [3,8,6,1,2,4,5,7] => [2,1,5] => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,2,5,3,7,8,4,6] => [3,7,5,8,1,2,4,6] => [2,2,4] => 6
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6,8] => [6,3,7,1,2,4,5,8] => [1,2,5] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,2,5,7,3,4,8,6] => [3,8,5,6,1,2,4,7] => [2,2,4] => 6
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,2,5,7,3,8,4,6] => [3,7,8,5,1,2,4,6] => [3,1,4] => 7
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,2,5,7,8,3,4,6] => [3,6,7,4,8,1,2,5] => [3,2,3] => 8
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [5,3,6,7,1,2,4,8] => [1,3,4] => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,2,5,3,4,6,8,7] => [8,4,1,2,3,5,6,7] => [1,1,6] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4,8,6,7] => [7,3,8,1,2,4,5,6] => [1,2,5] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [6,3,7,8,1,2,4,5] => [1,3,4] => 5
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => [5,3,6,7,8,1,2,4] => [1,4,3] => 6
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,2,5,3,4,6,7,8] => [4,5,1,2,3,6,7,8] => [2,6] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,5,2,3,6,7,8,4] => [5,6,2,8,1,3,4,7] => [2,2,4] => 6
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,5,2,3,6,7,4,8] => [5,7,3,1,2,4,6,8] => [2,1,5] => 5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,5,2,3,6,4,8,7] => [5,8,3,1,2,4,6,7] => [2,1,5] => 5
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,5,2,3,6,8,4,7] => [5,7,2,8,1,3,4,6] => [2,2,4] => 6
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,5,2,6,3,7,8,4] => [6,4,2,8,1,3,5,7] => [1,1,2,4] => 7
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2,6,3,7,4,8] => [7,5,3,1,2,4,6,8] => [1,1,1,5] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,7,8,3,4] => [4,2,7,5,8,1,3,6] => [1,2,2,3] => 9
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,2,6,7,3,4,8] => [6,4,2,7,1,3,5,8] => [1,1,2,4] => 7
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,5,2,6,3,4,8,7] => [8,5,3,1,2,4,6,7] => [1,1,1,5] => 6
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,3,8,4,7] => [7,4,2,8,1,3,5,6] => [1,1,2,4] => 7
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,2,6,8,3,4,7] => [6,4,2,7,8,1,3,5] => [1,1,3,3] => 8
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,2,6,3,4,7,8] => [5,6,3,1,2,4,7,8] => [2,1,5] => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,5,6,2,3,7,8,4] => [6,2,8,4,1,3,5,7] => [1,2,1,4] => 8
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,5,6,2,7,8,3,4] => [2,7,5,3,8,1,4,6] => [2,1,2,3] => 10
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,5,6,7,2,3,8,4] => [2,8,5,3,6,1,4,7] => [2,1,2,3] => 10
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,5,6,7,2,8,3,4] => [2,7,3,8,5,1,4,6] => [2,2,1,3] => 11
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,2,3,4] => [2,6,3,7,4,8,1,5] => [2,2,2,2] => 12
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,5,6,7,2,3,4,8] => [5,2,6,3,7,1,4,8] => [1,2,2,3] => 9
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,5,6,2,3,4,8,7] => [8,4,2,5,1,3,6,7] => [1,1,2,4] => 7
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,6,2,3,8,4,7] => [7,2,8,4,1,3,5,6] => [1,2,1,4] => 8
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,5,6,2,8,3,4,7] => [6,2,7,3,8,1,4,5] => [1,2,2,3] => 9
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,5,6,8,2,3,4,7] => [5,2,6,3,7,8,1,4] => [1,2,3,2] => 10
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,5,6,2,3,4,7,8] => [4,5,2,6,1,3,7,8] => [2,2,4] => 6
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,7,8,6] => [6,8,3,1,2,4,5,7] => [2,1,5] => 5
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6,8] => [7,3,4,1,2,5,6,8] => [1,2,5] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6,8] => [6,7,3,1,2,4,5,8] => [2,1,5] => 5
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,7,3,8,4,6] => [7,2,8,5,1,3,4,6] => [1,2,1,4] => 8
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,5,2,7,8,3,4,6] => [6,2,7,4,8,1,3,5] => [1,2,2,3] => 9
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6,8] => [5,6,2,7,1,3,4,8] => [2,2,4] => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,7,2,3,8,4,6] => [7,2,8,4,5,1,3,6] => [1,2,2,3] => 9
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [6,2,7,8,4,1,3,5] => [1,3,1,3] => 10
