Identifier
-
Mp00119:
Dyck paths
—to 321-avoiding permutation (Krattenthaler)⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
St000383: Integer compositions ⟶ ℤ
Values
[1,0] => [1] => [1] => [1] => 1
[1,0,1,0] => [1,2] => [2,1] => [1,1] => 1
[1,1,0,0] => [2,1] => [1,2] => [2] => 2
[1,0,1,0,1,0] => [1,2,3] => [3,2,1] => [1,1,1] => 1
[1,0,1,1,0,0] => [1,3,2] => [2,3,1] => [2,1] => 1
[1,1,0,0,1,0] => [2,1,3] => [3,1,2] => [1,2] => 2
[1,1,0,1,0,0] => [2,3,1] => [1,3,2] => [2,1] => 1
[1,1,1,0,0,0] => [3,1,2] => [2,1,3] => [1,2] => 2
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [4,3,2,1] => [1,1,1,1] => 1
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [3,4,2,1] => [2,1,1] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [4,2,3,1] => [1,2,1] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,4,3,1] => [2,1,1] => 1
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [3,2,4,1] => [1,2,1] => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [4,3,1,2] => [1,1,2] => 2
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [3,4,1,2] => [2,2] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [4,1,3,2] => [1,2,1] => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [1,4,3,2] => [2,1,1] => 1
[1,1,0,1,1,0,0,0] => [2,4,1,3] => [3,1,4,2] => [1,2,1] => 1
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [4,2,1,3] => [1,1,2] => 2
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [2,4,1,3] => [2,2] => 2
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [2,1,4,3] => [1,2,1] => 1
[1,1,1,1,0,0,0,0] => [4,1,2,3] => [3,2,1,4] => [1,1,2] => 2
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [5,4,3,2,1] => [1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [4,5,3,2,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [5,3,4,2,1] => [1,2,1,1] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [3,5,4,2,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [4,3,5,2,1] => [1,2,1,1] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [5,4,2,3,1] => [1,1,2,1] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [4,5,2,3,1] => [2,2,1] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [5,2,4,3,1] => [1,2,1,1] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,5,4,3,1] => [2,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [4,2,5,3,1] => [1,2,1,1] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [5,3,2,4,1] => [1,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [3,5,2,4,1] => [2,2,1] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [3,2,5,4,1] => [1,2,1,1] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [4,3,2,5,1] => [1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [5,4,3,1,2] => [1,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [4,5,3,1,2] => [2,1,2] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [5,3,4,1,2] => [1,2,2] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,5,4,1,2] => [2,1,2] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [4,3,5,1,2] => [1,2,2] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [5,4,1,3,2] => [1,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [4,5,1,3,2] => [2,2,1] => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [5,1,4,3,2] => [1,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [1,5,4,3,2] => [2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [4,1,5,3,2] => [1,2,1,1] => 1
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [5,3,1,4,2] => [1,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [3,5,1,4,2] => [2,2,1] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [3,1,5,4,2] => [1,2,1,1] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [4,3,1,5,2] => [1,1,2,1] => 1
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [5,4,2,1,3] => [1,1,1,2] => 2
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [4,5,2,1,3] => [2,1,2] => 2
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [5,2,4,1,3] => [1,2,2] => 2
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [2,5,4,1,3] => [2,1,2] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [4,2,5,1,3] => [1,2,2] => 2
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [5,2,1,4,3] => [1,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [2,5,1,4,3] => [2,2,1] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [2,1,5,4,3] => [1,2,1,1] => 1
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [4,2,1,5,3] => [1,1,2,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [5,3,2,1,4] => [1,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [3,5,2,1,4] => [2,1,2] => 2
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [3,2,5,1,4] => [1,2,2] => 2
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [3,2,1,5,4] => [1,1,2,1] => 1
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,2] => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => [2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => [1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [4,6,5,3,2,1] => [2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => [1,2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => [1,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [5,6,3,4,2,1] => [2,2,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [6,3,5,4,2,1] => [1,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [3,6,5,4,2,1] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [5,3,6,4,2,1] => [1,2,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => [1,1,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [4,6,3,5,2,1] => [2,2,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [4,3,6,5,2,1] => [1,2,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => [1,1,2,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => [1,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => [2,1,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => [1,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [4,6,5,2,3,1] => [2,1,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [5,4,6,2,3,1] => [1,2,2,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [6,5,2,4,3,1] => [1,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [5,6,2,4,3,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [6,2,5,4,3,1] => [1,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,6,5,4,3,1] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [5,2,6,4,3,1] => [1,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [6,4,2,5,3,1] => [1,1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [4,6,2,5,3,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [4,2,6,5,3,1] => [1,2,1,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [5,4,2,6,3,1] => [1,1,2,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => [1,1,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [5,6,3,2,4,1] => [2,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [6,3,5,2,4,1] => [1,2,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [3,6,5,2,4,1] => [2,1,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => [1,2,2,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [6,3,2,5,4,1] => [1,1,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [3,6,2,5,4,1] => [2,2,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [3,2,6,5,4,1] => [1,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [5,3,2,6,4,1] => [1,1,2,1,1] => 1
>>> Load all 2043 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => [1,1,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [4,6,3,2,5,1] => [2,1,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => [1,2,2,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [4,3,2,6,5,1] => [1,1,2,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => [1,1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => [1,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => [2,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [6,4,5,3,1,2] => [1,2,1,2] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [4,6,5,3,1,2] => [2,1,1,2] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [5,4,6,3,1,2] => [1,2,1,2] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [6,5,3,4,1,2] => [1,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => [2,2,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [6,3,5,4,1,2] => [1,2,1,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [3,6,5,4,1,2] => [2,1,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [5,3,6,4,1,2] => [1,2,1,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [6,4,3,5,1,2] => [1,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [4,6,3,5,1,2] => [2,2,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [4,3,6,5,1,2] => [1,2,1,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [5,4,3,6,1,2] => [1,1,2,2] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [6,5,4,1,3,2] => [1,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [5,6,4,1,3,2] => [2,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [6,4,5,1,3,2] => [1,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [4,6,5,1,3,2] => [2,1,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [5,4,6,1,3,2] => [1,2,2,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [6,5,1,4,3,2] => [1,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [5,6,1,4,3,2] => [2,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [6,1,5,4,3,2] => [1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [1,6,5,4,3,2] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [5,1,6,4,3,2] => [1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [6,4,1,5,3,2] => [1,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [4,6,1,5,3,2] => [2,2,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [4,1,6,5,3,2] => [1,2,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [5,4,1,6,3,2] => [1,1,2,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [6,5,3,1,4,2] => [1,1,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [5,6,3,1,4,2] => [2,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [6,3,5,1,4,2] => [1,2,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [3,6,5,1,4,2] => [2,1,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [5,3,6,1,4,2] => [1,2,2,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [6,3,1,5,4,2] => [1,1,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [3,6,1,5,4,2] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [3,1,6,5,4,2] => [1,2,1,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [5,3,1,6,4,2] => [1,1,2,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [6,4,3,1,5,2] => [1,1,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [4,6,3,1,5,2] => [2,1,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [4,3,6,1,5,2] => [1,2,2,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [4,3,1,6,5,2] => [1,1,2,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [5,4,3,1,6,2] => [1,1,1,2,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [6,5,4,2,1,3] => [1,1,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [5,6,4,2,1,3] => [2,1,1,2] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [6,4,5,2,1,3] => [1,2,1,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [4,6,5,2,1,3] => [2,1,1,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [5,4,6,2,1,3] => [1,2,1,2] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [6,5,2,4,1,3] => [1,1,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [5,6,2,4,1,3] => [2,2,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [6,2,5,4,1,3] => [1,2,1,2] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [2,6,5,4,1,3] => [2,1,1,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [5,2,6,4,1,3] => [1,2,1,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [6,4,2,5,1,3] => [1,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [4,6,2,5,1,3] => [2,2,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [4,2,6,5,1,3] => [1,2,1,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [5,4,2,6,1,3] => [1,1,2,2] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [6,5,2,1,4,3] => [1,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [5,6,2,1,4,3] => [2,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [6,2,5,1,4,3] => [1,2,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [2,6,5,1,4,3] => [2,1,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [5,2,6,1,4,3] => [1,2,2,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [6,2,1,5,4,3] => [1,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [2,6,1,5,4,3] => [2,2,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [2,1,6,5,4,3] => [1,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [5,2,1,6,4,3] => [1,1,2,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [6,4,2,1,5,3] => [1,1,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [4,6,2,1,5,3] => [2,1,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [4,2,6,1,5,3] => [1,2,2,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => [1,1,2,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [5,4,2,1,6,3] => [1,1,1,2,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [6,5,3,2,1,4] => [1,1,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [5,6,3,2,1,4] => [2,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [6,3,5,2,1,4] => [1,2,1,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [3,6,5,2,1,4] => [2,1,1,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [5,3,6,2,1,4] => [1,2,1,2] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [6,3,2,5,1,4] => [1,1,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [3,6,2,5,1,4] => [2,2,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [3,2,6,5,1,4] => [1,2,1,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [5,3,2,6,1,4] => [1,1,2,2] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [6,3,2,1,5,4] => [1,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [3,6,2,1,5,4] => [2,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [3,2,6,1,5,4] => [1,2,2,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,2,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [5,3,2,1,6,4] => [1,1,1,2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [6,4,3,2,1,5] => [1,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [4,6,3,2,1,5] => [2,1,1,2] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [4,3,6,2,1,5] => [1,2,1,2] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [4,3,2,6,1,5] => [1,1,2,2] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,2,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,2] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [6,7,5,4,3,2,1] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [7,5,6,4,3,2,1] => [1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [5,7,6,4,3,2,1] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => [6,5,7,4,3,2,1] => [1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [7,6,4,5,3,2,1] => [1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [6,7,4,5,3,2,1] => [2,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [7,4,6,5,3,2,1] => [1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [4,7,6,5,3,2,1] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6] => [6,4,7,5,3,2,1] => [1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => [7,5,4,6,3,2,1] => [1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => [5,7,4,6,3,2,1] => [2,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,4,5] => [5,4,7,6,3,2,1] => [1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => [6,5,4,7,3,2,1] => [1,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [7,6,5,3,4,2,1] => [1,1,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [6,7,5,3,4,2,1] => [2,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [7,5,6,3,4,2,1] => [1,2,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [5,7,6,3,4,2,1] => [2,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => [6,5,7,3,4,2,1] => [1,2,2,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [7,6,3,5,4,2,1] => [1,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [6,7,3,5,4,2,1] => [2,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [7,3,6,5,4,2,1] => [1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [3,7,6,5,4,2,1] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6] => [6,3,7,5,4,2,1] => [1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,7] => [7,5,3,6,4,2,1] => [1,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,7,5] => [5,7,3,6,4,2,1] => [2,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,3,5] => [5,3,7,6,4,2,1] => [1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [6,5,3,7,4,2,1] => [1,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => [7,6,4,3,5,2,1] => [1,1,1,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => [6,7,4,3,5,2,1] => [2,1,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,3,6,4,7] => [7,4,6,3,5,2,1] => [1,2,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,3,6,7,4] => [4,7,6,3,5,2,1] => [2,1,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6] => [6,4,7,3,5,2,1] => [1,2,2,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => [7,4,3,6,5,2,1] => [1,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,3,7,4] => [4,7,3,6,5,2,1] => [2,2,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,3,4] => [4,3,7,6,5,2,1] => [1,2,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [6,4,3,7,5,2,1] => [1,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => [7,5,4,3,6,2,1] => [1,1,1,2,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => [5,7,4,3,6,2,1] => [2,1,2,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,3,7,4,5] => [5,4,7,3,6,2,1] => [1,2,2,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,3,4,5] => [5,4,3,7,6,2,1] => [1,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => [6,5,4,3,7,2,1] => [1,1,1,2,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [7,6,5,4,2,3,1] => [1,1,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [6,7,5,4,2,3,1] => [2,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [7,5,6,4,2,3,1] => [1,2,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [5,7,6,4,2,3,1] => [2,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => [6,5,7,4,2,3,1] => [1,2,1,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [7,6,4,5,2,3,1] => [1,1,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [6,7,4,5,2,3,1] => [2,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [7,4,6,5,2,3,1] => [1,2,1,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [4,7,6,5,2,3,1] => [2,1,1,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6] => [6,4,7,5,2,3,1] => [1,2,1,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => [7,5,4,6,2,3,1] => [1,1,2,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,7,5] => [5,7,4,6,2,3,1] => [2,2,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => [5,4,7,6,2,3,1] => [1,2,1,2,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => [6,5,4,7,2,3,1] => [1,1,2,2,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [7,6,5,2,4,3,1] => [1,1,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [6,7,5,2,4,3,1] => [2,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [7,5,6,2,4,3,1] => [1,2,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [5,7,6,2,4,3,1] => [2,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => [6,5,7,2,4,3,1] => [1,2,2,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [7,6,2,5,4,3,1] => [1,1,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [6,7,2,5,4,3,1] => [2,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [7,2,6,5,4,3,1] => [1,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [2,7,6,5,4,3,1] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6] => [6,2,7,5,4,3,1] => [1,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,7] => [7,5,2,6,4,3,1] => [1,1,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,2,7,5] => [5,7,2,6,4,3,1] => [2,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,2,5] => [5,2,7,6,4,3,1] => [1,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [6,5,2,7,4,3,1] => [1,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,6,7] => [7,6,4,2,5,3,1] => [1,1,1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6] => [6,7,4,2,5,3,1] => [2,1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,6,4,7] => [7,4,6,2,5,3,1] => [1,2,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => [4,7,6,2,5,3,1] => [2,1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6] => [6,4,7,2,5,3,1] => [1,2,2,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,2,4,7] => [7,4,2,6,5,3,1] => [1,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,2,7,4] => [4,7,2,6,5,3,1] => [2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,2,4] => [4,2,7,6,5,3,1] => [1,2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [6,4,2,7,5,3,1] => [1,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => [7,5,4,2,6,3,1] => [1,1,1,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,2,4,7,5] => [5,7,4,2,6,3,1] => [2,1,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,4,5] => [5,4,7,2,6,3,1] => [1,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,4,5] => [5,4,2,7,6,3,1] => [1,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => [6,5,4,2,7,3,1] => [1,1,1,2,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => [7,6,5,3,2,4,1] => [1,1,1,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => [6,7,5,3,2,4,1] => [2,1,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => [7,5,6,3,2,4,1] => [1,2,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => [5,7,6,3,2,4,1] => [2,1,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => [6,5,7,3,2,4,1] => [1,2,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,3,6,7] => [7,6,3,5,2,4,1] => [1,1,2,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6] => [6,7,3,5,2,4,1] => [2,2,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,5,6,3,7] => [7,3,6,5,2,4,1] => [1,2,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => [3,7,6,5,2,4,1] => [2,1,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6] => [6,3,7,5,2,4,1] => [1,2,1,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,7] => [7,5,3,6,2,4,1] => [1,1,2,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,7,5] => [5,7,3,6,2,4,1] => [2,2,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,7,3,5] => [5,3,7,6,2,4,1] => [1,2,1,2,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,7,3,5,6] => [6,5,3,7,2,4,1] => [1,1,2,2,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => [7,6,3,2,5,4,1] => [1,1,1,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => [6,7,3,2,5,4,1] => [2,1,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,2,6,3,7] => [7,3,6,2,5,4,1] => [1,2,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,2,6,7,3] => [3,7,6,2,5,4,1] => [2,1,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6] => [6,3,7,2,5,4,1] => [1,2,2,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => [7,3,2,6,5,4,1] => [1,1,2,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,2,7,3] => [3,7,2,6,5,4,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,2,3] => [3,2,7,6,5,4,1] => [1,2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [6,3,2,7,5,4,1] => [1,1,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,7] => [7,5,3,2,6,4,1] => [1,1,1,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,7,5] => [5,7,3,2,6,4,1] => [2,1,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,7,3,5] => [5,3,7,2,6,4,1] => [1,2,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => [5,3,2,7,6,4,1] => [1,1,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => [6,5,3,2,7,4,1] => [1,1,1,2,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => [7,6,4,3,2,5,1] => [1,1,1,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => [6,7,4,3,2,5,1] => [2,1,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,6,4,7] => [7,4,6,3,2,5,1] => [1,2,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,6,7,4] => [4,7,6,3,2,5,1] => [2,1,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6] => [6,4,7,3,2,5,1] => [1,2,1,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,6,3,4,7] => [7,4,3,6,2,5,1] => [1,1,2,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,7,4] => [4,7,3,6,2,5,1] => [2,2,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,2,6,7,3,4] => [4,3,7,6,2,5,1] => [1,2,1,2,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6] => [6,4,3,7,2,5,1] => [1,1,2,2,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,2,3,4,7] => [7,4,3,2,6,5,1] => [1,1,1,2,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,2,3,7,4] => [4,7,3,2,6,5,1] => [2,1,2,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,2,7,3,4] => [4,3,7,2,6,5,1] => [1,2,2,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => [4,3,2,7,6,5,1] => [1,1,2,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6] => [6,4,3,2,7,5,1] => [1,1,1,2,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => [7,5,4,3,2,6,1] => [1,1,1,1,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [5,7,4,3,2,6,1] => [2,1,1,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,2,3,7,4,5] => [5,4,7,3,2,6,1] => [1,2,1,2,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => [5,4,3,7,2,6,1] => [1,1,2,2,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,2,3,4,5] => [5,4,3,2,7,6,1] => [1,1,1,2,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => [6,5,4,3,2,7,1] => [1,1,1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [7,6,5,4,3,1,2] => [1,1,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [6,7,5,4,3,1,2] => [2,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [7,5,6,4,3,1,2] => [1,2,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [5,7,6,4,3,1,2] => [2,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => [6,5,7,4,3,1,2] => [1,2,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [7,6,4,5,3,1,2] => [1,1,2,1,2] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [6,7,4,5,3,1,2] => [2,2,1,2] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [7,4,6,5,3,1,2] => [1,2,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [4,7,6,5,3,1,2] => [2,1,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,4,6] => [6,4,7,5,3,1,2] => [1,2,1,1,2] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => [7,5,4,6,3,1,2] => [1,1,2,1,2] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,4,7,5] => [5,7,4,6,3,1,2] => [2,2,1,2] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,4,5] => [5,4,7,6,3,1,2] => [1,2,1,1,2] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => [6,5,4,7,3,1,2] => [1,1,2,1,2] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [7,6,5,3,4,1,2] => [1,1,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [6,7,5,3,4,1,2] => [2,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [7,5,6,3,4,1,2] => [1,2,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [5,7,6,3,4,1,2] => [2,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => [6,5,7,3,4,1,2] => [1,2,2,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [7,6,3,5,4,1,2] => [1,1,2,1,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [6,7,3,5,4,1,2] => [2,2,1,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [7,3,6,5,4,1,2] => [1,2,1,1,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [3,7,6,5,4,1,2] => [2,1,1,1,2] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,3,6] => [6,3,7,5,4,1,2] => [1,2,1,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,7] => [7,5,3,6,4,1,2] => [1,1,2,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,7,5] => [5,7,3,6,4,1,2] => [2,2,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,3,5] => [5,3,7,6,4,1,2] => [1,2,1,1,2] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,3,5,6] => [6,5,3,7,4,1,2] => [1,1,2,1,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [7,6,4,3,5,1,2] => [1,1,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => [6,7,4,3,5,1,2] => [2,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4,7] => [7,4,6,3,5,1,2] => [1,2,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,3,6,7,4] => [4,7,6,3,5,1,2] => [2,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6] => [6,4,7,3,5,1,2] => [1,2,2,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,3,4,7] => [7,4,3,6,5,1,2] => [1,1,2,1,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,3,7,4] => [4,7,3,6,5,1,2] => [2,2,1,2] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,3,4] => [4,3,7,6,5,1,2] => [1,2,1,1,2] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6] => [6,4,3,7,5,1,2] => [1,1,2,1,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => [7,5,4,3,6,1,2] => [1,1,1,2,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,3,4,7,5] => [5,7,4,3,6,1,2] => [2,1,2,2] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,7,4,5] => [5,4,7,3,6,1,2] => [1,2,2,2] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,3,4,5] => [5,4,3,7,6,1,2] => [1,1,2,1,2] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => [6,5,4,3,7,1,2] => [1,1,1,2,2] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [7,6,5,4,1,3,2] => [1,1,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [6,7,5,4,1,3,2] => [2,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [7,5,6,4,1,3,2] => [1,2,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [5,7,6,4,1,3,2] => [2,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,5,6] => [6,5,7,4,1,3,2] => [1,2,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [7,6,4,5,1,3,2] => [1,1,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [6,7,4,5,1,3,2] => [2,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [7,4,6,5,1,3,2] => [1,2,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [4,7,6,5,1,3,2] => [2,1,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6] => [6,4,7,5,1,3,2] => [1,2,1,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => [7,5,4,6,1,3,2] => [1,1,2,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,7,5] => [5,7,4,6,1,3,2] => [2,2,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => [5,4,7,6,1,3,2] => [1,2,1,2,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,4,5,6] => [6,5,4,7,1,3,2] => [1,1,2,2,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [7,6,5,1,4,3,2] => [1,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [6,7,5,1,4,3,2] => [2,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [7,5,6,1,4,3,2] => [1,2,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [5,7,6,1,4,3,2] => [2,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,5,6] => [6,5,7,1,4,3,2] => [1,2,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [7,6,1,5,4,3,2] => [1,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [6,7,1,5,4,3,2] => [2,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [7,1,6,5,4,3,2] => [1,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [1,7,6,5,4,3,2] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6] => [6,1,7,5,4,3,2] => [1,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,7] => [7,5,1,6,4,3,2] => [1,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => [5,7,1,6,4,3,2] => [2,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,1,5] => [5,1,7,6,4,3,2] => [1,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [6,5,1,7,4,3,2] => [1,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,6,7] => [7,6,4,1,5,3,2] => [1,1,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6] => [6,7,4,1,5,3,2] => [2,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,6,4,7] => [7,4,6,1,5,3,2] => [1,2,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,6,7,4] => [4,7,6,1,5,3,2] => [2,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,7,4,6] => [6,4,7,1,5,3,2] => [1,2,2,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,1,4,7] => [7,4,1,6,5,3,2] => [1,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,1,7,4] => [4,7,1,6,5,3,2] => [2,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,1,4] => [4,1,7,6,5,3,2] => [1,2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [6,4,1,7,5,3,2] => [1,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,7] => [7,5,4,1,6,3,2] => [1,1,1,2,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,1,4,7,5] => [5,7,4,1,6,3,2] => [2,1,2,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,4,5] => [5,4,7,1,6,3,2] => [1,2,2,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,4,5] => [5,4,1,7,6,3,2] => [1,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6] => [6,5,4,1,7,3,2] => [1,1,1,2,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7] => [7,6,5,3,1,4,2] => [1,1,1,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,5,7,6] => [6,7,5,3,1,4,2] => [2,1,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,7] => [7,5,6,3,1,4,2] => [1,2,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,7,5] => [5,7,6,3,1,4,2] => [2,1,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,7,5,6] => [6,5,7,3,1,4,2] => [1,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,5,3,6,7] => [7,6,3,5,1,4,2] => [1,1,2,2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6] => [6,7,3,5,1,4,2] => [2,2,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,5,6,3,7] => [7,3,6,5,1,4,2] => [1,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,3] => [3,7,6,5,1,4,2] => [2,1,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,1,5,7,3,6] => [6,3,7,5,1,4,2] => [1,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,7] => [7,5,3,6,1,4,2] => [1,1,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,7,5] => [5,7,3,6,1,4,2] => [2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,7,3,5] => [5,3,7,6,1,4,2] => [1,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,7,3,5,6] => [6,5,3,7,1,4,2] => [1,1,2,2,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,1,3,6,7] => [7,6,3,1,5,4,2] => [1,1,1,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6] => [6,7,3,1,5,4,2] => [2,1,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,1,6,3,7] => [7,3,6,1,5,4,2] => [1,2,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,1,6,7,3] => [3,7,6,1,5,4,2] => [2,1,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6] => [6,3,7,1,5,4,2] => [1,2,2,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,1,3,7] => [7,3,1,6,5,4,2] => [1,1,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,1,7,3] => [3,7,1,6,5,4,2] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,1,3] => [3,1,7,6,5,4,2] => [1,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [6,3,1,7,5,4,2] => [1,1,2,1,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,7] => [7,5,3,1,6,4,2] => [1,1,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,7,5] => [5,7,3,1,6,4,2] => [2,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,7,3,5] => [5,3,7,1,6,4,2] => [1,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,1,3,5] => [5,3,1,7,6,4,2] => [1,1,2,1,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6] => [6,5,3,1,7,4,2] => [1,1,1,2,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,6,7] => [7,6,4,3,1,5,2] => [1,1,1,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [6,7,4,3,1,5,2] => [2,1,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,6,4,7] => [7,4,6,3,1,5,2] => [1,2,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,6,7,4] => [4,7,6,3,1,5,2] => [2,1,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6] => [6,4,7,3,1,5,2] => [1,2,1,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1,6,3,4,7] => [7,4,3,6,1,5,2] => [1,1,2,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,1,6,3,7,4] => [4,7,3,6,1,5,2] => [2,2,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,1,6,7,3,4] => [4,3,7,6,1,5,2] => [1,2,1,2,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,1,7,3,4,6] => [6,4,3,7,1,5,2] => [1,1,2,2,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,1,3,4,7] => [7,4,3,1,6,5,2] => [1,1,1,2,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,1,3,7,4] => [4,7,3,1,6,5,2] => [2,1,2,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,1,7,3,4] => [4,3,7,1,6,5,2] => [1,2,2,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,1,3,4] => [4,3,1,7,6,5,2] => [1,1,2,1,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,1,3,4,6] => [6,4,3,1,7,5,2] => [1,1,1,2,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => [7,5,4,3,1,6,2] => [1,1,1,1,2,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,7,5] => [5,7,4,3,1,6,2] => [2,1,1,2,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,1,3,7,4,5] => [5,4,7,3,1,6,2] => [1,2,1,2,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,1,7,3,4,5] => [5,4,3,7,1,6,2] => [1,1,2,2,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,1,3,4,5] => [5,4,3,1,7,6,2] => [1,1,1,2,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6] => [6,5,4,3,1,7,2] => [1,1,1,1,2,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => [7,6,5,4,2,1,3] => [1,1,1,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => [6,7,5,4,2,1,3] => [2,1,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => [7,5,6,4,2,1,3] => [1,2,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,4,6,7,5] => [5,7,6,4,2,1,3] => [2,1,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,4,7,5,6] => [6,5,7,4,2,1,3] => [1,2,1,1,2] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => [7,6,4,5,2,1,3] => [1,1,2,1,2] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => [6,7,4,5,2,1,3] => [2,2,1,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,6,4,7] => [7,4,6,5,2,1,3] => [1,2,1,1,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,6,7,4] => [4,7,6,5,2,1,3] => [2,1,1,1,2] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6] => [6,4,7,5,2,1,3] => [1,2,1,1,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => [7,5,4,6,2,1,3] => [1,1,2,1,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,2,6,4,7,5] => [5,7,4,6,2,1,3] => [2,2,1,2] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,6,7,4,5] => [5,4,7,6,2,1,3] => [1,2,1,1,2] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => [6,5,4,7,2,1,3] => [1,1,2,1,2] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7] => [7,6,5,2,4,1,3] => [1,1,1,2,2] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,4,2,5,7,6] => [6,7,5,2,4,1,3] => [2,1,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,7] => [7,5,6,2,4,1,3] => [1,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,7,5] => [5,7,6,2,4,1,3] => [2,1,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,7,5,6] => [6,5,7,2,4,1,3] => [1,2,2,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2,6,7] => [7,6,2,5,4,1,3] => [1,1,2,1,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6] => [6,7,2,5,4,1,3] => [2,2,1,2] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,2,7] => [7,2,6,5,4,1,3] => [1,2,1,1,2] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,2] => [2,7,6,5,4,1,3] => [2,1,1,1,2] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6] => [6,2,7,5,4,1,3] => [1,2,1,1,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,7] => [7,5,2,6,4,1,3] => [1,1,2,1,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,7,5] => [5,7,2,6,4,1,3] => [2,2,1,2] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,4,6,7,2,5] => [5,2,7,6,4,1,3] => [1,2,1,1,2] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,4,7,2,5,6] => [6,5,2,7,4,1,3] => [1,1,2,1,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [7,6,4,2,5,1,3] => [1,1,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6] => [6,7,4,2,5,1,3] => [2,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4,7] => [7,4,6,2,5,1,3] => [1,2,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,6,7,4] => [4,7,6,2,5,1,3] => [2,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6] => [6,4,7,2,5,1,3] => [1,2,2,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,6,2,4,7] => [7,4,2,6,5,1,3] => [1,1,2,1,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,6,2,7,4] => [4,7,2,6,5,1,3] => [2,2,1,2] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,6,7,2,4] => [4,2,7,6,5,1,3] => [1,2,1,1,2] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6] => [6,4,2,7,5,1,3] => [1,1,2,1,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,7] => [7,5,4,2,6,1,3] => [1,1,1,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,6,2,4,7,5] => [5,7,4,2,6,1,3] => [2,1,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,7,4,5] => [5,4,7,2,6,1,3] => [1,2,2,2] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,6,7,2,4,5] => [5,4,2,7,6,1,3] => [1,1,2,1,2] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6] => [6,5,4,2,7,1,3] => [1,1,1,2,2] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7] => [7,6,5,2,1,4,3] => [1,1,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,5,7,6] => [6,7,5,2,1,4,3] => [2,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,7] => [7,5,6,2,1,4,3] => [1,2,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,7,5] => [5,7,6,