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,5,7,8,2,3,4,6] => [5,2,6,7,3,8,1,4] => [1,3,2,2] => 11
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6,8] => [4,5,2,6,7,1,3,8] => [2,3,3] => 7
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,5,2,3,4,6,8,7] => [8,3,4,1,2,5,6,7] => [1,2,5] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [7,8,3,1,2,4,5,6] => [2,1,5] => 5
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,5,2,3,8,4,6,7] => [6,7,2,8,1,3,4,5] => [2,2,4] => 6
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,5,2,8,3,4,6,7] => [5,6,2,7,8,1,3,4] => [2,3,3] => 7
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [4,5,2,6,7,8,1,3] => [2,4,2] => 8
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8] => [3,4,5,1,2,6,7,8] => [3,5] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,4] => [5,6,8,2,1,3,4,7] => [3,1,4] => 7
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,6,7,4,8] => [5,7,2,3,1,4,6,8] => [2,2,4] => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,1,2,3,6,8,4,7] => [5,7,8,2,1,3,4,6] => [3,1,4] => 7
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,6,4,7,8] => [6,2,3,4,1,5,7,8] => [1,3,4] => 5
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,2,6,3,7,8,4] => [6,4,8,2,1,3,5,7] => [1,2,1,4] => 8
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,1,2,6,3,7,4,8] => [7,5,2,3,1,4,6,8] => [1,1,2,4] => 7
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,7,3,8,4] => [4,8,6,2,1,3,5,7] => [2,1,1,4] => 9
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,1,2,6,7,8,3,4] => [4,7,5,1,8,2,3,6] => [2,1,2,3] => 10
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,1,2,6,7,3,4,8] => [6,4,7,2,1,3,5,8] => [1,2,1,4] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,3,4,8,7] => [8,5,2,3,1,4,6,7] => [1,1,2,4] => 7
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,1,2,6,3,8,4,7] => [7,4,8,2,1,3,5,6] => [1,2,1,4] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,1,2,6,8,3,4,7] => [6,4,7,1,8,2,3,5] => [1,2,2,3] => 9
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,1,2,6,3,4,7,8] => [5,6,2,3,1,4,7,8] => [2,2,4] => 6
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => [6,8,4,2,1,3,5,7] => [2,1,1,4] => 9
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,1,6,2,3,7,4,8] => [7,4,5,2,1,3,6,8] => [1,2,1,4] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => [8,6,4,2,1,3,5,7] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [5,1,6,2,7,8,3,4] => [7,5,3,1,8,2,4,6] => [1,1,1,2,3] => 11
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,6,7,2,3,8,4] => [8,5,3,1,6,2,4,7] => [1,1,1,2,3] => 11
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,1,6,7,8,2,3,4] => [6,3,1,7,4,8,2,5] => [1,1,2,2,2] => 13
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [5,1,6,2,3,4,8,7] => [8,4,5,2,1,3,6,7] => [1,2,1,4] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [5,1,6,2,3,8,4,7] => [7,8,4,2,1,3,5,6] => [2,1,1,4] => 9
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,1,6,2,8,3,4,7] => [6,7,3,1,8,2,4,5] => [2,1,2,3] => 10
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [5,1,6,2,3,4,7,8] => [4,5,6,2,1,3,7,8] => [3,1,4] => 7
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,6,1,2,3,7,8,4] => [6,8,3,1,4,2,5,7] => [2,1,2,3] => 10
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1,2,7,3,8,4] => [8,6,3,1,4,2,5,7] => [1,1,1,2,3] => 11
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [5,6,1,2,7,8,3,4] => [7,5,1,8,3,2,4,6] => [1,1,2,1,3] => 12
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,6,1,2,7,3,4,8] => [6,7,3,1,4,2,5,8] => [2,1,2,3] => 10
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,6,1,7,2,3,8,4] => [8,5,1,6,3,2,4,7] => [1,1,2,1,3] => 12
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [5,6,1,7,2,8,3,4] => [7,1,8,5,3,2,4,6] => [1,2,1,1,3] => 13
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,6,1,7,8,2,3,4] => [6,1,7,4,2,8,3,5] => [1,2,1,2,2] => 14
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,6,7,1,2,3,8,4] => [8,4,1,5,2,6,3,7] => [1,1,2,2,2] => 13
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [5,6,7,1,2,8,3,4] => [7,1,8,4,2,5,3,6] => [1,2,1,2,2] => 14
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [6,1,7,2,8,4,3,5] => [1,2,2,1,2] => 15