2,1,4,3] => [2,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,7,5,6] => [6,5,7,2,1,4,3] => [1,2,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,1,5,2,6,7] => [7,6,2,5,1,4,3] => [1,1,2,2,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6] => [6,7,2,5,1,4,3] => [2,2,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,1,5,6,2,7] => [7,2,6,5,1,4,3] => [1,2,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,2] => [2,7,6,5,1,4,3] => [2,1,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6] => [6,2,7,5,1,4,3] => [1,2,1,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,7] => [7,5,2,6,1,4,3] => [1,1,2,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,7,5] => [5,7,2,6,1,4,3] => [2,2,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,7,2,5] => [5,2,7,6,1,4,3] => [1,2,1,2,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,1,7,2,5,6] => [6,5,2,7,1,4,3] => [1,1,2,2,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,1,2,6,7] => [7,6,2,1,5,4,3] => [1,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => [6,7,2,1,5,4,3] => [2,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,1,6,2,7] => [7,2,6,1,5,4,3] => [1,2,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,1,6,7,2] => [2,7,6,1,5,4,3] => [2,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6] => [6,2,7,1,5,4,3] => [1,2,2,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,1,2,7] => [7,2,1,6,5,4,3] => [1,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,1,7,2] => [2,7,1,6,5,4,3] => [2,2,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => [2,1,7,6,5,4,3] => [1,2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [6,2,1,7,5,4,3] => [1,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,7] => [7,5,2,1,6,4,3] => [1,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,1,2,7,5] => [5,7,2,1,6,4,3] => [2,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,1,7,2,5] => [5,2,7,1,6,4,3] => [1,2,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,1,2,5] => [5,2,1,7,6,4,3] => [1,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,1,2,5,6] => [6,5,2,1,7,4,3] => [1,1,1,2,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,6,7] => [7,6,4,2,1,5,3] => [1,1,1,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [6,7,4,2,1,5,3] => [2,1,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,6,4,7] => [7,4,6,2,1,5,3] => [1,2,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,6,7,4] => [4,7,6,2,1,5,3] => [2,1,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6] => [6,4,7,2,1,5,3] => [1,2,1,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,6,2,4,7] => [7,4,2,6,1,5,3] => [1,1,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,6,2,7,4] => [4,7,2,6,1,5,3] => [2,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,6,7,2,4] => [4,2,7,6,1,5,3] => [1,2,1,2,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6] => [6,4,2,7,1,5,3] => [1,1,2,2,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,1,2,4,7] => [7,4,2,1,6,5,3] => [1,1,1,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,1,2,7,4] => [4,7,2,1,6,5,3] => [2,1,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,1,7,2,4] => [4,2,7,1,6,5,3] => [1,2,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,1,2,4] => [4,2,1,7,6,5,3] => [1,1,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6] => [6,4,2,1,7,5,3] => [1,1,1,2,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,7] => [7,5,4,2,1,6,3] => [1,1,1,1,2,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,7,5] => [5,7,4,2,1,6,3] => [2,1,1,2,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,1,2,7,4,5] => [5,4,7,2,1,6,3] => [1,2,1,2,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,1,7,2,4,5] => [5,4,2,7,1,6,3] => [1,1,2,2,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,1,2,4,5] => [5,4,2,1,7,6,3] => [1,1,1,2,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6] => [6,5,4,2,1,7,3] => [1,1,1,1,2,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => [7,6,5,3,2,1,4] => [1,1,1,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => [6,7,5,3,2,1,4] => [2,1,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => [7,5,6,3,2,1,4] => [1,2,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,7,5] => [5,7,6,3,2,1,4] => [2,1,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => [6,5,7,3,2,1,4] => [1,2,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,5,3,6,7] => [7,6,3,5,2,1,4] => [1,1,2,1,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6] => [6,7,3,5,2,1,4] => [2,2,1,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,5,6,3,7] => [7,3,6,5,2,1,4] => [1,2,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,3] => [3,7,6,5,2,1,4] => [2,1,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6] => [6,3,7,5,2,1,4] => [1,2,1,1,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,7] => [7,5,3,6,2,1,4] => [1,1,2,1,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,7,5] => [5,7,3,6,2,1,4] => [2,2,1,2] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,7,3,5] => [5,3,7,6,2,1,4] => [1,2,1,1,2] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,7,3,5,6] => [6,5,3,7,2,1,4] => [1,1,2,1,2] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [7,6,3,2,5,1,4] => [1,1,1,2,2] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6] => [6,7,3,2,5,1,4] => [2,1,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3,7] => [7,3,6,2,5,1,4] => [1,2,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,5,2,6,7,3] => [3,7,6,2,5,1,4] => [2,1,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6] => [6,3,7,2,5,1,4] => [1,2,2,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,5,6,2,3,7] => [7,3,2,6,5,1,4] => [1,1,2,1,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,5,6,2,7,3] => [3,7,2,6,5,1,4] => [2,2,1,2] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,2,3] => [3,2,7,6,5,1,4] => [1,2,1,1,2] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6] => [6,3,2,7,5,1,4] => [1,1,2,1,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,7] => [7,5,3,2,6,1,4] => [1,1,1,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,7,5] => [5,7,3,2,6,1,4] => [2,1,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,7,3,5] => [5,3,7,2,6,1,4] => [1,2,2,2] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,7,2,3,5] => [5,3,2,7,6,1,4] => [1,1,2,1,2] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6] => [6,5,3,2,7,1,4] => [1,1,1,2,2] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,6,7] => [7,6,3,2,1,5,4] => [1,1,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [6,7,3,2,1,5,4] => [2,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,1,2,6,3,7] => [7,3,6,2,1,5,4] => [1,2,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,1,2,6,7,3] => [3,7,6,2,1,5,4] => [2,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6] => [6,3,7,2,1,5,4] => [1,2,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,1,6,2,3,7] => [7,3,2,6,1,5,4] => [1,1,2,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,1,6,2,7,3] => [3,7,2,6,1,5,4] => [2,2,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,1,6,7,2,3] => [3,2,7,6,1,5,4] => [1,2,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6] => [6,3,2,7,1,5,4] => [1,1,2,2,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,1,2,3,7] => [7,3,2,1,6,5,4] => [1,1,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,1,2,7,3] => [3,7,2,1,6,5,4] => [2,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,1,7,2,3] => [3,2,7,1,6,5,4] => [1,2,2,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,2,3] => [3,2,1,7,6,5,4] => [1,1,2,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,1,2,3,6] => [6,3,2,1,7,5,4] => [1,1,1,2,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,7] => [7,5,3,2,1,6,4] => [1,1,1,1,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,7,5] => [5,7,3,2,1,6,4] => [2,1,1,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,7,3,5] => [5,3,7,2,1,6,4] => [1,2,1,2,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,7,2,3,5] => [5,3,2,7,1,6,4] => [1,1,2,2,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,1,2,3,5] => [5,3,2,1,7,6,4] => [1,1,1,2,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6] => [6,5,3,2,1,7,4] => [1,1,1,1,2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => [7,6,4,3,2,1,5] => [1,1,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => [6,7,4,3,2,1,5] => [2,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,6,4,7] => [7,4,6,3,2,1,5] => [1,2,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => [4,7,6,3,2,1,5] => [2,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6] => [6,4,7,3,2,1,5] => [1,2,1,1,2] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,6,3,4,7] => [7,4,3,6,2,1,5] => [1,1,2,1,2] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,6,3,7,4] => [4,7,3,6,2,1,5] => [2,2,1,2] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,6,7,3,4] => [4,3,7,6,2,1,5] => [1,2,1,1,2] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6] => [6,4,3,7,2,1,5] => [1,1,2,1,2] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,6,2,3,4,7] => [7,4,3,2,6,1,5] => [1,1,1,2,2] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => [4,7,3,2,6,1,5] => [2,1,2,2] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,6,2,7,3,4] => [4,3,7,2,6,1,5] => [1,2,2,2] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,6,7,2,3,4] => [4,3,2,7,6,1,5] => [1,1,2,1,2] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6] => [6,4,3,2,7,1,5] => [1,1,1,2,2] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,7] => [7,4,3,2,1,6,5] => [1,1,1,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,1,2,3,7,4] => [4,7,3,2,1,6,5] => [2,1,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,1,2,7,3,4] => [4,3,7,2,1,6,5] => [1,2,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,1,7,2,3,4] => [4,3,2,7,1,6,5] => [1,1,2,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,1,2,3,4] => [4,3,2,1,7,6,5] => [1,1,1,2,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6] => [6,4,3,2,1,7,5] => [1,1,1,1,2,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [7,5,4,3,2,1,6] => [1,1,1,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,7,5] => [5,7,4,3,2,1,6] => [2,1,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,7,4,5] => [5,4,7,3,2,1,6] => [1,2,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1,2,7,3,4,5] => [5,4,3,7,2,1,6] => [1,1,2,1,2] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1,7,2,3,4,5] => [5,4,3,2,7,1,6] => [1,1,1,2,2] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5] => [5,4,3,2,1,7,6] => [1,1,1,1,2,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => [1,1,1,1,1,2] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [8,6,7,5,4,3,2,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => [7,6,8,5,4,3,2,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [8,7,5,6,4,3,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [7,8,5,6,4,3,2,1] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [8,5,7,6,4,3,2,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,5,7] => [7,5,8,6,4,3,2,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,5,6,8] => [8,6,5,7,4,3,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,5,8,6] => [6,8,5,7,4,3,2,1] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,5,6] => [6,5,8,7,4,3,2,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,5,6,7] => [7,6,5,8,4,3,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [8,7,6,4,5,3,2,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [7,8,6,4,5,3,2,1] => [2,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [8,6,7,4,5,3,2,1] => [1,2,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [6,8,7,4,5,3,2,1] => [2,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => [7,6,8,4,5,3,2,1] => [1,2,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [8,7,4,6,5,3,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [7,8,4,6,5,3,2,1] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [8,4,7,6,5,3,2,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,4,7] => [7,4,8,6,5,3,2,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,4,6,8] => [8,6,4,7,5,3,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,4,8,6] => [6,8,4,7,5,3,2,1] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,4,6] => [6,4,8,7,5,3,2,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,4,6,7] => [7,6,4,8,5,3,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,4,5,7,8] => [8,7,5,4,6,3,2,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => [7,8,5,4,6,3,2,1] => [2,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5,8] => [8,5,7,4,6,3,2,1] => [1,2,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,4,7,8,5] => [5,8,7,4,6,3,2,1] => [2,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,4,8,5,7] => [7,5,8,4,6,3,2,1] => [1,2,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,4,5,8] => [8,5,4,7,6,3,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,4,8,5] => [5,8,4,7,6,3,2,1] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,4,5] => [5,4,8,7,6,3,2,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,4,5,7] => [7,5,4,8,6,3,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,4,5,6,8] => [8,6,5,4,7,3,2,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,4,5,8,6] => [6,8,5,4,7,3,2,1] => [2,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,4,8,5,6] => [6,5,8,4,7,3,2,1] => [1,2,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,4,5,6] => [6,5,4,8,7,3,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => [7,6,5,4,8,3,2,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [8,7,6,5,3,4,2,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [7,8,6,5,3,4,2,1] => [2,1,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [8,6,7,5,3,4,2,1] => [1,2,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [6,8,7,5,3,4,2,1] => [2,1,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,6,7] => [7,6,8,5,3,4,2,1] => [1,2,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [8,7,5,6,3,4,2,1] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [7,8,5,6,3,4,2,1] => [2,2,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [8,5,7,6,3,4,2,1] => [1,2,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [5,8,7,6,3,4,2,1] => [2,1,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,5,7] => [7,5,8,6,3,4,2,1] => [1,2,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => [8,6,5,7,3,4,2,1] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,8,6] => [6,8,5,7,3,4,2,1] => [2,2,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,5,6] => [6,5,8,7,3,4,2,1] => [1,2,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => [7,6,5,8,3,4,2,1] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [8,7,6,3,5,4,2,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6,8,7] => [7,8,6,3,5,4,2,1] => [2,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [8,6,7,3,5,4,2,1] => [1,2,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [6,8,7,3,5,4,2,1] => [2,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,6,7] => [7,6,8,3,5,4,2,1] => [1,2,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [8,7,3,6,5,4,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [8,3,7,6,5,4,2,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,3,7] => [7,3,8,6,5,4,2,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,4,5,7,3,6,8] => [8,6,3,7,5,4,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,3,6] => [6,3,8,7,5,4,2,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,3,6,7] => [7,6,3,8,5,4,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,3,5,7,8] => [8,7,5,3,6,4,2,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,6,3,5,8,7] => [7,8,5,3,6,4,2,1] => [2,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,3,7,5,8] => [8,5,7,3,6,4,2,1] => [1,2,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,4,6,3,7,8,5] => [5,8,7,3,6,4,2,1] => [2,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,3,8,5,7] => [7,5,8,3,6,4,2,1] => [1,2,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,6,7,3,8,5] => [5,8,3,7,6,4,2,1] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,3,5] => [5,3,8,7,6,4,2,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,3,5,7] => [7,5,3,8,6,4,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,3,5,6,8] => [8,6,5,3,7,4,2,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,3,5,8,6] => [6,8,5,3,7,4,2,1] => [2,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,7,3,8,5,6] => [6,5,8,3,7,4,2,1] => [1,2,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,3,5,6,7] => [7,6,5,3,8,4,2,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,3,4,6,7,8] => [8,7,6,4,3,5,2,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,3,4,6,8,7] => [7,8,6,4,3,5,2,1] => [2,1,1,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => [8,6,7,4,3,5,2,1] => [1,2,1,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,3,4,7,8,6] => [6,8,7,4,3,5,2,1] => [2,1,1,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => [7,6,8,4,3,5,2,1] => [1,2,1,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,4,7,8] => [8,7,4,6,3,5,2,1] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,8,7] => [7,8,4,6,3,5,2,1] => [2,2,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,3,6,7,4,8] => [8,4,7,6,3,5,2,1] => [1,2,1,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,3,6,7,8,4] => [4,8,7,6,3,5,2,1] => [2,1,1,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,3,6,8,4,7] => [7,4,8,6,3,5,2,1] => [1,2,1,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,2,5,3,7,4,6,8] => [8,6,4,7,3,5,2,1] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,8,6] => [6,8,4,7,3,5,2,1] => [2,2,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,3,7,8,4,6] => [6,4,8,7,3,5,2,1] => [1,2,1,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,3,8,4,6,7] => [7,6,4,8,3,5,2,1] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,3,4,7,8] => [8,7,4,3,6,5,2,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,2,5,6,3,4,8,7] => [7,8,4,3,6,5,2,1] => [2,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,3,7,4,8] => [8,4,7,3,6,5,2,1] => [1,2,2,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,3,7,8,4] => [4,8,7,3,6,5,2,1] => [2,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,5,6,3,8,4,7] => [7,4,8,3,6,5,2,1] => [1,2,2,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,5,6,7,3,4,8] => [8,4,3,7,6,5,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,3,8,4] => [4,8,3,7,6,5,2,1] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,3,4] => [4,3,8,7,6,5,2,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,3,4,6,8] => [8,6,4,3,7,5,2,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,3,4,8,6] => [6,8,4,3,7,5,2,1] => [2,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,3,8,4,6] => [6,4,8,3,7,5,2,1] => [1,2,2,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,5,7,8,3,4,6] => [6,4,3,8,7,5,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,3,4,6,7] => [7,6,4,3,8,5,2,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,3,4,5,7,8] => [8,7,5,4,3,6,2,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => [7,8,5,4,3,6,2,1] => [2,1,1,2,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,6,3,4,7,5,8] => [8,5,7,4,3,6,2,1] => [1,2,1,2,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,3,4,7,8,5] => [5,8,7,4,3,6,2,1] => [2,1,1,2,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,3,4,8,5,7] => [7,5,8,4,3,6,2,1] => [1,2,1,2,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,6,3,7,4,5,8] => [8,5,4,7,3,6,2,1] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,8,5] => [5,8,4,7,3,6,2,1] => [2,2,2,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,3,7,8,4,5] => [5,4,8,7,3,6,2,1] => [1,2,1,2,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,3,8,4,5,7] => [7,5,4,8,3,6,2,1] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,3,4,5,8] => [8,5,4,3,7,6,2,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,6,7,3,4,8,5] => [5,8,4,3,7,6,2,1] => [2,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,3,4,5] => [5,4,3,8,7,6,2,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,6,8,3,4,5,7] => [7,5,4,3,8,6,2,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,3,4,5,6,8] => [8,6,5,4,3,7,2,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,3,4,5,8,6] => [6,8,5,4,3,7,2,1] => [2,1,1,2,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,3,4,8,5,6] => [6,5,8,4,3,7,2,1] => [1,2,1,2,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,3,8,4,5,6] => [6,5,4,8,3,7,2,1] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,3,4,5,6] => [6,5,4,3,8,7,2,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [7,6,5,4,3,8,2,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [8,7,6,5,4,2,3,1] => [1,1,1,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [7,8,6,5,4,2,3,1] => [2,1,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [8,6,7,5,4,2,3,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [6,8,7,5,4,2,3,1] => [2,1,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => [7,6,8,5,4,2,3,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [8,7,5,6,4,2,3,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,2,4,6,7,5,8] => [8,5,7,6,4,2,3,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [5,8,7,6,4,2,3,1] => [2,1,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,5,6,8] => [8,6,5,7,4,2,3,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,5,8,6] => [6,8,5,7,4,2,3,1] => [2,2,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,7,8,5,6] => [6,5,8,7,4,2,3,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => [7,6,5,8,4,2,3,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [8,7,6,4,5,2,3,1] => [1,1,1,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,4,6,8,7] => [7,8,6,4,5,2,3,1] => [2,1,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [8,6,7,4,5,2,3,1] => [1,2,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [6,8,7,4,5,2,3,1] => [2,1,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => [7,6,8,4,5,2,3,1] => [1,2,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [8,7,4,6,5,2,3,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [8,4,7,6,5,2,3,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [4,8,7,6,5,2,3,1] => [2,1,1,1,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,4,7] => [7,4,8,6,5,2,3,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,4,6,8] => [8,6,4,7,5,2,3,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,8,6] => [6,8,4,7,5,2,3,1] => [2,2,1,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,4,6] => [6,4,8,7,5,2,3,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,4,6,7] => [7,6,4,8,5,2,3,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => [8,7,5,4,6,2,3,1] => [1,1,1,2,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5,8] => [8,5,7,4,6,2,3,1] => [1,2,2,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,7,8,5] => [5,8,7,4,6,2,3,1] => [2,1,2,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,8,5,7] => [7,5,8,4,6,2,3,1] => [1,2,2,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,4,8,5] => [5,8,4,7,6,2,3,1] => [2,2,1,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,4,5] => [5,4,8,7,6,2,3,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => [8,6,5,4,7,2,3,1] => [1,1,1,2,2,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,4,5,8,6] => [6,8,5,4,7,2,3,1] => [2,1,2,2,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,8,5,6] => [6,5,8,4,7,2,3,1] => [1,2,2,2,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,7,8,4,5,6] => [6,5,4,8,7,2,3,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => [7,6,5,4,8,2,3,1] => [1,1,1,2,2,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [8,7,6,5,2,4,3,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [7,8,6,5,2,4,3,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [8,6,7,5,2,4,3,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [6,8,7,5,2,4,3,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,6,7] => [7,6,8,5,2,4,3,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,5,7,8] => [8,7,5,6,2,4,3,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [7,8,5,6,2,4,3,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [8,5,7,6,2,4,3,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [5,8,7,6,2,4,3,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,4,2,7,5,6,8] => [8,6,5,7,2,4,3,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,8,6] => [6,8,5,7,2,4,3,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,5,6] => [6,5,8,7,2,4,3,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,5,6,7] => [7,6,5,8,2,4,3,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [8,7,6,2,5,4,3,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,5,2,6,8,7] => [7,8,6,2,5,4,3,1] => [2,1,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [8,6,7,2,5,4,3,1] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [6,8,7,2,5,4,3,1] => [2,1,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,6,7] => [7,6,8,2,5,4,3,1] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [8,7,2,6,5,4,3,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [7,8,2,6,5,4,3,1] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [8,2,7,6,5,4,3,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,2,7] => [7,2,8,6,5,4,3,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,2,6,8] => [8,6,2,7,5,4,3,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,2,8,6] => [6,8,2,7,5,4,3,1] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,2,6] => [6,2,8,7,5,4,3,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,2,6,7] => [7,6,2,8,5,4,3,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,3,4,6,2,5,7,8] => [8,7,5,2,6,4,3,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,3,4,6,2,5,8,7] => [7,8,5,2,6,4,3,1] => [2,1,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,2,7,5,8] => [8,5,7,2,6,4,3,1] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,2,7,8,5] => [5,8,7,2,6,4,3,1] => [2,1,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,4,6,2,8,5,7] => [7,5,8,2,6,4,3,1] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,2,8,5] => [5,8,2,7,6,4,3,1] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,2,5] => [5,2,8,7,6,4,3,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,8,2,5,7] => [7,5,2,8,6,4,3,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,3,4,7,2,5,6,8] => [8,6,5,2,7,4,3,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,2,5,8,6] => [6,8,5,2,7,4,3,1] => [2,1,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,7,2,8,5,6] => [6,5,8,2,7,4,3,1] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,7,8,2,5,6] => [6,5,2,8,7,4,3,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,2,5,6,7] => [7,6,5,2,8,4,3,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,2,4,6,7,8] => [8,7,6,4,2,5,3,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,2,4,6,8,7] => [7,8,6,4,2,5,3,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,2,4,7,6,8] => [8,6,7,4,2,5,3,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,2,4,7,8,6] => [6,8,7,4,2,5,3,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,3,5,2,4,8,6,7] => [7,6,8,4,2,5,3,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,3,5,2,6,4,7,8] => [8,7,4,6,2,5,3,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,2,6,7,4,8] => [8,4,7,6,2,5,3,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,2,6,7,8,4] => [4,8,7,6,2,5,3,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,2,6,8,4,7] => [7,4,8,6,2,5,3,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,2,7,4,6,8] => [8,6,4,7,2,5,3,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,8,6] => [6,8,4,7,2,5,3,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,2,7,8,4,6] => [6,4,8,7,2,5,3,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,2,8,4,6,7] => [7,6,4,8,2,5,3,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,2,4,7,8] => [8,7,4,2,6,5,3,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,5,6,2,4,8,7] => [7,8,4,2,6,5,3,1] => [2,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,2,7,4,8] => [8,4,7,2,6,5,3,1] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,5,6,2,7,8,4] => [4,8,7,2,6,5,3,1] => [2,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,5,6,2,8,4,7] => [7,4,8,2,6,5,3,1] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,2,4,8] => [8,4,2,7,6,5,3,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,2,8,4] => [4,8,2,7,6,5,3,1] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,2,4] => [4,2,8,7,6,5,3,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,2,4,7] => [7,4,2,8,6,5,3,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,2,4,6,8] => [8,6,4,2,7,5,3,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,2,4,8,6] => [6,8,4,2,7,5,3,1] => [2,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,2,8,4,6] => [6,4,8,2,7,5,3,1] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,2,4,6] => [6,4,2,8,7,5,3,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,2,4,6,7] => [7,6,4,2,8,5,3,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,2,4,5,7,8] => [8,7,5,4,2,6,3,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,2,4,5,8,7] => [7,8,5,4,2,6,3,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,2,4,7,5,8] => [8,5,7,4,2,6,3,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,6,2,4,7,8,5] => [5,8,7,4,2,6,3,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,2,4,8,5,7] => [7,5,8,4,2,6,3,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,2,7,4,5,8] => [8,5,4,7,2,6,3,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,2,7,4,8,5] => [5,8,4,7,2,6,3,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,2,7,8,4,5] => [5,4,8,7,2,6,3,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,6,2,8,4,5,7] => [7,5,4,8,2,6,3,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,6,7,2,4,5,8] => [8,5,4,2,7,6,3,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,6,7,2,4,8,5] => [5,8,4,2,7,6,3,1] => [2,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,2,8,4,5] => [5,4,8,2,7,6,3,1] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,2,4,5] => [5,4,2,8,7,6,3,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,6,8,2,4,5,7] => [7,5,4,2,8,6,3,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,2,4,5,6,8] => [8,6,5,4,2,7,3,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,7,2,4,5,8,6] => [6,8,5,4,2,7,3,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,7,2,4,8,5,6] => [6,5,8,4,2,7,3,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,7,2,8,4,5,6] => [6,5,4,8,2,7,3,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,2,4,5,6] => [6,5,4,2,8,7,3,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [7,6,5,4,2,8,3,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8] => [8,7,6,5,3,2,4,1] => [1,1,1,1,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,2,3,5,6,8,7] => [7,8,6,5,3,2,4,1] => [2,1,1,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,3,5,7,6,8] => [8,6,7,5,3,2,4,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,2,3,5,7,8,6] => [6,8,7,5,3,2,4,1] => [2,1,1,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => [7,6,8,5,3,2,4,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => [8,7,5,6,3,2,4,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7] => [7,8,5,6,3,2,4,1] => [2,2,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,2,3,6,7,5,8] => [8,5,7,6,3,2,4,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,2,3,6,7,8,5] => [5,8,7,6,3,2,4,1] => [2,1,1,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,2,3,6,8,5,7] => [7,5,8,6,3,2,4,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => [8,6,5,7,3,2,4,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,2,3,7,5,8,6] => [6,8,5,7,3,2,4,1] => [2,2,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,2,3,7,8,5,6] => [6,5,8,7,3,2,4,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => [7,6,5,8,3,2,4,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,3,6,7,8] => [8,7,6,3,5,2,4,1] => [1,1,1,2,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,3,6,8,7] => [7,8,6,3,5,2,4,1] => [2,1,2,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,8] => [8,6,7,3,5,2,4,1] => [1,2,2,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,3,7,8,6] => [6,8,7,3,5,2,4,1] => [2,1,2,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,8,6,7] => [7,6,8,3,5,2,4,1] => [1,2,2,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3,7,8] => [8,7,3,6,5,2,4,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,2,5,6,7,3,8] => [8,3,7,6,5,2,4,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,8,3] => [3,8,7,6,5,2,4,1] => [2,1,1,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,2,5,6,8,3,7] => [7,3,8,6,5,2,4,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,2,5,7,3,6,8] => [8,6,3,7,5,2,4,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,8,6] => [6,8,3,7,5,2,4,1] => [2,2,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,2,5,7,8,3,6] => [6,3,8,7,5,2,4,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,2,5,8,3,6,7] => [7,6,3,8,5,2,4,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,6,3,5,7,8] => [8,7,5,3,6,2,4,1] => [1,1,1,2,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,6,3,5,8,7] => [7,8,5,3,6,2,4,1] => [2,1,2,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5,8] => [8,5,7,3,6,2,4,1] => [1,2,2,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,3,7,8,5] => [5,8,7,3,6,2,4,1] => [2,1,2,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,8,5,7] => [7,5,8,3,6,2,4,1] => [1,2,2,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,2,6,7,3,5,8] => [8,5,3,7,6,2,4,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,6,7,3,8,5] => [5,8,3,7,6,2,4,1] => [2,2,1,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,2,6,7,8,3,5] => [5,3,8,7,6,2,4,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,2,6,8,3,5,7] => [7,5,3,8,6,2,4,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,7,3,5,6,8] => [8,6,5,3,7,2,4,1] => [1,1,1,2,2,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,7,3,5,8,6] => [6,8,5,3,7,2,4,1] => [2,1,2,2,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,8,5,6] => [6,5,8,3,7,2,4,1] => [1,2,2,2,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,2,7,8,3,5,6] => [6,5,3,8,7,2,4,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,8,3,5,6,7] => [7,6,5,3,8,2,4,1] => [1,1,1,2,2,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,2,3,6,7,8] => [8,7,6,3,2,5,4,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,5,2,3,6,8,7] => [7,8,6,3,2,5,4,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,2,3,7,8,6] => [6,8,7,3,2,5,4,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,2,3,8,6,7] => [7,6,8,3,2,5,4,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,2,6,3,7,8] => [8,7,3,6,2,5,4,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,8,7] => [7,8,3,6,2,5,4,1] => [2,2,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,7,3,8] => [8,3,7,6,2,5,4,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,2,6,7,8,3] => [3,8,7,6,2,5,4,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,6,8,3,7] => [7,3,8,6,2,5,4,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,4,5,2,7,3,6,8] => [8,6,3,7,2,5,4,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,8,6] => [6,8,3,7,2,5,4,1] => [2,2,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,7,8,3,6] => [6,3,8,7,2,5,4,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,2,8,3,6,7] => [7,6,3,8,2,5,4,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,2,3,7,8] => [8,7,3,2,6,5,4,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,4,5,6,2,3,8,7] => [7,8,3,2,6,5,4,1] => [2,1,2,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,2,7,3,8] => [8,3,7,2,6,5,4,1] => [1,2,2,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,5,6,2,7,8,3] => [3,8,7,2,6,5,4,1] => [2,1,2,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,5,6,2,8,3,7] => [7,3,8,2,6,5,4,1] => [1,2,2,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,2,3,8] => [8,3,2,7,6,5,4,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,2,8,3] => [3,8,2,7,6,5,4,1] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,2,3] => [3,2,8,7,6,5,4,1] => [1,2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,4,5,6,8,2,3,7] => [7,3,2,8,6,5,4,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,4,5,7,2,3,6,8] => [8,6,3,2,7,5,4,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,5,7,2,3,8,6] => [6,8,3,2,7,5,4,1] => [2,1,2,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,4,5,7,8,2,3,6] => [6,3,2,8,7,5,4,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,2,3,6,7] => [7,6,3,2,8,5,4,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,2,3,5,7,8] => [8,7,5,3,2,6,4,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,4,6,2,3,5,8,7] => [7,8,5,3,2,6,4,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,4,6,2,3,7,5,8] => [8,5,7,3,2,6,4,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,6,2,3,7,8,5] => [5,8,7,3,2,6,4,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,2,3,8,5,7] => [7,5,8,3,2,6,4,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,2,7,3,5,8] => [8,5,3,7,2,6,4,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,2,7,3,8,5] => [5,8,3,7,2,6,4,1] => [2,2,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,4,6,2,7,8,3,5] => [5,3,8,7,2,6,4,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,2,8,3,5,7] => [7,5,3,8,2,6,4,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,2,3,5,8] => [8,5,3,2,7,6,4,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,2,3,8,5] => [5,8,3,2,7,6,4,1] => [2,1,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,2,8,3,5] => [5,3,8,2,7,6,4,1] => [1,2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,2,3,5] => [5,3,2,8,7,6,4,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,2,3,5,7] => [7,5,3,2,8,6,4,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,7,2,3,5,8,6] => [6,8,5,3,2,7,4,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,2,3,8,5,6] => [6,5,8,3,2,7,4,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,4,7,2,8,3,5,6] => [6,5,3,8,2,7,4,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,2,3,5,6] => [6,5,3,2,8,7,4,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => [7,6,5,3,2,8,4,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,2,3,4,6,7,8] => [8,7,6,4,3,2,5,1] => [1,1,1,1,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,2,3,4,6,8,7] => [7,8,6,4,3,2,5,1] => [2,1,1,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => [8,6,7,4,3,2,5,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,2,3,4,7,8,6] => [6,8,7,4,3,2,5,1] => [2,1,1,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => [7,6,8,4,3,2,5,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,2,3,6,4,7,8] => [8,7,4,6,3,2,5,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,5,2,3,6,4,8,7] => [7,8,4,6,3,2,5,1] => [2,2,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,3,6,7,8,4] => [4,8,7,6,3,2,5,1] => [2,1,1,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,2,3,6,8,4,7] => [7,4,8,6,3,2,5,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,5,2,3,7,4,6,8] => [8,6,4,7,3,2,5,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,3,7,4,8,6] => [6,8,4,7,3,2,5,1] => [2,2,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,2,3,7,8,4,6] => [6,4,8,7,3,2,5,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,2,3,8,4,6,7] => [7,6,4,8,3,2,5,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,6,3,4,7,8] => [8,7,4,3,6,2,5,1] => [1,1,1,2,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,6,3,4,8,7] => [7,8,4,3,6,2,5,1] => [2,1,2,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4,8] => [8,4,7,3,6,2,5,1] => [1,2,2,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,7,8,4] => [4,8,7,3,6,2,5,1] => [2,1,2,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,8,4,7] => [7,4,8,3,6,2,5,1] => [1,2,2,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,2,6,7,3,4,8] => [8,4,3,7,6,2,5,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,6,7,3,8,4] => [4,8,3,7,6,2,5,1] => [2,2,1,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,2,6,7,8,3,4] => [4,3,8,7,6,2,5,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,2,6,8,3,4,7] => [7,4,3,8,6,2,5,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,7,3,4,6,8] => [8,6,4,3,7,2,5,1] => [1,1,1,2,2,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,7,3,4,8,6] => [6,8,4,3,7,2,5,1] => [2,1,2,2,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,8,4,6] => [6,4,8,3,7,2,5,1] => [1,2,2,2,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,2,7,8,3,4,6] => [6,4,3,8,7,2,5,