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [5,1,6,2,7,3,8,4] => [1,2,2,2,1] => 16
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,1,2,3,4,8] => [4,5,1,6,2,7,3,8] => [2,2,2,2] => 12
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [5,6,1,2,3,8,4,7] => [7,8,3,1,4,2,5,6] => [2,1,2,3] => 10
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,6,1,2,8,3,4,7] => [6,7,1,8,3,2,4,5] => [2,2,1,3] => 11
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,6,1,8,2,3,4,7] => [5,6,1,7,2,8,3,4] => [2,2,2,2] => 12
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => [4,5,1,6,2,7,8,3] => [2,2,3,1] => 13
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,6,1,2,3,4,7,8] => [3,4,5,1,6,2,7,8] => [3,2,3] => 8
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,7,8,6] => [6,8,2,3,1,4,5,7] => [2,2,4] => 6
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,7,4,8,6] => [8,6,2,3,1,4,5,7] => [1,1,2,4] => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,7,8,4,6] => [7,5,8,2,1,3,4,6] => [1,2,1,4] => 8
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6,8] => [6,7,2,3,1,4,5,8] => [2,2,4] => 6
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,7,3,4,8,6] => [8,5,6,2,1,3,4,7] => [1,2,1,4] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,7,3,8,4,6] => [7,8,5,2,1,3,4,6] => [2,1,1,4] => 9
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,7,8,3,4,6] => [6,7,4,1,8,2,3,5] => [2,1,2,3] => 10
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6,8] => [5,6,7,2,1,3,4,8] => [3,1,4] => 7
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [5,1,7,2,3,4,8,6] => [8,4,5,1,6,2,3,7] => [1,2,2,3] => 9
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [5,1,7,2,3,8,4,6] => [7,8,4,1,5,2,3,6] => [2,1,2,3] => 10
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,1,7,2,8,3,4,6] => [6,7,1,8,4,2,3,5] => [2,2,1,3] => 11
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,1,7,8,2,3,4,6] => [5,6,1,7,3,8,2,4] => [2,2,2,2] => 12
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6,8] => [4,5,6,1,7,2,3,8] => [3,2,3] => 8
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,7,1,2,3,4,8,6] => [8,3,4,1,5,6,2,7] => [1,2,3,2] => 10
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [5,7,1,2,3,8,4,6] => [7,8,3,1,4,5,2,6] => [2,1,3,2] => 11
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,7,1,2,8,3,4,6] => [6,7,1,8,3,4,2,5] => [2,2,2,2] => 12
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,7,1,8,2,3,4,6] => [5,6,1,7,8,3,2,4] => [2,3,1,2] => 13
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => [4,5,1,6,7,2,8,3] => [2,3,2,1] => 14
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6,8] => [3,4,5,1,6,7,2,8] => [3,3,2] => 9
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [8,2,3,4,1,5,6,7] => [1,3,4] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [5,1,2,3,4,8,6,7] => [7,8,2,3,1,4,5,6] => [2,2,4] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,8,4,6,7] => [6,7,8,2,1,3,4,5] => [3,1,4] => 7
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,1,2,8,3,4,6,7] => [5,6,7,1,8,2,3,4] => [3,2,3] => 8
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [5,1,8,2,3,4,6,7] => [4,5,6,1,7,8,2,3] => [3,3,2] => 9
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [3,4,5,1,6,7,8,2] => [3,4,1] => 10
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8] => [2,3,4,5,1,6,7,8] => [4,4] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,5] => [5,6,8,1,2,3,4,7] => [3,5] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,6,7,5,8] => [5,7,1,2,3,4,6,8] => [2,6] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7] => [5,8,1,2,3,4,6,7] => [2,6] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,6,8,5,7] => [5,7,8,1,2,3,4,6] => [3,5] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => [1,7] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,6,4,7,8,5] => [6,4,8,1,2,3,5,7] => [1,2,5] => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,6,4,7,5,8] => [7,5,1,2,3,4,6,8] => [1,1,6] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,2,3,6,7,4,8,5] => [4,8,6,1,2,3,5,7] => [2,1,5] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,2,3,6,7,8,4,5] => [4,7,5,8,1,2,3,6] => [2,2,4] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,2,3,6,7,4,5,8] => [6,4,7,1,2,3,5,8] => [1,2,5] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,6,4,5,8,7] => [8,5,1,2,3,4,6,7] => [1,1,6] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,2,3,6,4,8,5,7] => [7,4,8,1,2,3,5,6] => [1,2,5] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,2,3,6,8,4,5,7] => [6,4,7,8,1,2,3,5] => [1,3,4] => 5