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,8,3,4,6,7] => [7,6,4,3,8,2,5,1] => [1,1,1,2,2,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,2,3,4,8,7] => [7,8,4,3,2,6,5,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,6,2,3,7,8,4] => [4,8,7,3,2,6,5,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,8,4,7] => [7,4,8,3,2,6,5,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,2,7,3,8,4] => [4,8,3,7,2,6,5,1] => [2,2,2,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,2,7,8,3,4] => [4,3,8,7,2,6,5,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,5,6,2,8,3,4,7] => [7,4,3,8,2,6,5,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,5,6,7,2,3,4,8] => [8,4,3,2,7,6,5,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,2,3,8,4] => [4,8,3,2,7,6,5,1] => [2,1,2,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,5,6,7,2,8,3,4] => [4,3,8,2,7,6,5,1] => [1,2,2,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,2,3,4] => [4,3,2,8,7,6,5,1] => [1,1,2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,5,7,2,3,4,6,8] => [8,6,4,3,2,7,5,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,7,2,3,4,8,6] => [6,8,4,3,2,7,5,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,5,7,2,3,8,4,6] => [6,4,8,3,2,7,5,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,2,8,3,4,6] => [6,4,3,8,2,7,5,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,5,7,8,2,3,4,6] => [6,4,3,2,8,7,5,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [7,6,4,3,2,8,5,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,2,3,4,5,7,8] => [8,7,5,4,3,2,6,1] => [1,1,1,1,1,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => [7,8,5,4,3,2,6,1] => [2,1,1,1,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,2,3,4,7,5,8] => [8,5,7,4,3,2,6,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,3,4,7,8,5] => [5,8,7,4,3,2,6,1] => [2,1,1,1,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,2,3,4,8,5,7] => [7,5,8,4,3,2,6,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,8,5] => [5,8,4,7,3,2,6,1] => [2,2,1,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,2,3,7,8,4,5] => [5,4,8,7,3,2,6,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,6,2,3,8,4,5,7] => [7,5,4,8,3,2,6,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,7,3,4,5,8] => [8,5,4,3,7,2,6,1] => [1,1,1,2,2,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,7,3,4,8,5] => [5,8,4,3,7,2,6,1] => [2,1,2,2,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,8,4,5] => [5,4,8,3,7,2,6,1] => [1,2,2,2,1] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,8,3,4,5,7] => [7,5,4,3,8,2,6,1] => [1,1,1,2,2,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,2,3,4,5,8] => [8,5,4,3,2,7,6,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,7,2,3,4,8,5] => [5,8,4,3,2,7,6,1] => [2,1,1,2,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,6,7,2,3,8,4,5] => [5,4,8,3,2,7,6,1] => [1,2,1,2,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,2,8,3,4,5] => [5,4,3,8,2,7,6,1] => [1,1,2,2,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,2,3,4,5] => [5,4,3,2,8,7,6,1] => [1,1,1,2,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [7,5,4,3,2,8,6,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,8] => [8,6,5,4,3,2,7,1] => [1,1,1,1,1,2,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => [6,8,5,4,3,2,7,1] => [2,1,1,1,2,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,2,3,4,8,5,6] => [6,5,8,4,3,2,7,1] => [1,2,1,1,2,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,2,3,8,4,5,6] => [6,5,4,8,3,2,7,1] => [1,1,2,1,2,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,8,3,4,5,6] => [6,5,4,3,8,2,7,1] => [1,1,1,2,2,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [6,5,4,3,2,8,7,1] => [1,1,1,1,2,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [7,6,5,4,3,2,8,1] => [1,1,1,1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [7,8,6,5,4,3,1,2] => [2,1,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [8,6,7,5,4,3,1,2] => [1,2,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [6,8,7,5,4,3,1,2] => [2,1,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,6,7] => [7,6,8,5,4,3,1,2] => [1,2,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [8,7,5,6,4,3,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [7,8,5,6,4,3,1,2] => [2,2,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,4,6,7,5,8] => [8,5,7,6,4,3,1,2] => [1,2,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [5,8,7,6,4,3,1,2] => [2,1,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,7,5,6,8] => [8,6,5,7,4,3,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,5,6] => [6,5,8,7,4,3,1,2] => [1,2,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,5,6,7] => [7,6,5,8,4,3,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [8,7,6,4,5,3,1,2] => [1,1,1,2,1,2] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [7,8,6,4,5,3,1,2] => [2,1,2,1,2] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6,8] => [8,6,7,4,5,3,1,2] => [1,2,2,1,2] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [6,8,7,4,5,3,1,2] => [2,1,2,1,2] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,6,7] => [7,6,8,4,5,3,1,2] => [1,2,2,1,2] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,3,5,6,4,7,8] => [8,7,4,6,5,3,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [7,8,4,6,5,3,1,2] => [2,2,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,6,7,4,8] => [8,4,7,6,5,3,1,2] => [1,2,1,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [4,8,7,6,5,3,1,2] => [2,1,1,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,3,5,6,8,4,7] => [7,4,8,6,5,3,1,2] => [1,2,1,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,7,4,6,8] => [8,6,4,7,5,3,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,4,8,6] => [6,8,4,7,5,3,1,2] => [2,2,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,7,8,4,6] => [6,4,8,7,5,3,1,2] => [1,2,1,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,3,5,8,4,6,7] => [7,6,4,8,5,3,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,6,4,5,7,8] => [8,7,5,4,6,3,1,2] => [1,1,1,2,1,2] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,6,4,7,8,5] => [5,8,7,4,6,3,1,2] => [2,1,2,1,2] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,4,8,5,7] => [7,5,8,4,6,3,1,2] => [1,2,2,1,2] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,4,5,8] => [8,5,4,7,6,3,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,6,7,4,8,5] => [5,8,4,7,6,3,1,2] => [2,2,1,1,2] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,4,5] => [5,4,8,7,6,3,1,2] => [1,2,1,1,1,2] => 2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,6,8,4,5,7] => [7,5,4,8,6,3,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,7,4,5,8,6] => [6,8,5,4,7,3,1,2] => [2,1,2,1,2] => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,4,5,6] => [6,5,4,8,7,3,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,4,5,6,7] => [7,6,5,4,8,3,1,2] => [1,1,1,2,1,2] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [8,7,6,5,3,4,1,2] => [1,1,1,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [7,8,6,5,3,4,1,2] => [2,1,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [6,8,7,5,3,4,1,2] => [2,1,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,6,7] => [7,6,8,5,3,4,1,2] => [1,2,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [8,7,5,6,3,4,1,2] => [1,1,2,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [7,8,5,6,3,4,1,2] => [2,2,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [8,5,7,6,3,4,1,2] => [1,2,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [5,8,7,6,3,4,1,2] => [2,1,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,5,7] => [7,5,8,6,3,4,1,2] => [1,2,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,7,5,6,8] => [8,6,5,7,3,4,1,2] => [1,1,2,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,8,6] => [6,8,5,7,3,4,1,2] => [2,2,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,5,6] => [6,5,8,7,3,4,1,2] => [1,2,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => [7,6,5,8,3,4,1,2] => [1,1,2,2,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [8,7,6,3,5,4,1,2] => [1,1,1,2,1,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3,7,8,6] => [6,8,7,3,5,4,1,2] => [2,1,2,1,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,6,7] => [7,6,8,3,5,4,1,2] => [1,2,2,1,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,4,5,6,3,7,8] => [8,7,3,6,5,4,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [7,8,3,6,5,4,1,2] => [2,2,1,1,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [8,3,7,6,5,4,1,2] => [1,2,1,1,1,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [3,8,7,6,5,4,1,2] => [2,1,1,1,1,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,3,7] => [7,3,8,6,5,4,1,2] => [1,2,1,1,1,2] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,3,8,6] => [6,8,3,7,5,4,1,2] => [2,2,1,1,2] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,3,6] => [6,3,8,7,5,4,1,2] => [1,2,1,1,1,2] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,3,6,7] => [7,6,3,8,5,4,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,3,5,7,8] => [8,7,5,3,6,4,1,2] => [1,1,1,2,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,3,5,8,7] => [7,8,5,3,6,4,1,2] => [2,1,2,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,3,7,8,5] => [5,8,7,3,6,4,1,2] => [2,1,2,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,3,8,5,7] => [7,5,8,3,6,4,1,2] => [1,2,2,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,4,6,7,3,5,8] => [8,5,3,7,6,4,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,3,8,5] => [5,8,3,7,6,4,1,2] => [2,2,1,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,3,5] => [5,3,8,7,6,4,1,2] => [1,2,1,1,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,3,5,7] => [7,5,3,8,6,4,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,3,5,8,6] => [6,8,5,3,7,4,1,2] => [2,1,2,1,2] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,7,3,8,5,6] => [6,5,8,3,7,4,1,2] => [1,2,2,1,2] => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,3,5,6] => [6,5,3,8,7,4,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,3,5,6,7] => [7,6,5,3,8,4,1,2] => [1,1,1,2,1,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => [8,7,6,4,3,5,1,2] => [1,1,1,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,3,4,6,8,7] => [7,8,6,4,3,5,1,2] => [2,1,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,3,4,7,6,8] => [8,6,7,4,3,5,1,2] => [1,2,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,5,3,4,7,8,6] => [6,8,7,4,3,5,1,2] => [2,1,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,3,4,8,6,7] => [7,6,8,4,3,5,1,2] => [1,2,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,4,7,8] => [8,7,4,6,3,5,1,2] => [1,1,2,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,8,7] => [7,8,4,6,3,5,1,2] => [2,2,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,3,6,7,4,8] => [8,4,7,6,3,5,1,2] => [1,2,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,3,6,8,4,7] => [7,4,8,6,3,5,1,2] => [1,2,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,7,4,6,8] => [8,6,4,7,3,5,1,2] => [1,1,2,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,8,6] => [6,8,4,7,3,5,1,2] => [2,2,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,3,7,8,4,6] => [6,4,8,7,3,5,1,2] => [1,2,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,8,4,6,7] => [7,6,4,8,3,5,1,2] => [1,1,2,2,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,3,4,7,8] => [8,7,4,3,6,5,1,2] => [1,1,1,2,1,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,3,4,8,7] => [7,8,4,3,6,5,1,2] => [2,1,2,1,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,5,6,3,7,4,8] => [8,4,7,3,6,5,1,2] => [1,2,2,1,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,3,7,8,4] => [4,8,7,3,6,5,1,2] => [2,1,2,1,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,3,8,4,7] => [7,4,8,3,6,5,1,2] => [1,2,2,1,2] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,5,6,7,3,4,8] => [8,4,3,7,6,5,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,3,8,4] => [4,8,3,7,6,5,1,2] => [2,2,1,1,2] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,3,4] => [4,3,8,7,6,5,1,2] => [1,2,1,1,1,2] => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,3,4,7] => [7,4,3,8,6,5,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,3,4,8,6] => [6,8,4,3,7,5,1,2] => [2,1,2,1,2] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,3,8,4,6] => [6,4,8,3,7,5,1,2] => [1,2,2,1,2] => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,3,4,6] => [6,4,3,8,7,5,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,3,4,6,7] => [7,6,4,3,8,5,1,2] => [1,1,1,2,1,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7,8] => [8,7,5,4,3,6,1,2] => [1,1,1,1,2,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => [7,8,5,4,3,6,1,2] => [2,1,1,2,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,6,3,4,7,5,8] => [8,5,7,4,3,6,1,2] => [1,2,1,2,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,3,4,7,8,5] => [5,8,7,4,3,6,1,2] => [2,1,1,2,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,3,4,8,5,7] => [7,5,8,4,3,6,1,2] => [1,2,1,2,2] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,7,4,5,8] => [8,5,4,7,3,6,1,2] => [1,1,2,2,2] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,8,5] => [5,8,4,7,3,6,1,2] => [2,2,2,2] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,3,7,8,4,5] => [5,4,8,7,3,6,1,2] => [1,2,1,2,2] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,8,4,5,7] => [7,5,4,8,3,6,1,2] => [1,1,2,2,2] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,6,7,3,4,5,8] => [8,5,4,3,7,6,1,2] => [1,1,1,2,1,2] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,3,4,8,5] => [5,8,4,3,7,6,1,2] => [2,1,2,1,2] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,3,8,4,5] => [5,4,8,3,7,6,1,2] => [1,2,2,1,2] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,3,4,5] => [5,4,3,8,7,6,1,2] => [1,1,2,1,1,2] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,3,4,5,7] => [7,5,4,3,8,6,1,2] => [1,1,1,2,1,2] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => [8,6,5,4,3,7,1,2] => [1,1,1,1,2,2] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,3,4,5,8,6] => [6,8,5,4,3,7,1,2] => [2,1,1,2,2] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,3,4,8,5,6] => [6,5,8,4,3,7,1,2] => [1,2,1,2,2] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,8,4,5,6] => [6,5,4,8,3,7,1,2] => [1,1,2,2,2] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,3,4,5,6] => [6,5,4,3,8,7,1,2] => [1,1,1,2,1,2] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [7,6,5,4,3,8,1,2] => [1,1,1,1,2,2] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [8,7,6,5,4,1,3,2] => [1,1,1,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [7,8,6,5,4,1,3,2] => [2,1,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [8,6,7,5,4,1,3,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [6,8,7,5,4,1,3,2] => [2,1,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,6,7] => [7,6,8,5,4,1,3,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,4,6,5,7,8] => [8,7,5,6,4,1,3,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [7,8,5,6,4,1,3,2] => [2,2,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [8,5,7,6,4,1,3,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [5,8,7,6,4,1,3,2] => [2,1,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,3,1,4,6,8,5,7] => [7,5,8,6,4,1,3,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,7,5,6,8] => [8,6,5,7,4,1,3,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,5,6] => [6,5,8,7,4,1,3,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,5,6,7] => [7,6,5,8,4,1,3,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [8,7,6,4,5,1,3,2] => [1,1,1,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [8,6,7,4,5,1,3,2] => [1,2,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,4,7,8,6] => [6,8,7,4,5,1,3,2] => [2,1,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [8,7,4,6,5,1,3,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,6,4,8,7] => [7,8,4,6,5,1,3,2] => [2,2,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [8,4,7,6,5,1,3,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [4,8,7,6,5,1,3,2] => [2,1,1,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,4,7] => [7,4,8,6,5,1,3,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,3,1,5,7,4,6,8] => [8,6,4,7,5,1,3,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,4,8,6] => [6,8,4,7,5,1,3,2] => [2,2,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,4,6] => [6,4,8,7,5,1,3,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,3,1,5,8,4,6,7] => [7,6,4,8,5,1,3,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,4,5,7,8] => [8,7,5,4,6,1,3,2] => [1,1,1,2,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5,8] => [8,5,7,4,6,1,3,2] => [1,2,2,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,7,8,5] => [5,8,7,4,6,1,3,2] => [2,1,2,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,8,5,7] => [7,5,8,4,6,1,3,2] => [1,2,2,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,4,8,5] => [5,8,4,7,6,1,3,2] => [2,2,1,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,4,5] => [5,4,8,7,6,1,3,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,4,5,7] => [7,5,4,8,6,1,3,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,7,4,5,6,8] => [8,6,5,4,7,1,3,2] => [1,1,1,2,2,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,4,5,8,6] => [6,8,5,4,7,1,3,2] => [2,1,2,2,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,8,5,6] => [6,5,8,4,7,1,3,2] => [1,2,2,2,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,4,5,6] => [6,5,4,8,7,1,3,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,4,5,6,7] => [7,6,5,4,8,1,3,2] => [1,1,1,2,2,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [8,7,6,5,1,4,3,2] => [1,1,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [7,8,6,5,1,4,3,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [8,6,7,5,1,4,3,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [6,8,7,5,1,4,3,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,6,7] => [7,6,8,5,1,4,3,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [8,7,5,6,1,4,3,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [7,8,5,6,1,4,3,2] => [2,2,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [8,5,7,6,1,4,3,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [5,8,7,6,1,4,3,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,5,7] => [7,5,8,6,1,4,3,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,5,6,8] => [8,6,5,7,1,4,3,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,8,6] => [6,8,5,7,1,4,3,2] => [2,2,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,5,6] => [6,5,8,7,1,4,3,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,5,6,7] => [7,6,5,8,1,4,3,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [8,7,6,1,5,4,3,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [7,8,6,1,5,4,3,2] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [8,6,7,1,5,4,3,2] => [1,2,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [6,8,7,1,5,4,3,2] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,6,7] => [7,6,8,1,5,4,3,2] => [1,2,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [8,7,1,6,5,4,3,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [7,8,1,6,5,4,3,2] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [8,1,7,6,5,4,3,2] => [1,2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,1,7] => [7,1,8,6,5,4,3,2] => [1,2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,1,6,8] => [8,6,1,7,5,4,3,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,1,8,6] => [6,8,1,7,5,4,3,2] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,1,6] => [6,1,8,7,5,4,3,2] => [1,2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,1,6,7] => [7,6,1,8,5,4,3,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,1,5,7,8] => [8,7,5,1,6,4,3,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,4,6,1,5,8,7] => [7,8,5,1,6,4,3,2] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,1,7,5,8] => [8,5,7,1,6,4,3,2] => [1,2,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,1,7,8,5] => [5,8,7,1,6,4,3,2] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,1,8,5,7] => [7,5,8,1,6,4,3,2] => [1,2,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,1,5,8] => [8,5,1,7,6,4,3,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,1,8,5] => [5,8,1,7,6,4,3,2] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,1,5] => [5,1,8,7,6,4,3,2] => [1,2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,1,5,7] => [7,5,1,8,6,4,3,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,1,5,6,8] => [8,6,5,1,7,4,3,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,1,5,8,6] => [6,8,5,1,7,4,3,2] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,1,8,5,6] => [6,5,8,1,7,4,3,2] => [1,2,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,1,5,6] => [6,5,1,8,7,4,3,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,1,5,6,7] => [7,6,5,1,8,4,3,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,1,4,6,7,8] => [8,7,6,4,1,5,3,2] => [1,1,1,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,1,4,6,8,7] => [7,8,6,4,1,5,3,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,4,7,6,8] => [8,6,7,4,1,5,3,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,3,5,1,4,7,8,6] => [6,8,7,4,1,5,3,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,4,8,6,7] => [7,6,8,4,1,5,3,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,1,6,4,7,8] => [8,7,4,6,1,5,3,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,8,7] => [7,8,4,6,1,5,3,2] => [2,2,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,1,6,7,4,8] => [8,4,7,6,1,5,3,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,1,6,7,8,4] => [4,8,7,6,1,5,3,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,3,5,1,6,8,4,7] => [7,4,8,6,1,5,3,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,3,5,1,7,4,6,8] => [8,6,4,7,1,5,3,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,8,6] => [6,8,4,7,1,5,3,2] => [2,2,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,1,7,8,4,6] => [6,4,8,7,1,5,3,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,1,8,4,6,7] => [7,6,4,8,1,5,3,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,1,4,7,8] => [8,7,4,1,6,5,3,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,5,6,1,4,8,7] => [7,8,4,1,6,5,3,2] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,1,7,4,8] => [8,4,7,1,6,5,3,2] => [1,2,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,1,7,8,4] => [4,8,7,1,6,5,3,2] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,1,8,4,7] => [7,4,8,1,6,5,3,2] => [1,2,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,1,4,8] => [8,4,1,7,6,5,3,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,1,8,4] => [4,8,1,7,6,5,3,2] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,1,4] => [4,1,8,7,6,5,3,2] => [1,2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,1,4,7] => [7,4,1,8,6,5,3,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,5,7,1,4,6,8] => [8,6,4,1,7,5,3,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,1,4,8,6] => [6,8,4,1,7,5,3,2] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,1,8,4,6] => [6,4,8,1,7,5,3,2] => [1,2,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,1,4,6] => [6,4,1,8,7,5,3,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,8,1,4,6,7] => [7,6,4,1,8,5,3,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,1,4,5,7,8] => [8,7,5,4,1,6,3,2] => [1,1,1,1,2,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,1,4,5,8,7] => [7,8,5,4,1,6,3,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,6,1,4,7,5,8] => [8,5,7,4,1,6,3,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,1,4,7,8,5] => [5,8,7,4,1,6,3,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,1,4,8,5,7] => [7,5,8,4,1,6,3,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,6,1,7,4,5,8] => [8,5,4,7,1,6,3,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,6,1,7,4,8,5] => [5,8,4,7,1,6,3,2] => [2,2,2,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,6,1,7,8,4,5] => [5,4,8,7,1,6,3,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,1,8,4,5,7] => [7,5,4,8,1,6,3,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,6,7,1,4,5,8] => [8,5,4,1,7,6,3,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,6,7,1,4,8,5] => [5,8,4,1,7,6,3,2] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,6,7,1,8,4,5] => [5,4,8,1,7,6,3,2] => [1,2,2,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,1,4,5] => [5,4,1,8,7,6,3,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,6,8,1,4,5,7] => [7,5,4,1,8,6,3,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,1,4,5,6,8] => [8,6,5,4,1,7,3,2] => [1,1,1,1,2,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,1,4,5,8,6] => [6,8,5,4,1,7,3,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,1,4,8,5,6] => [6,5,8,4,1,7,3,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,7,8,1,4,5,6] => [6,5,4,1,8,7,3,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [7,6,5,4,1,8,3,2] => [1,1,1,1,2,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7,8] => [8,7,6,5,3,1,4,2] => [1,1,1,1,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,4,1,3,5,7,6,8] => [8,6,7,5,3,1,4,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,4,1,3,5,7,8,6] => [6,8,7,5,3,1,4,2] => [2,1,1,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,1,3,5,8,6,7] => [7,6,8,5,3,1,4,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,1,3,6,5,7,8] => [8,7,5,6,3,1,4,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [7,8,5,6,3,1,4,2] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,4,1,3,6,7,5,8] => [8,5,7,6,3,1,4,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,1,3,6,7,8,5] => [5,8,7,6,3,1,4,2] => [2,1,1,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,1,3,6,8,5,7] => [7,5,8,6,3,1,4,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,4,1,3,7,5,6,8] => [8,6,5,7,3,1,4,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,1,3,7,5,8,6] => [6,8,5,7,3,1,4,2] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,1,3,7,8,5,6] => [6,5,8,7,3,1,4,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,1,3,8,5,6,7] => [7,6,5,8,3,1,4,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,3,6,7,8] => [8,7,6,3,5,1,4,2] => [1,1,1,2,2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,3,6,8,7] => [7,8,6,3,5,1,4,2] => [2,1,2,2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,8] => [8,6,7,3,5,1,4,2] => [1,2,2,2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,3,7,8,6] => [6,8,7,3,5,1,4,2] => [2,1,2,2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,8,6,7] => [7,6,8,3,5,1,4,2] => [1,2,2,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3,7,8] => [8,7,3,6,5,1,4,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,1,5,6,7,3,8] => [8,3,7,6,5,1,4,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,8,3] => [3,8,7,6,5,1,4,2] => [2,1,1,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,1,5,6,8,3,7] => [7,3,8,6,5,1,4,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6,8] => [8,6,3,7,5,1,4,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,8,6] => [6,8,3,7,5,1,4,2] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,1,5,7,8,3,6] => [6,3,8,7,5,1,4,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,4,1,5,8,3,6,7] => [7,6,3,8,5,1,4,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,1,6,3,5,7,8] => [8,7,5,3,6,1,4,2] => [1,1,1,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7] => [7,8,5,3,6,1,4,2] => [2,1,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5,8] => [8,5,7,3,6,1,4,2] => [1,2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,7,8,5] => [5,8,7,3,6,1,4,2] => [2,1,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,7] => [7,5,8,3,6,1,4,2] => [1,2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,4,1,6,7,3,5,8] => [8,5,3,7,6,1,4,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,1,6,7,3,8,5] => [5,8,3,7,6,1,4,2] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,1,6,7,8,3,5] => [5,3,8,7,6,1,4,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,1,6,8,3,5,7] => [7,5,3,8,6,1,4,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,4,1,7,3,5,6,8] => [8,6,5,3,7,1,4,2] => [1,1,1,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,1,7,3,5,8,6] => [6,8,5,3,7,1,4,2] => [2,1,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,8,5,6] => [6,5,8,3,7,1,4,2] => [1,2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,1,7,8,3,5,6] => [6,5,3,8,7,1,4,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,1,8,3,5,6,7] => [7,6,5,3,8,1,4,2] => [1,1,1,2,2,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,1,3,6,7,8] => [8,7,6,3,1,5,4,2] => [1,1,1,1,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,4,5,1,3,6,8,7] => [7,8,6,3,1,5,4,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,1,3,7,8,6] => [6,8,7,3,1,5,4,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,1,3,8,6,7] => [7,6,8,3,1,5,4,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,4,5,1,6,3,7,8] => [8,7,3,6,1,5,4,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,8,7] => [7,8,3,6,1,5,4,2] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,4,5,1,6,7,3,8] => [8,3,7,6,1,5,4,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,1,6,7,8,3] => [3,8,7,6,1,5,4,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,1,6,8,3,7] => [7,3,8,6,1,5,4,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,4,5,1,7,3,6,8] => [8,6,3,7,1,5,4,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,8,6] => [6,8,3,7,1,5,4,2] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,1,7,8,3,6] => [6,3,8,7,1,5,4,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,4,5,1,8,3,6,7] => [7,6,3,8,1,5,4,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,1,3,7,8] => [8,7,3,1,6,5,4,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,4,5,6,1,3,8,7] => [7,8,3,1,6,5,4,2] => [2,1,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,4,5,6,1,7,3,8] => [8,3,7,1,6,5,4,2] => [1,2,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,1,7,8,3] => [3,8,7,1,6,5,4,2] => [2,1,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,1,8,3,7] => [7,3,8,1,6,5,4,2] => [1,2,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,1,3,8] => [8,3,1,7,6,5,4,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,1,8,3] => [3,8,1,7,6,5,4,2] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,1,3] => [3,1,8,7,6,5,4,2] => [1,2,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,1,3,7] => [7,3,1,8,6,5,4,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,4,5,7,1,3,6,8] => [8,6,3,1,7,5,4,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,4,5,7,1,3,8,6] => [6,8,3,1,7,5,4,2] => [2,1,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,4,5,7,1,8,3,6] => [6,3,8,1,7,5,4,2] => [1,2,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,1,3,6] => [6,3,1,8,7,5,4,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,1,3,5,7,8] => [8,7,5,3,1,6,4,2] => [1,1,1,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,1,3,5,8,7] => [7,8,5,3,1,6,4,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,4,6,1,3,7,5,8] => [8,5,7,3,1,6,4,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,1,3,7,8,5] => [5,8,7,3,1,6,4,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,1,3,8,5,7] => [7,5,8,3,1,6,4,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,4,6,1,7,3,5,8] => [8,5,3,7,1,6,4,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,1,7,3,8,5] => [5,8,3,7,1,6,4,2] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,1,7,8,3,5] => [5,3,8,7,1,6,4,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,1,8,3,5,7] => [7,5,3,8,1,6,4,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,1,3,5,8] => [8,5,3,1,7,6,4,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,1,3,8,5] => [5,8,3,1,7,6,4,2] => [2,1,2,1,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,4,6,7,1,8,3,5] => [5,3,8,1,7,6,4,2] => [1,2,2,1,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,1,3,5] => [5,3,1,8,7,6,4,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,1,3,5,7] => [7,5,3,1,8,6,4,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,4,7,1,3,5,6,8] => [8,6,5,3,1,7,4,2] => [1,1,1,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,4,7,1,3,5,8,6] => [6,8,5,3,1,7,4,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,4,7,1,3,8,5,6] => [6,5,8,3,1,7,4,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,4,7,1,8,3,5,6] => [6,5,3,8,1,7,4,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,1,3,5,6] => [6,5,3,1,8,7,4,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,1,3,5,6,7] => [7,6,5,3,1,8,4,2] => [1,1,1,1,2,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,1,3,4,6,7,8] => [8,7,6,4,3,1,5,2] => [1,1,1,1,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,1,3,4,6,8,7] => [7,8,6,4,3,1,5,2] => [2,1,1,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,1,3,4,7,6,8] => [8,6,7,4,3,1,5,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,1,3,4,7,8,6] => [6,8,7,4,3,1,5,2] => [2,1,1,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,1,3,4,8,6,7] => [7,6,8,4,3,1,5,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,5,1,3,6,4,7,8] => [8,7,4,6,3,1,5,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,1,3,6,4,8,7] => [7,8,4,6,3,1,5,2] => [2,2,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,1,3,6,7,4,8] => [8,4,7,6,3,1,5,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,1,3,6,7,8,4] => [4,8,7,6,3,1,5,2] => [2,1,1,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,1,3,6,8,4,7] => [7,4,8,6,3,1,5,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,5,1,3,7,4,6,8] => [8,6,4,7,3,1,5,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,1,3,7,4,8,6] => [6,8,4,7,3,1,5,2] => [2,2,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,1,3,7,8,4,6] => [6,4,8,7,3,1,5,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,1,3,8,4,6,7] => [7,6,4,8,3,1,5,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,5,1,6,3,4,7,8] => [8,7,4,3,6,1,5,2] => [1,1,1,2,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,5,1,6,3,4,8,7] => [7,8,4,3,6,1,5,2] => [2,1,2,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4,8] => [8,4,7,3,6,1,5,2] => [1,2,2,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,1,6,3,7,8,4] => [4,8,7,3,6,1,5,2] => [2,1,2,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,8,4,7] => [7,4,8,3,6,1,5,2] => [1,2,2,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,1,6,7,3,4,8] => [8,4,3,7,6,1,5,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,1,6,7,3,8,4] => [4,8,3,7,6,1,5,2] => [2,2,1,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,1,6,7,8,3,4] => [4,3,8,7,6,1,5,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,5,1,6,8,3,4,7] => [7,4,3,8,6,1,5,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,5,1,7,3,4,6,8] => [8,6,4,3,7,1,5,2] => [1,1,1,2,2,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,1,7,3,4,8,6] => [6,8,4,3,7,1,5,2] => [2,1,2,2,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,8,4,6] => [6,4,8,3,7,1,5,2] => [1,2,2,2,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,1,7,8,3,4,6] => [6,4,3,8,7,1,5,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,1,8,3,4,6,7] => [7,6,4,3,8,1,5,2] => [1,1,1,2,2,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,1,3,4,8,7] => [7,8,4,3,1,6,5,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,5,6,1,3,7,4,8] => [8,4,7,3,1,6,5,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,5,6,1,3,7,8,4] => [4,8,7,3,1,6,5,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,5,6,1,3,8,4,7] => [7,4,8,3,1,6,5,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,1,7,3,4,8] => [8,4,3,7,1,6,5,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,5,6,1,7,3,8,4] => [4,8,3,7,1,6,5,2] => [2,2,2,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,1,7,8,3,4] => [4,3,8,7,1,6,5,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,1,8,3,4,7] => [7,4,3,8,1,6,5,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,5,6,7,1,3,4,8] => [8,4,3,1,7,6,5,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,1,3,8,4] => [4,8,3,1,7,6,5,2] => [2,1,2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,1,8,3,4] => [4,3,8,1,7,6,5,2] => [1,2,2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,1,3,4] => [4,3,1,8,7,6,5,2] => [1,1,2,1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,5,6,8,1,3,4,7] => [7,4,3,1,8,6,5,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,5,7,1,3,4,8,6] => [6,8,4,3,1,7,5,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,5,7,1,3,8,4,6] => [6,4,8,3,1,7,5,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,5,7,1,8,3,4,6] => [6,4,3,8,1,7,5,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,5,7,8,1,3,4,6] => [6,4,3,1,8,7,5,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,5,8,1,3,4,6,7] => [7,6,4,3,1,8,5,2] => [1,1,1,1,2,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,6,1,3,4,5,7,8] => [8,7,5,4,3,1,6,2] => [1,1,1,1,1,2,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,1,3,4,5,8,7] => [7,8,5,4,3,1,6,2] => [2,1,1,1,2,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,6,1,3,4,7,5,8] => [8,5,7,4,3,1,6,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,1,3,4,7,8,5] => [5,8,7,4,3,1,6,2] => [2,1,1,1,2,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,1,3,4,8,5,7] => [7,5,8,4,3,1,6,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,6,1,3,7,4,5,8] => [8,5,4,7,3,1,6,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,6,1,3,7,4,8,5] => [5,8,4,7,3,1,6,2] => [2,2,1,2,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,1,3,8,4,5,7] => [7,5,4,8,3,1,6,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,6,1,7,3,4,5,8] => [8,5,4,3,7,1,6,2] => [1,1,1,2,2,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,1,7,3,4,8,5] => [5,8,4,3,7,1,6,2] => [2,1,2,2,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,6,1,7,3,8,4,5] => [5,4,8,3,7,1,6,2] => [1,2,2,2,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,6,1,7,8,3,4,5] => [5,4,3,8,7,1,6,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,6,1,8,3,4,5,7] => [7,5,4,3,8,1,6,2] => [1,1,1,2,2,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,1,3,4,5,8] => [8,5,4,3,1,7,6,2] => [1,1,1,1,2,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,6,7,1,3,4,8,5] => [5,8,4,3,1,7,6,2] => [2,1,1,2,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,6,7,1,3,8,4,5] => [5,4,8,3,1,7,6,2] => [1,2,1,2,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,1,8,3,4,5] => [5,4,3,8,1,7,6,2] => [1,1,2,2,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,1,3,4,5] => [5,4,3,1,8,7,6,2] => [1,1,1,2,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => [7,5,4,3,1,8,6,2] => [1,1,1,1,2,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,1,3,4,5,6,8] => [8,6,5,4,3,1,7,2] => [1,1,1,1,1,2,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,1,3,4,5,8,6] => [6,8,5,4,3,1,7,2] => [2,1,1,1,2,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,1,3,4,8,5,6] => [6,5,8,4,3,1,7,2] => [1,2,1,1,2,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,7,1,3,8,4,5,6] => [6,5,4,8,3,1,7,2] => [1,1,2,1,2,1] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,1,8,3,4,5,6] => [6,5,4,3,8,1,7,2] => [1,1,1,2,2,1] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [6,5,4,3,1,8,7,2] => [1,1,1,1,2,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [7,6,5,4,3,1,8,2] => [1,1,1,1,1,2,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,6,8,7] => [7,8,6,5,4,2,1,3] => [2,1,1,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,2,4,5,7,6,8] => [8,6,7,5,4,2,1,3] => [1,2,1,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,2,4,5,7,8,6] => [6,8,7,5,4,2,1,3] => [2,1,1,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,8,6,7] => [7,6,8,5,4,2,1,3] => [1,2,1,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,4,6,5,7,8] => [8,7,5,6,4,2,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,4,6,5,8,7] => [7,8,5,6,4,2,1,3] => [2,2,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,2,4,6,7,5,8] => [8,5,7,6,4,2,1,3] => [1,2,1,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,4,6,7,8,5] => [5,8,7,6,4,2,1,3] => [2,1,1,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,2,4,6,8,5,7] => [7,5,8,6,4,2,1,3] => [1,2,1,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => [8,6,5,7,4,2,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,2,4,7,5,8,6] => [6,8,5,7,4,2,1,3] => [2,2,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,2,4,7,8,5,6] => [6,5,8,7,4,2,1,3] => [1,2,1,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,2,4,8,5,6,7] => [7,6,5,8,4,2,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,2,5,4,6,7,8] => [8,7,6,4,5,2,1,3] => [1,1,1,2,1,2] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,5,4,6,8,7] => [7,8,6,4,5,2,1,3] => [2,1,2,1,2] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => [8,6,7,4,5,2,1,3] => [1,2,2,1,2] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,2,5,4,7,8,6] => [6,8,7,4,5,2,1,3] => [2,1,2,1,2] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,1,2,5,4,8,6,7] => [7,6,8,4,5,2,1,3] => [1,2,2,1,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,2,5,6,4,7,8] => [8,7,4,6,5,2,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,1,2,5,6,4,8,7] => [7,8,4,6,5,2,1,3] => [2,2,1,1,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,6,7,4,8] => [8,4,7,6,5,2,1,3] => [1,2,1,1,1,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,5,6,7,8,4] => [4,8,7,6,5,2,1,3] => [2,1,1,1,1,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,1,2,5,6,8,4,7] => [7,4,8,6,5,2,1,3] => [1,2,1,1,1,2] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,8] => [8,6,4,7,5,2,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,2,5,7,4,8,6] => [6,8,4,7,5,2,1,3] => [2,2,1,1,2] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,2,5,7,8,4,6] => [6,4,8,7,5,2,1,3] => [1,2,1,1,1,2] => 2