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [5,6,1,2,3,4,7,8] => [2,6] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,2,6,3,4,7,8,5] => [6,8,4,1,2,3,5,7] => [2,1,5] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,2,6,3,4,7,5,8] => [7,4,5,1,2,3,6,8] => [1,2,5] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,2,6,3,7,4,8,5] => [8,6,4,1,2,3,5,7] => [1,1,1,5] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,2,6,3,7,8,4,5] => [7,5,3,8,1,2,4,6] => [1,1,2,4] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,2,6,7,3,4,8,5] => [8,5,3,6,1,2,4,7] => [1,1,2,4] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,2,6,7,3,8,4,5] => [7,3,8,5,1,2,4,6] => [1,2,1,4] => 8
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,7,8,3,4,5] => [6,3,7,4,8,1,2,5] => [1,2,2,3] => 9
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5,8] => [5,6,3,7,1,2,4,8] => [2,2,4] => 6
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,8,7] => [8,4,5,1,2,3,6,7] => [1,2,5] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,2,6,3,4,8,5,7] => [7,8,4,1,2,3,5,6] => [2,1,5] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => [6,7,3,8,1,2,4,5] => [2,2,4] => 6
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,8,3,4,5,7] => [5,6,3,7,8,1,2,4] => [2,3,3] => 7
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,3,4,5,7,8] => [4,5,6,1,2,3,7,8] => [3,5] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,6,2,3,4,7,8,5] => [6,8,3,4,1,2,5,7] => [2,2,4] => 6
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,6,2,3,4,7,5,8] => [7,3,4,5,1,2,6,8] => [1,3,4] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,6,2,3,7,4,8,5] => [8,6,3,4,1,2,5,7] => [1,1,2,4] => 7
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,6,2,3,7,8,4,5] => [7,5,8,3,1,2,4,6] => [1,2,1,4] => 8
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,2,3,7,4,5,8] => [6,7,3,4,1,2,5,8] => [2,2,4] => 6
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,6,2,7,3,4,8,5] => [8,5,6,3,1,2,4,7] => [1,2,1,4] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,5] => [7,8,5,3,1,2,4,6] => [2,1,1,4] => 9
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,6,2,7,8,3,4,5] => [6,7,4,2,8,1,3,5] => [2,1,2,3] => 10
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,6,2,7,3,4,5,8] => [5,6,7,3,1,2,4,8] => [3,1,4] => 7
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,6,7,2,3,4,8,5] => [8,4,5,2,6,1,3,7] => [1,2,2,3] => 9
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,7,2,3,8,4,5] => [7,8,4,2,5,1,3,6] => [2,1,2,3] => 10
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,6,7,2,8,3,4,5] => [6,7,2,8,4,1,3,5] => [2,2,1,3] => 11
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [5,6,2,7,3,8,1,4] => [2,2,2,2] => 12
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,6,7,2,3,4,5,8] => [4,5,6,2,7,1,3,8] => [3,2,3] => 8
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,8,7] => [8,3,4,5,1,2,6,7] => [1,3,4] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [7,8,3,4,1,2,5,6] => [2,2,4] => 6
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,6,2,3,8,4,5,7] => [6,7,8,3,1,2,4,5] => [3,1,4] => 7
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,6,2,8,3,4,5,7] => [5,6,7,2,8,1,3,4] => [3,2,3] => 8
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [4,5,6,2,7,8,1,3] => [3,3,2] => 9
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,6,2,3,4,5,7,8] => [3,4,5,6,1,2,7,8] => [4,4] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,7,8,5] => [6,8,2,3,4,1,5,7] => [2,3,3] => 7
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,7,5,8] => [7,2,3,4,5,1,6,8] => [1,4,3] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,3,7,4,8,5] => [8,6,2,3,4,1,5,7] => [1,1,3,3] => 8
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,1,2,3,7,8,4,5] => [7,5,8,2,3,1,4,6] => [1,2,2,3] => 9
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [6,1,2,3,7,4,5,8] => [6,7,2,3,4,1,5,8] => [2,3,3] => 7
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,7,3,4,8,5] => [8,5,6,2,3,1,4,7] => [1,2,2,3] => 9