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,2,5,8,4,6,7] => [7,6,4,8,5,2,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,2,6,4,5,7,8] => [8,7,5,4,6,2,1,3] => [1,1,1,2,1,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,2,6,4,5,8,7] => [7,8,5,4,6,2,1,3] => [2,1,2,1,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5,8] => [8,5,7,4,6,2,1,3] => [1,2,2,1,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,2,6,4,7,8,5] => [5,8,7,4,6,2,1,3] => [2,1,2,1,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,1,2,6,4,8,5,7] => [7,5,8,4,6,2,1,3] => [1,2,2,1,2] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,2,6,7,4,5,8] => [8,5,4,7,6,2,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,2,6,7,4,8,5] => [5,8,4,7,6,2,1,3] => [2,2,1,1,2] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,1,2,6,7,8,4,5] => [5,4,8,7,6,2,1,3] => [1,2,1,1,1,2] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,1,2,6,8,4,5,7] => [7,5,4,8,6,2,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => [8,6,5,4,7,2,1,3] => [1,1,1,2,1,2] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,2,7,4,8,5,6] => [6,5,8,4,7,2,1,3] => [1,2,2,1,2] => 2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,1,2,7,8,4,5,6] => [6,5,4,8,7,2,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => [7,6,5,4,8,2,1,3] => [1,1,1,2,1,2] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7,8] => [8,7,6,5,2,4,1,3] => [1,1,1,1,2,2] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,2,5,7,8,6] => [6,8,7,5,2,4,1,3] => [2,1,1,2,2] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,2,5,8,6,7] => [7,6,8,5,2,4,1,3] => [1,2,1,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,5,7,8] => [8,7,5,6,2,4,1,3] => [1,1,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7] => [7,8,5,6,2,4,1,3] => [2,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,2,6,7,5,8] => [8,5,7,6,2,4,1,3] => [1,2,1,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,2,6,7,8,5] => [5,8,7,6,2,4,1,3] => [2,1,1,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,2,6,8,5,7] => [7,5,8,6,2,4,1,3] => [1,2,1,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,7,5,6,8] => [8,6,5,7,2,4,1,3] => [1,1,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,8,6] => [6,8,5,7,2,4,1,3] => [2,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,2,7,8,5,6] => [6,5,8,7,2,4,1,3] => [1,2,1,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,8,5,6,7] => [7,6,5,8,2,4,1,3] => [1,1,2,2,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,2,6,7,8] => [8,7,6,2,5,4,1,3] => [1,1,1,2,1,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6,8] => [8,6,7,2,5,4,1,3] => [1,2,2,1,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,5,2,7,8,6] => [6,8,7,2,5,4,1,3] => [2,1,2,1,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,5,2,8,6,7] => [7,6,8,2,5,4,1,3] => [1,2,2,1,2] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,6,2,7,8] => [8,7,2,6,5,4,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,6,2,8,7] => [7,8,2,6,5,4,1,3] => [2,2,1,1,2] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,7,2,8] => [8,2,7,6,5,4,1,3] => [1,2,1,1,1,2] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,2] => [2,8,7,6,5,4,1,3] => [2,1,1,1,1,2] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,6,8,2,7] => [7,2,8,6,5,4,1,3] => [1,2,1,1,1,2] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,4,5,7,2,6,8] => [8,6,2,7,5,4,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,4,5,7,2,8,6] => [6,8,2,7,5,4,1,3] => [2,2,1,1,2] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,4,5,7,8,2,6] => [6,2,8,7,5,4,1,3] => [1,2,1,1,1,2] => 2
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,4,5,8,2,6,7] => [7,6,2,8,5,4,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,4,6,2,5,7,8] => [8,7,5,2,6,4,1,3] => [1,1,1,2,1,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,5,8,7] => [7,8,5,2,6,4,1,3] => [2,1,2,1,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,4,6,2,7,5,8] => [8,5,7,2,6,4,1,3] => [1,2,2,1,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,4,6,2,7,8,5] => [5,8,7,2,6,4,1,3] => [2,1,2,1,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,4,6,2,8,5,7] => [7,5,8,2,6,4,1,3] => [1,2,2,1,2] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,4,6,7,2,5,8] => [8,5,2,7,6,4,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,4,6,7,2,8,5] => [5,8,2,7,6,4,1,3] => [2,2,1,1,2] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,4,6,7,8,2,5] => [5,2,8,7,6,4,1,3] => [1,2,1,1,1,2] => 2
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,4,6,8,2,5,7] => [7,5,2,8,6,4,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,4,7,2,5,6,8] => [8,6,5,2,7,4,1,3] => [1,1,1,2,1,2] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,1,4,7,2,5,8,6] => [6,8,5,2,7,4,1,3] => [2,1,2,1,2] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,1,4,7,2,8,5,6] => [6,5,8,2,7,4,1,3] => [1,2,2,1,2] => 2
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,1,4,7,8,2,5,6] => [6,5,2,8,7,4,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,4,8,2,5,6,7] => [7,6,5,2,8,4,1,3] => [1,1,1,2,1,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,5,2,4,6,7,8] => [8,7,6,4,2,5,1,3] => [1,1,1,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,5,2,4,6,8,7] => [7,8,6,4,2,5,1,3] => [2,1,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,2,4,7,6,8] => [8,6,7,4,2,5,1,3] => [1,2,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,5,2,4,7,8,6] => [6,8,7,4,2,5,1,3] => [2,1,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,5,2,4,8,6,7] => [7,6,8,4,2,5,1,3] => [1,2,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,4,7,8] => [8,7,4,6,2,5,1,3] => [1,1,2,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7] => [7,8,4,6,2,5,1,3] => [2,2,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,2,6,7,4,8] => [8,4,7,6,2,5,1,3] => [1,2,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,2,6,7,8,4] => [4,8,7,6,2,5,1,3] => [2,1,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,2,6,8,4,7] => [7,4,8,6,2,5,1,3] => [1,2,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,7,4,6,8] => [8,6,4,7,2,5,1,3] => [1,1,2,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,8,6] => [6,8,4,7,2,5,1,3] => [2,2,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,2,7,8,4,6] => [6,4,8,7,2,5,1,3] => [1,2,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,8,4,6,7] => [7,6,4,8,2,5,1,3] => [1,1,2,2,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,5,6,2,4,7,8] => [8,7,4,2,6,5,1,3] => [1,1,1,2,1,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,1,5,6,2,4,8,7] => [7,8,4,2,6,5,1,3] => [2,1,2,1,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,5,6,2,7,4,8] => [8,4,7,2,6,5,1,3] => [1,2,2,1,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,1,5,6,2,7,8,4] => [4,8,7,2,6,5,1,3] => [2,1,2,1,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,1,5,6,2,8,4,7] => [7,4,8,2,6,5,1,3] => [1,2,2,1,2] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,5,6,7,2,4,8] => [8,4,2,7,6,5,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,1,5,6,7,2,8,4] => [4,8,2,7,6,5,1,3] => [2,2,1,1,2] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,1,5,6,7,8,2,4] => [4,2,8,7,6,5,1,3] => [1,2,1,1,1,2] => 2
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,1,5,6,8,2,4,7] => [7,4,2,8,6,5,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,5,7,2,4,6,8] => [8,6,4,2,7,5,1,3] => [1,1,1,2,1,2] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,1,5,7,2,4,8,6] => [6,8,4,2,7,5,1,3] => [2,1,2,1,2] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,1,5,7,2,8,4,6] => [6,4,8,2,7,5,1,3] => [1,2,2,1,2] => 2
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,1,5,7,8,2,4,6] => [6,4,2,8,7,5,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,1,5,8,2,4,6,7] => [7,6,4,2,8,5,1,3] => [1,1,1,2,1,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7,8] => [8,7,5,4,2,6,1,3] => [1,1,1,1,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,6,2,4,5,8,7] => [7,8,5,4,2,6,1,3] => [2,1,1,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,6,2,4,7,5,8] => [8,5,7,4,2,6,1,3] => [1,2,1,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,6,2,4,7,8,5] => [5,8,7,4,2,6,1,3] => [2,1,1,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,6,2,4,8,5,7] => [7,5,8,4,2,6,1,3] => [1,2,1,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,7,4,5,8] => [8,5,4,7,2,6,1,3] => [1,1,2,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,8,5] => [5,8,4,7,2,6,1,3] => [2,2,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,2,7,8,4,5] => [5,4,8,7,2,6,1,3] => [1,2,1,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,8,4,5,7] => [7,5,4,8,2,6,1,3] => [1,1,2,2,2] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,6,7,2,4,5,8] => [8,5,4,2,7,6,1,3] => [1,1,1,2,1,2] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,1,6,7,2,4,8,5] => [5,8,4,2,7,6,1,3] => [2,1,2,1,2] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,1,6,7,2,8,4,5] => [5,4,8,2,7,6,1,3] => [1,2,2,1,2] => 2
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [3,1,6,7,8,2,4,5] => [5,4,2,8,7,6,1,3] => [1,1,2,1,1,2] => 2
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,1,6,8,2,4,5,7] => [7,5,4,2,8,6,1,3] => [1,1,1,2,1,2] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,7,2,4,5,6,8] => [8,6,5,4,2,7,1,3] => [1,1,1,1,2,2] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,7,2,4,5,8,6] => [6,8,5,4,2,7,1,3] => [2,1,1,2,2] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,7,2,4,8,5,6] => [6,5,8,4,2,7,1,3] => [1,2,1,2,2] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,8,4,5,6] => [6,5,4,8,2,7,1,3] => [1,1,2,2,2] => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,7,8,2,4,5,6] => [6,5,4,2,8,7,1,3] => [1,1,1,2,1,2] => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [7,6,5,4,2,8,1,3] => [1,1,1,1,2,2] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8] => [8,7,6,5,2,1,4,3] => [1,1,1,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,5,6,8,7] => [7,8,6,5,2,1,4,3] => [2,1,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,4,1,2,5,7,6,8] => [8,6,7,5,2,1,4,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,4,1,2,5,7,8,6] => [6,8,7,5,2,1,4,3] => [2,1,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,4,1,2,5,8,6,7] => [7,6,8,5,2,1,4,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,4,1,2,6,5,7,8] => [8,7,5,6,2,1,4,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [7,8,5,6,2,1,4,3] => [2,2,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [3,4,1,2,6,7,5,8] => [8,5,7,6,2,1,4,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,1,2,6,7,8,5] => [5,8,7,6,2,1,4,3] => [2,1,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,1,2,6,8,5,7] => [7,5,8,6,2,1,4,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,4,1,2,7,5,6,8] => [8,6,5,7,2,1,4,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,1,2,7,5,8,6] => [6,8,5,7,2,1,4,3] => [2,2,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,1,2,7,8,5,6] => [6,5,8,7,2,1,4,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,1,2,8,5,6,7] => [7,6,5,8,2,1,4,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,2,6,7,8] => [8,7,6,2,5,1,4,3] => [1,1,1,2,2,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,2,6,8,7] => [7,8,6,2,5,1,4,3] => [2,1,2,2,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6,8] => [8,6,7,2,5,1,4,3] => [1,2,2,2,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2,7,8,6] => [6,8,7,2,5,1,4,3] => [2,1,2,2,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,8,6,7] => [7,6,8,2,5,1,4,3] => [1,2,2,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2,7,8] => [8,7,2,6,5,1,4,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,6,2,8,7] => [7,8,2,6,5,1,4,3] => [2,2,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,1,5,6,7,2,8] => [8,2,7,6,5,1,4,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,8,2] => [2,8,7,6,5,1,4,3] => [2,1,1,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,1,5,6,8,2,7] => [7,2,8,6,5,1,4,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,1,5,7,2,6,8] => [8,6,2,7,5,1,4,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,8,6] => [6,8,2,7,5,1,4,3] => [2,2,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,1,5,7,8,2,6] => [6,2,8,7,5,1,4,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,1,5,8,2,6,7] => [7,6,2,8,5,1,4,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,4,1,6,2,5,7,8] => [8,7,5,2,6,1,4,3] => [1,1,1,2,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,1,6,2,5,8,7] => [7,8,5,2,6,1,4,3] => [2,1,2,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5,8] => [8,5,7,2,6,1,4,3] => [1,2,2,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,2,7,8,5] => [5,8,7,2,6,1,4,3] => [2,1,2,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,8,5,7] => [7,5,8,2,6,1,4,3] => [1,2,2,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,1,6,7,2,5,8] => [8,5,2,7,6,1,4,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,1,6,7,2,8,5] => [5,8,2,7,6,1,4,3] => [2,2,1,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,4,1,6,7,8,2,5] => [5,2,8,7,6,1,4,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,4,1,6,8,2,5,7] => [7,5,2,8,6,1,4,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,4,1,7,2,5,6,8] => [8,6,5,2,7,1,4,3] => [1,1,1,2,2,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,4,1,7,2,5,8,6] => [6,8,5,2,7,1,4,3] => [2,1,2,2,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,8,5,6] => [6,5,8,2,7,1,4,3] => [1,2,2,2,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,4,1,7,8,2,5,6] => [6,5,2,8,7,1,4,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,1,8,2,5,6,7] => [7,6,5,2,8,1,4,3] => [1,1,1,2,2,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,1,2,6,8,7] => [7,8,6,2,1,5,4,3] => [2,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,5,1,2,7,8,6] => [6,8,7,2,1,5,4,3] => [2,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,1,6,2,7,8] => [8,7,2,6,1,5,4,3] => [1,1,2,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,8,7] => [7,8,2,6,1,5,4,3] => [2,2,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,1,6,7,2,8] => [8,2,7,6,1,5,4,3] => [1,2,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,1,6,7,8,2] => [2,8,7,6,1,5,4,3] => [2,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,5,1,6,8,2,7] => [7,2,8,6,1,5,4,3] => [1,2,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,5,1,7,2,6,8] => [8,6,2,7,1,5,4,3] => [1,1,2,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,8,6] => [6,8,2,7,1,5,4,3] => [2,2,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,1,7,8,2,6] => [6,2,8,7,1,5,4,3] => [1,2,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,1,2,7,8] => [8,7,2,1,6,5,4,3] => [1,1,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,1,2,8,7] => [7,8,2,1,6,5,4,3] => [2,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,1,7,2,8] => [8,2,7,1,6,5,4,3] => [1,2,2,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,1,7,8,2] => [2,8,7,1,6,5,4,3] => [2,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,1,8,2,7] => [7,2,8,1,6,5,4,3] => [1,2,2,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,1,2,8] => [8,2,1,7,6,5,4,3] => [1,1,2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,1,8,2] => [2,8,1,7,6,5,4,3] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,1,2] => [2,1,8,7,6,5,4,3] => [1,2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,1,2,7] => [7,2,1,8,6,5,4,3] => [1,1,2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,5,7,1,2,6,8] => [8,6,2,1,7,5,4,3] => [1,1,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,5,7,1,2,8,6] => [6,8,2,1,7,5,4,3] => [2,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,1,8,2,6] => [6,2,8,1,7,5,4,3] => [1,2,2,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,1,2,6] => [6,2,1,8,7,5,4,3] => [1,1,2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,1,2,6,7] => [7,6,2,1,8,5,4,3] => [1,1,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,4,6,1,2,5,7,8] => [8,7,5,2,1,6,4,3] => [1,1,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,1,2,5,8,7] => [7,8,5,2,1,6,4,3] => [2,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,1,2,7,5,8] => [8,5,7,2,1,6,4,3] => [1,2,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,1,2,7,8,5] => [5,8,7,2,1,6,4,3] => [2,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [3,4,6,1,2,8,5,7] => [7,5,8,2,1,6,4,3] => [1,2,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [3,4,6,1,7,2,5,8] => [8,5,2,7,1,6,4,3] => [1,1,2,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,1,7,2,8,5] => [5,8,2,7,1,6,4,3] => [2,2,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,1,7,8,2,5] => [5,2,8,7,1,6,4,3] => [1,2,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,4,6,1,8,2,5,7] => [7,5,2,8,1,6,4,3] => [1,1,2,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,4,6,7,1,2,5,8] => [8,5,2,1,7,6,4,3] => [1,1,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,1,2,8,5] => [5,8,2,1,7,6,4,3] => [2,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,4,6,7,1,8,2,5] => [5,2,8,1,7,6,4,3] => [1,2,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,1,2,5] => [5,2,1,8,7,6,4,3] => [1,1,2,1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,6,8,1,2,5,7] => [7,5,2,1,8,6,4,3] => [1,1,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,1,2,5,6,8] => [8,6,5,2,1,7,4,3] => [1,1,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,1,2,5,8,6] => [6,8,5,2,1,7,4,3] => [2,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,4,7,1,2,8,5,6] => [6,5,8,2,1,7,4,3] => [1,2,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,4,7,1,8,2,5,6] => [6,5,2,8,1,7,4,3] => [1,1,2,2,1,1] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,7,8,1,2,5,6] => [6,5,2,1,8,7,4,3] => [1,1,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,1,2,5,6,7] => [7,6,5,2,1,8,4,3] => [1,1,1,1,2,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,1,2,4,6,7,8] => [8,7,6,4,2,1,5,3] => [1,1,1,1,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,1,2,4,7,6,8] => [8,6,7,4,2,1,5,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,1,2,4,7,8,6] => [6,8,7,4,2,1,5,3] => [2,1,1,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,1,2,4,8,6,7] => [7,6,8,4,2,1,5,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,5,1,2,6,4,7,8] => [8,7,4,6,2,1,5,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,1,2,6,4,8,7] => [7,8,4,6,2,1,5,3] => [2,2,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,1,2,6,7,4,8] => [8,4,7,6,2,1,5,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,1,2,6,7,8,4] => [4,8,7,6,2,1,5,3] => [2,1,1,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,5,1,2,6,8,4,7] => [7,4,8,6,2,1,5,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,1,2,7,4,6,8] => [8,6,4,7,2,1,5,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,1,2,7,4,8,6] => [6,8,4,7,2,1,5,3] => [2,2,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,1,2,7,8,4,6] => [6,4,8,7,2,1,5,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [3,5,1,2,8,4,6,7] => [7,6,4,8,2,1,5,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