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,1,2,7,3,8,4,5] => [7,8,5,2,3,1,4,6] => [2,1,2,3] => 10
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,1,2,7,8,3,4,5] => [6,7,4,8,2,1,3,5] => [2,2,1,3] => 11
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [6,1,2,7,3,4,5,8] => [5,6,7,2,3,1,4,8] => [3,2,3] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,7,2,3,4,8,5] => [8,4,5,6,2,1,3,7] => [1,3,1,3] => 10
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,1,7,2,3,8,4,5] => [7,8,4,5,2,1,3,6] => [2,2,1,3] => 11
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,1,7,2,8,3,4,5] => [6,7,8,4,2,1,3,5] => [3,1,1,3] => 12
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [6,1,7,8,2,3,4,5] => [5,6,7,3,1,8,2,4] => [3,1,2,2] => 13
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [6,1,7,2,3,4,5,8] => [4,5,6,7,2,1,3,8] => [4,1,3] => 9
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => [8,3,4,5,1,6,2,7] => [1,3,2,2] => 11
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,7,1,2,3,8,4,5] => [7,8,3,4,1,5,2,6] => [2,2,2,2] => 12
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,7,1,2,8,3,4,5] => [6,7,8,3,1,4,2,5] => [3,1,2,2] => 13
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [6,7,1,8,2,3,4,5] => [5,6,7,1,8,3,2,4] => [3,2,1,2] => 14
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => [4,5,6,1,7,2,8,3] => [3,2,2,1] => 15
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5,8] => [3,4,5,6,1,7,2,8] => [4,2,2] => 10
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [8,2,3,4,5,1,6,7] => [1,4,3] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,8,5,7] => [7,8,2,3,4,1,5,6] => [2,3,3] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,8,4,5,7] => [6,7,8,2,3,1,4,5] => [3,2,3] => 8
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [6,1,2,8,3,4,5,7] => [5,6,7,8,2,1,3,4] => [4,1,3] => 9
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [4,5,6,7,1,8,2,3] => [4,2,2] => 10
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => [3,4,5,6,1,7,8,2] => [4,3,1] => 11
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8] => [2,3,4,5,6,1,7,8] => [5,3] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => [6,8,1,2,3,4,5,7] => [2,6] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => [1,7] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6] => [8,6,1,2,3,4,5,7] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,7,8,5,6] => [7,5,8,1,2,3,4,6] => [1,2,5] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,7,5,6,8] => [6,7,1,2,3,4,5,8] => [2,6] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,2,3,7,4,5,8,6] => [8,5,6,1,2,3,4,7] => [1,2,5] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,2,3,7,4,8,5,6] => [7,8,5,1,2,3,4,6] => [2,1,5] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,3,7,8,4,5,6] => [6,7,4,8,1,2,3,5] => [2,2,4] => 6
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [5,6,7,1,2,3,4,8] => [3,5] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => [8,4,5,6,1,2,3,7] => [1,3,4] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,2,7,3,4,8,5,6] => [7,8,4,5,1,2,3,6] => [2,2,4] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [6,7,8,4,1,2,3,5] => [3,1,4] => 7
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [5,6,7,3,8,1,2,4] => [3,2,3] => 8
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6,8] => [4,5,6,7,1,2,3,8] => [4,4] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => [8,3,4,5,6,1,2,7] => [1,4,3] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [7,8,3,4,5,1,2,6] => [2,3,3] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,7,2,3,8,4,5,6] => [6,7,8,3,4,1,2,5] => [3,2,3] => 8
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,7,2,8,3,4,5,6] => [5,6,7,8,3,1,2,4] => [4,1,3] => 9
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [4,5,6,7,2,8,1,3] => [4,2,2] => 10
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8] => [3,4,5,6,7,1,2,8] => [5,3] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [8,2,3,4,5,6,1,7] => [1,5,2] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => [7,8,2,3,4,5,1,6] => [2,4,2] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [7,1,2,3,8,4,5,6] => [6,7,8,2,3,4,1,5] => [3,3,2] => 9
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [7,1,2,8,3,4,5,6] => [5,6,7,8,2,3,1,4] => [4,2,2] => 10
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [4,5,6,7,8,2,1,3] => [5,1,2] => 11
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [3,4,5,6,7,1,8,2] => [5,2,1] => 12
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8] => [2,3,4,5,6,7,1,8] => [6,2] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => [1,7] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,8,6,7] => [7,8,1,2,3,4,5,6] => [2,6] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,3,4,8,5,6,7] => [6,7,8,1,2,3,4,5] => [3,5] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [5,6,7,8,1,2,3,4] => [4,4] => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [4,5,6,7,8,1,2,3] => [5,3] => 5
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [3,4,5,6,7,8,1,2] => [6,2] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => [7,1] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [8] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => [9,1,2,3,4,5,6,7,8] => [1,8] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [1,8] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => [10,1,2,3,4,5,6,7,8,9] => [1,9] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => [9,2,3,4,5,6,7,1,8] => [1,6,2] => 8
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => [1,3,4,5,6,7,8,9,2] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [1,9] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => [11,1,2,3,4,5,6,7,8,9,10] => [1,10] => 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,10,2] => [9,1] => 9
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [1,10] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,11,1,3,4,5,6,7,8,9,10] => [1,3,4,5,6,7,8,9,10,11,2] => [10,1] => 10
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,9] => [8,1,2,3,4,5,6,7,9] => [1,8] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [1,8] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8,10] => [9,1,2,3,4,5,6,7,8,10] => [1,9] => 1
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,9,1,4,5,6,7,8] => [1,2,4,5,6,7,8,9,3] => [8,1] => 8
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [1,9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,1,2] => [1,2,3,4,5,8,6,9,7] => [6,2,1] => 14
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,5,6,8,9,1,2,7] => [1,2,3,4,7,8,5,9,6] => [6,2,1] => 14
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,7,8,9,1,2,6] => [7,1,2,3,4,8,5,9,6] => [1,5,2,1] => 15
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,9,2,4,5,6,7,8] => [4,1,5,6,7,8,9,2,3] => [1,6,2] => 8
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,9,1,2,4,5,6,7,8] => [3,1,4,5,6,7,8,9,2] => [1,7,1] => 9
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => [3,4,5,6,7,8,1,9,2] => [6,2,1] => 14
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,9,1] => [8,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,1] => [1,2,3,4,5,6,7,9,8] => [8,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,9,1,8] => [1,2,3,4,5,6,8,9,7] => [8,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,8,9,1,7] => [8,1,2,3,4,5,6,9,7] => [1,7,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,1] => [1,2,3,4,5,6,7,8,10,9] => [9,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,10,1,9] => [1,2,3,4,5,6,7,9,10,8] => [9,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,7,9,10,1,8] => [9,1,2,3,4,5,6,7,10,8] => [1,8,1] => 10
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,5,1,8,9,6,7] => [8,1,2,3,4,6,9,5,7] => [1,6,2] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,11,1] => [1,2,3,4,5,6,7,8,9,11,10] => [10,1] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,9,11,1,10] => [1,2,3,4,5,6,7,8,10,11,9] => [10,1] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,9,1,7,8] => [1,2,3,4,5,7,8,9,6] => [8,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,7,10,1,8,9] => [1,2,3,4,5,6,8,9,10,7] => [9,1] => 9
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,9,1,6,7,8] => [1,2,3,4,6,7,8,9,5] => [8,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,6,10,1,7,8,9] => [1,2,3,4,5,7,8,9,10,6] => [9,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [5,5] => 5
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,9,1,5,6,7,8] => [1,2,3,5,6,7,8,9,4] => [8,1] => 8
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,10,1,6,7,8,9] => [1,2,3,4,6,7,8,9,10,5] => [9,1] => 9
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [1,8] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [1,8] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => [6,1,2,3,4,5,7,8,9] => [1,8] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,7,6,8,9] => [7,1,2,3,4,5,6,8,9] => [1,8] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => [1,2,4,6,9,3,5,7,8,10] => [5,5] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [1,3,5,7,10,2,4,6,8,9] => [5,5] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,6,9,10,8] => [2,4,6,8,10,1,3,5,7,9] => [5,5] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,8,9,10,7] => [2,4,7,8,10,1,3,5,6,9] => [5,5] => 5
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [1,9] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [1,9] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,10,5] => [5,6,7,8,10,1,2,3,4,9] => [5,5] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [1,9] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [1,9] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => [1,9] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,2] => [3,1,4,5,6,7,9,2,8] => [1,6,2] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,10,1] => [9,1] => 9
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [5,5] => 5
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => [2,3,4,5,6,7,8,9,10,11,1] => [10,1] => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [6,7,8,9,10,1,2,3,4,5] => [5,5] => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,4,5,7,1,8,9,6] => [7,1,2,3,4,5,9,6,8] => [1,6,2] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,8,9,10,1,2,7] => [8,1,2,3,4,5,9,6,10,7] => [1,6,2,1] => 17
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => [6,2,3,7,8,1,4,9,10,5] => [1,4,4,1] => 15
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,8,9,1,2,3,4,10,5] => [10,5,1,6,2,7,3,8,4,9] => [1,1,2,2,2,2] => 21
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,10,1,2,4,5,6,7,8,9] => [3,1,4,5,6,7,8,9,10,2] => [1,8,1] => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9,11] => [10,1,2,3,4,5,6,7,8,9,11] => [1,10] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,10,1,4,5,6,7,8,9] => [1,2,4,5,6,7,8,9,10,3] => [9,1] => 9
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,10,1,5,6,7,8,9] => [1,2,3,5,6,7,8,9,10,4] => [9,1] => 9
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,9,3] => [4,1,2,5,6,7,9,3,8] => [1,6,2] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,8,1,9,7] => [9,1,2,3,4,5,7,6,8] => [1,6,2] => 8
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,1,4,9,2,5,6,7,8] => [3,1,5,6,7,8,9,2,4] => [1,6,2] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,9,1,6,8] => [7,1,2,3,4,5,8,9,6] => [1,7,1] => 9
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,6,1,7,8,9,5] => [6,1,2,3,4,7,9,5,8] => [1,6,2] => 8
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,6,8,9,2,7] => [8,2,3,4,5,6,9,1,7] => [1,6,2] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,7,6,10,8,9] => [2,4,6,9,10,1,3,5,7,8] => [5,5] => 5
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,4,6,8,10,1,2,5,7,9] => [6,1,2,3,7,8,4,9,10,5] => [1,5,3,1] => 16
[1,0,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,3,11,1,4,5,6,7,8,9,10] => [1,2,4,5,6,7,8,9,10,11,3] => [10,1] => 10
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [1,3,5,7,9,12,2,4,6,8,10,11] => [6,6] => 6
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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
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + 2\ q^{2}$
$F_{4} = 1 + 3\ q + 5\ q^{2} + 4\ q^{3} + q^{4}$
$F_{5} = 1 + 4\ q + 9\ q^{2} + 12\ q^{3} + 10\ q^{4} + 4\ q^{5} + 2\ q^{6}$
$F_{6} = 1 + 5\ q + 14\ q^{2} + 25\ q^{3} + 31\ q^{4} + 26\ q^{5} + 16\ q^{6} + 9\ q^{7} + 4\ q^{8} + q^{9}$
$F_{7} = 1 + 6\ q + 20\ q^{2} + 44\ q^{3} + 70\ q^{4} + 82\ q^{5} + 74\ q^{6} + 54\ q^{7} + 38\ q^{8} + 22\ q^{9} + 12\ q^{10} + 4\ q^{11} + 2\ q^{12}$
Description
The major index of the composition.
The descents of a composition $[c_1,c_2,\dots,c_k]$ are the partial sums $c_1, c_1+c_2,\dots, c_1+\dots+c_{k-1}$, excluding the sum of all parts. The major index of a composition is the sum of its descents.
For details about the major index see Permutations/Descents-Major.
The descents of a composition $[c_1,c_2,\dots,c_k]$ are the partial sums $c_1, c_1+c_2,\dots, c_1+\dots+c_{k-1}$, excluding the sum of all parts. The major index of a composition is the sum of its descents.
For details about the major index see Permutations/Descents-Major.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
Lehmer-code to major-code bijection
Description
Sends a permutation to the unique permutation such that the Lehmer code is sent to the major code.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation $\sigma$ is given by $L(\sigma) = l_1 \ldots l_n$ with $l_i = \# \{ j > i : \sigma_j < \sigma_i \}$. In particular, $l_i$ is the number of boxes in the $i$-th column of the Rothe diagram. For example, the Lehmer code of $\sigma = [4,3,1,5,2]$ is $32010$. The Lehmer code $L : \mathfrak{S}_n\ \tilde\longrightarrow\ S_n$ is a bijection between permutations of size $n$ and sequences $l_1\ldots l_n \in \mathbf{N}^n$ with $l_i \leq i$.
* The major code $M(\sigma)$ of a permutation $\sigma \in \mathfrak{S}_n$ is a way to encode a permutation as a sequence $m_1 m_2 \ldots m_n$ with $m_i \geq i$. To define $m_i$, let $\operatorname{del}_i(\sigma)$ be the normalized permutation obtained by removing all $\sigma_j < i$ from the one-line notation of $\sigma$. The $i$-th index is then given by
$$m_i = \operatorname{maj}(\operatorname{del}_i(\sigma)) - \operatorname{maj}(\operatorname{del}_{i-1}(\sigma)).$$
For example, the permutation $[9,3,5,7,2,1,4,6,8]$ has major code $[5, 0, 1, 0, 1, 2, 0, 1, 0]$ since
$$\operatorname{maj}([8,2,4,6,1,3,5,7]) = 5, \quad \operatorname{maj}([7,1,3,5,2,4,6]) = 5, \quad \operatorname{maj}([6,2,4,1,3,5]) = 4,$$
$$\operatorname{maj}([5,1,3,2,4]) = 4, \quad \operatorname{maj}([4,2,1,3]) = 3, \quad \operatorname{maj}([3,1,2]) = 1, \quad \operatorname{maj}([2,1]) = 1.$$
Observe that the sum of the major code of $\sigma$ equals the major index of $\sigma$.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation $\sigma$ is given by $L(\sigma) = l_1 \ldots l_n$ with $l_i = \# \{ j > i : \sigma_j < \sigma_i \}$. In particular, $l_i$ is the number of boxes in the $i$-th column of the Rothe diagram. For example, the Lehmer code of $\sigma = [4,3,1,5,2]$ is $32010$. The Lehmer code $L : \mathfrak{S}_n\ \tilde\longrightarrow\ S_n$ is a bijection between permutations of size $n$ and sequences $l_1\ldots l_n \in \mathbf{N}^n$ with $l_i \leq i$.
* The major code $M(\sigma)$ of a permutation $\sigma \in \mathfrak{S}_n$ is a way to encode a permutation as a sequence $m_1 m_2 \ldots m_n$ with $m_i \geq i$. To define $m_i$, let $\operatorname{del}_i(\sigma)$ be the normalized permutation obtained by removing all $\sigma_j < i$ from the one-line notation of $\sigma$. The $i$-th index is then given by
$$m_i = \operatorname{maj}(\operatorname{del}_i(\sigma)) - \operatorname{maj}(\operatorname{del}_{i-1}(\sigma)).$$
For example, the permutation $[9,3,5,7,2,1,4,6,8]$ has major code $[5, 0, 1, 0, 1, 2, 0, 1, 0]$ since
$$\operatorname{maj}([8,2,4,6,1,3,5,7]) = 5, \quad \operatorname{maj}([7,1,3,5,2,4,6]) = 5, \quad \operatorname{maj}([6,2,4,1,3,5]) = 4,$$
$$\operatorname{maj}([5,1,3,2,4]) = 4, \quad \operatorname{maj}([4,2,1,3]) = 3, \quad \operatorname{maj}([3,1,2]) = 1, \quad \operatorname{maj}([2,1]) = 1.$$
Observe that the sum of the major code of $\sigma$ equals the major index of $\sigma$.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
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