,5,1,6,2,4,7,8] => [8,7,4,2,6,1,5,3] => [1,1,1,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,1,6,2,4,8,7] => [7,8,4,2,6,1,5,3] => [2,1,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4,8] => [8,4,7,2,6,1,5,3] => [1,2,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,1,6,2,7,8,4] => [4,8,7,2,6,1,5,3] => [2,1,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,8,4,7] => [7,4,8,2,6,1,5,3] => [1,2,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [3,5,1,6,7,2,4,8] => [8,4,2,7,6,1,5,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,1,6,7,2,8,4] => [4,8,2,7,6,1,5,3] => [2,2,1,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,1,6,7,8,2,4] => [4,2,8,7,6,1,5,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,5,1,7,2,4,6,8] => [8,6,4,2,7,1,5,3] => [1,1,1,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,1,7,2,4,8,6] => [6,8,4,2,7,1,5,3] => [2,1,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,8,4,6] => [6,4,8,2,7,1,5,3] => [1,2,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,1,7,8,2,4,6] => [6,4,2,8,7,1,5,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,5,1,8,2,4,6,7] => [7,6,4,2,8,1,5,3] => [1,1,1,2,2,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,5,6,1,2,4,7,8] => [8,7,4,2,1,6,5,3] => [1,1,1,1,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,1,2,4,8,7] => [7,8,4,2,1,6,5,3] => [2,1,1,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,1,2,7,4,8] => [8,4,7,2,1,6,5,3] => [1,2,1,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,1,2,7,8,4] => [4,8,7,2,1,6,5,3] => [2,1,1,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,1,7,2,4,8] => [8,4,2,7,1,6,5,3] => [1,1,2,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,1,7,2,8,4] => [4,8,2,7,1,6,5,3] => [2,2,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,1,7,8,2,4] => [4,2,8,7,1,6,5,3] => [1,2,1,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [3,5,6,1,8,2,4,7] => [7,4,2,8,1,6,5,3] => [1,1,2,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,1,2,4,8] => [8,4,2,1,7,6,5,3] => [1,1,1,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,1,2,8,4] => [4,8,2,1,7,6,5,3] => [2,1,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,1,8,2,4] => [4,2,8,1,7,6,5,3] => [1,2,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,1,2,4] => [4,2,1,8,7,6,5,3] => [1,1,2,1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,1,2,4,7] => [7,4,2,1,8,6,5,3] => [1,1,1,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,1,2,4,6,8] => [8,6,4,2,1,7,5,3] => [1,1,1,1,2,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,1,2,4,8,6] => [6,8,4,2,1,7,5,3] => [2,1,1,2,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,1,2,8,4,6] => [6,4,8,2,1,7,5,3] => [1,2,1,2,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,5,7,1,8,2,4,6] => [6,4,2,8,1,7,5,3] => [1,1,2,2,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,1,2,4,6] => [6,4,2,1,8,7,5,3] => [1,1,1,2,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,1,2,4,5,7,8] => [8,7,5,4,2,1,6,3] => [1,1,1,1,1,2,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,1,2,4,5,8,7] => [7,8,5,4,2,1,6,3] => [2,1,1,1,2,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,6,1,2,4,7,5,8] => [8,5,7,4,2,1,6,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,1,2,4,7,8,5] => [5,8,7,4,2,1,6,3] => [2,1,1,1,2,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,6,1,2,4,8,5,7] => [7,5,8,4,2,1,6,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,6,1,2,7,4,5,8] => [8,5,4,7,2,1,6,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,1,2,7,4,8,5] => [5,8,4,7,2,1,6,3] => [2,2,1,2,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,1,2,7,8,4,5] => [5,4,8,7,2,1,6,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,1,2,8,4,5,7] => [7,5,4,8,2,1,6,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [3,6,1,7,2,4,5,8] => [8,5,4,2,7,1,6,3] => [1,1,1,2,2,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,6,1,7,2,4,8,5] => [5,8,4,2,7,1,6,3] => [2,1,2,2,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,6,1,7,2,8,4,5] => [5,4,8,2,7,1,6,3] => [1,2,2,2,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,1,7,8,2,4,5] => [5,4,2,8,7,1,6,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,6,1,8,2,4,5,7] => [7,5,4,2,8,1,6,3] => [1,1,1,2,2,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [3,6,7,1,2,4,5,8] => [8,5,4,2,1,7,6,3] => [1,1,1,1,2,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,6,7,1,2,4,8,5] => [5,8,4,2,1,7,6,3] => [2,1,1,2,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,6,7,1,2,8,4,5] => [5,4,8,2,1,7,6,3] => [1,2,1,2,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,6,7,1,8,2,4,5] => [5,4,2,8,1,7,6,3] => [1,1,2,2,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,6,7,8,1,2,4,5] => [5,4,2,1,8,7,6,3] => [1,1,1,2,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,1,2,4,5,7] => [7,5,4,2,1,8,6,3] => [1,1,1,1,2,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,7,1,2,4,5,6,8] => [8,6,5,4,2,1,7,3] => [1,1,1,1,1,2,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,7,1,2,4,5,8,6] => [6,8,5,4,2,1,7,3] => [2,1,1,1,2,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,1,2,4,8,5,6] => [6,5,8,4,2,1,7,3] => [1,2,1,1,2,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,1,2,8,4,5,6] => [6,5,4,8,2,1,7,3] => [1,1,2,1,2,1] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,1,8,2,4,5,6] => [6,5,4,2,8,1,7,3] => [1,1,1,2,2,1] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,1,2,4,5,6] => [6,5,4,2,1,8,7,3] => [1,1,1,1,2,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [7,6,5,4,2,1,8,3] => [1,1,1,1,1,2,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,2,3,5,6,8,7] => [7,8,6,5,3,2,1,4] => [2,1,1,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,3,5,7,6,8] => [8,6,7,5,3,2,1,4] => [1,2,1,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,3,5,7,8,6] => [6,8,7,5,3,2,1,4] => [2,1,1,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,3,5,8,6,7] => [7,6,8,5,3,2,1,4] => [1,2,1,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,3,6,5,7,8] => [8,7,5,6,3,2,1,4] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => [7,8,5,6,3,2,1,4] => [2,2,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,3,6,7,5,8] => [8,5,7,6,3,2,1,4] => [1,2,1,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,3,6,7,8,5] => [5,8,7,6,3,2,1,4] => [2,1,1,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,1,2,3,6,8,5,7] => [7,5,8,6,3,2,1,4] => [1,2,1,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => [8,6,5,7,3,2,1,4] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,1,2,3,7,5,8,6] => [6,8,5,7,3,2,1,4] => [2,2,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,1,2,3,7,8,5,6] => [6,5,8,7,3,2,1,4] => [1,2,1,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => [7,6,5,8,3,2,1,4] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,2,5,3,6,7,8] => [8,7,6,3,5,2,1,4] => [1,1,1,2,1,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,1,2,5,3,6,8,7] => [7,8,6,3,5,2,1,4] => [2,1,2,1,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6,8] => [8,6,7,3,5,2,1,4] => [1,2,2,1,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,5,3,7,8,6] => [6,8,7,3,5,2,1,4] => [2,1,2,1,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,1,2,5,3,8,6,7] => [7,6,8,3,5,2,1,4] => [1,2,2,1,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,2,5,6,3,7,8] => [8,7,3,6,5,2,1,4] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,1,2,5,6,3,8,7] => [7,8,3,6,5,2,1,4] => [2,2,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,6,7,3,8] => [8,3,7,6,5,2,1,4] => [1,2,1,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,8,3] => [3,8,7,6,5,2,1,4] => [2,1,1,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,1,2,5,6,8,3,7] => [7,3,8,6,5,2,1,4] => [1,2,1,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6,8] => [8,6,3,7,5,2,1,4] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,1,2,5,7,3,8,6] => [6,8,3,7,5,2,1,4] => [2,2,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,1,2,5,7,8,3,6] => [6,3,8,7,5,2,1,4] => [1,2,1,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,1,2,5,8,3,6,7] => [7,6,3,8,5,2,1,4] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,1,2,6,3,5,7,8] => [8,7,5,3,6,2,1,4] => [1,1,1,2,1,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,1,2,6,3,5,8,7] => [7,8,5,3,6,2,1,4] => [2,1,2,1,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5,8] => [8,5,7,3,6,2,1,4] => [1,2,2,1,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,1,2,6,3,7,8,5] => [5,8,7,3,6,2,1,4] => [2,1,2,1,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,1,2,6,3,8,5,7] => [7,5,8,3,6,2,1,4] => [1,2,2,1,2] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,6,7,3,5,8] => [8,5,3,7,6,2,1,4] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,1,2,6,7,3,8,5] => [5,8,3,7,6,2,1,4] => [2,2,1,1,2] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,1,2,6,7,8,3,5] => [5,3,8,7,6,2,1,4] => [1,2,1,1,1,2] => 2
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,1,2,6,8,3,5,7] => [7,5,3,8,6,2,1,4] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,7,3,5,6,8] => [8,6,5,3,7,2,1,4] => [1,1,1,2,1,2] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,1,2,7,3,5,8,6] => [6,8,5,3,7,2,1,4] => [2,1,2,1,2] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [4,1,2,7,3,8,5,6] => [6,5,8,3,7,2,1,4] => [1,2,2,1,2] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,1,2,7,8,3,5,6] => [6,5,3,8,7,2,1,4] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,1,2,8,3,5,6,7] => [7,6,5,3,8,2,1,4] => [1,1,1,2,1,2] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,3,6,7,8] => [8,7,6,3,2,5,1,4] => [1,1,1,1,2,2] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,1,5,2,3,6,8,7] => [7,8,6,3,2,5,1,4] => [2,1,1,2,2] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,5,2,3,7,8,6] => [6,8,7,3,2,5,1,4] => [2,1,1,2,2] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,5,2,3,8,6,7] => [7,6,8,3,2,5,1,4] => [1,2,1,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,3,7,8] => [8,7,3,6,2,5,1,4] => [1,1,2,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7] => [7,8,3,6,2,5,1,4] => [2,2,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,2,6,7,3,8] => [8,3,7,6,2,5,1,4] => [1,2,1,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,2,6,7,8,3] => [3,8,7,6,2,5,1,4] => [2,1,1,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,2,6,8,3,7] => [7,3,8,6,2,5,1,4] => [1,2,1,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,7,3,6,8] => [8,6,3,7,2,5,1,4] => [1,1,2,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,8,6] => [6,8,3,7,2,5,1,4] => [2,2,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,2,7,8,3,6] => [6,3,8,7,2,5,1,4] => [1,2,1,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,8,3,6,7] => [7,6,3,8,2,5,1,4] => [1,1,2,2,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,1,5,6,2,3,7,8] => [8,7,3,2,6,5,1,4] => [1,1,1,2,1,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,1,5,6,2,7,3,8] => [8,3,7,2,6,5,1,4] => [1,2,2,1,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,7,8,3] => [3,8,7,2,6,5,1,4] => [2,1,2,1,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [4,1,5,6,2,8,3,7] => [7,3,8,2,6,5,1,4] => [1,2,2,1,2] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [4,1,5,6,7,2,3,8] => [8,3,2,7,6,5,1,4] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,5,6,7,2,8,3] => [3,8,2,7,6,5,1,4] => [2,2,1,1,2] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,8,2,3] => [3,2,8,7,6,5,1,4] => [1,2,1,1,1,2] => 2
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,5,6,8,2,3,7] => [7,3,2,8,6,5,1,4] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,5,7,2,3,6,8] => [8,6,3,2,7,5,1,4] => [1,1,1,2,1,2] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,1,5,7,2,3,8,6] => [6,8,3,2,7,5,1,4] => [2,1,2,1,2] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,5,7,2,8,3,6] => [6,3,8,2,7,5,1,4] => [1,2,2,1,2] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,1,5,7,8,2,3,6] => [6,3,2,8,7,5,1,4] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,1,5,8,2,3,6,7] => [7,6,3,2,8,5,1,4] => [1,1,1,2,1,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7,8] => [8,7,5,3,2,6,1,4] => [1,1,1,1,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,1,6,2,3,5,8,7] => [7,8,5,3,2,6,1,4] => [2,1,1,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,1,6,2,3,7,5,8] => [8,5,7,3,2,6,1,4] => [1,2,1,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,1,6,2,3,7,8,5] => [5,8,7,3,2,6,1,4] => [2,1,1,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,1,6,2,3,8,5,7] => [7,5,8,3,2,6,1,4] => [1,2,1,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,7,3,5,8] => [8,5,3,7,2,6,1,4] => [1,1,2,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,8,5] => [5,8,3,7,2,6,1,4] => [2,2,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,2,7,8,3,5] => [5,3,8,7,2,6,1,4] => [1,2,1,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,8,3,5,7] => [7,5,3,8,2,6,1,4] => [1,1,2,2,2] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [4,1,6,7,2,3,5,8] => [8,5,3,2,7,6,1,4] => [1,1,1,2,1,2] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,1,6,7,2,3,8,5] => [5,8,3,2,7,6,1,4] => [2,1,2,1,2] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,1,6,7,2,8,3,5] => [5,3,8,2,7,6,1,4] => [1,2,2,1,2] => 2
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,1,6,8,2,3,5,7] => [7,5,3,2,8,6,1,4] => [1,1,1,2,1,2] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,1,7,2,3,5,6,8] => [8,6,5,3,2,7,1,4] => [1,1,1,1,2,2] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,1,7,2,3,5,8,6] => [6,8,5,3,2,7,1,4] => [2,1,1,2,2] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,1,7,2,3,8,5,6] => [6,5,8,3,2,7,1,4] => [1,2,1,2,2] => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,8,3,5,6] => [6,5,3,8,2,7,1,4] => [1,1,2,2,2] => 2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,1,7,8,2,3,5,6] => [6,5,3,2,8,7,1,4] => [1,1,1,2,1,2] => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [7,6,5,3,2,8,1,4] => [1,1,1,1,2,2] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,1,2,3,6,7,8] => [8,7,6,3,2,1,5,4] => [1,1,1,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,5,1,2,3,6,8,7] => [7,8,6,3,2,1,5,4] => [2,1,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,5,1,2,3,7,6,8] => [8,6,7,3,2,1,5,4] => [1,2,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,5,1,2,3,7,8,6] => [6,8,7,3,2,1,5,4] => [2,1,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,1,2,3,8,6,7] => [7,6,8,3,2,1,5,4] => [1,2,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,5,1,2,6,3,7,8] => [8,7,3,6,2,1,5,4] => [1,1,2,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,1,2,6,3,8,7] => [7,8,3,6,2,1,5,4] => [2,2,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,5,1,2,6,7,3,8] => [8,3,7,6,2,1,5,4] => [1,2,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,1,2,6,7,8,3] => [3,8,7,6,2,1,5,4] => [2,1,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,5,1,2,6,8,3,7] => [7,3,8,6,2,1,5,4] => [1,2,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,1,2,7,3,6,8] => [8,6,3,7,2,1,5,4] => [1,1,2,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,5,1,2,7,3,8,6] => [6,8,3,7,2,1,5,4] => [2,2,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,5,1,2,7,8,3,6] => [6,3,8,7,2,1,5,4] => [1,2,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,1,2,8,3,6,7] => [7,6,3,8,2,1,5,4] => [1,1,2,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,5,1,6,2,3,7,8] => [8,7,3,2,6,1,5,4] => [1,1,1,2,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,1,6,2,3,8,7] => [7,8,3,2,6,1,5,4] => [2,1,2,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3,8] => [8,3,7,2,6,1,5,4] => [1,2,2,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,5,1,6,2,7,8,3] => [3,8,7,2,6,1,5,4] => [2,1,2,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,8,3,7] => [7,3,8,2,6,1,5,4] => [1,2,2,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,5,1,6,7,2,3,8] => [8,3,2,7,6,1,5,4] => [1,1,2,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,1,6,7,2,8,3] => [3,8,2,7,6,1,5,4] => [2,2,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,1,6,7,8,2,3] => [3,2,8,7,6,1,5,4] => [1,2,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,1,6,8,2,3,7] => [7,3,2,8,6,1,5,4] => [1,1,2,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,5,1,7,2,3,6,8] => [8,6,3,2,7,1,5,4] => [1,1,1,2,2,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,5,1,7,2,3,8,6] => [6,8,3,2,7,1,5,4] => [2,1,2,2,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,8,3,6] => [6,3,8,2,7,1,5,4] => [1,2,2,2,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,1,7,8,2,3,6] => [6,3,2,8,7,1,5,4] => [1,1,2,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,1,8,2,3,6,7] => [7,6,3,2,8,1,5,4] => [1,1,1,2,2,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,1,2,3,7,8] => [8,7,3,2,1,6,5,4] => [1,1,1,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,1,2,3,8,7] => [7,8,3,2,1,6,5,4] => [2,1,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,5,6,1,2,7,3,8] => [8,3,7,2,1,6,5,4] => [1,2,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,1,2,7,8,3] => [3,8,7,2,1,6,5,4] => [2,1,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,1,2,8,3,7] => [7,3,8,2,1,6,5,4] => [1,2,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,5,6,1,7,2,3,8] => [8,3,2,7,1,6,5,4] => [1,1,2,2,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,1,7,2,8,3] => [3,8,2,7,1,6,5,4] => [2,2,2,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,5,6,1,7,8,2,3] => [3,2,8,7,1,6,5,4] => [1,2,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,1,8,2,3,7] => [7,3,2,8,1,6,5,4] => [1,1,2,2,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,1,2,3,8] => [8,3,2,1,7,6,5,4] => [1,1,1,2,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,1,2,8,3] => [3,8,2,1,7,6,5,4] => [2,1,2,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,1,8,2,3] => [3,2,8,1,7,6,5,4] => [1,2,2,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,1,2,3] => [3,2,1,8,7,6,5,4] => [1,1,2,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,1,2,3,7] => [7,3,2,1,8,6,5,4] => [1,1,1,2,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,1,2,3,6,8] => [8,6,3,2,1,7,5,4] => [1,1,1,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,5,7,1,2,8,3,6] => [6,3,8,2,1,7,5,4] => [1,2,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,1,8,2,3,6] => [6,3,2,8,1,7,5,4] => [1,1,2,2,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,5,7,8,1,2,3,6] => [6,3,2,1,8,7,5,4] => [1,1,1,2,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => [7,6,3,2,1,8,5,4] => [1,1,1,1,2,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,6,1,2,3,5,7,8] => [8,7,5,3,2,1,6,4] => [1,1,1,1,1,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,1,2,3,5,8,7] => [7,8,5,3,2,1,6,4] => [2,1,1,1,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,6,1,2,3,7,5,8] => [8,5,7,3,2,1,6,4] => [1,2,1,1,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,6,1,2,3,7,8,5] => [5,8,7,3,2,1,6,4] => [2,1,1,1,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,1,2,3,8,5,7] => [7,5,8,3,2,1,6,4] => [1,2,1,1,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [4,6,1,2,7,3,5,8] => [8,5,3,7,2,1,6,4] => [1,1,2,1,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,1,2,7,3,8,5] => [5,8,3,7,2,1,6,4] => [2,2,1,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,6,1,2,7,8,3,5] => [5,3,8,7,2,1,6,4] => [1,2,1,1,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,6,1,2,8,3,5,7] => [7,5,3,8,2,1,6,4] => [1,1,2,1,2,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,1,7,2,3,5,8] => [8,5,3,2,7,1,6,4] => [1,1,1,2,2,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,1,7,2,3,8,5] => [5,8,3,2,7,1,6,4] => [2,1,2,2,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,6,1,7,2,8,3,5] => [5,3,8,2,7,1,6,4] => [1,2,2,2,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,1,7,8,2,3,5] => [5,3,2,8,7,1,6,4] => [1,1,2,1,2,1] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,1,8,2,3,5,7] => [7,5,3,2,8,1,6,4] => [1,1,1,2,2,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,6,7,1,2,3,5,8] => [8,5,3,2,1,7,6,4] => [1,1,1,1,2,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,1,2,3,8,5] => [5,8,3,2,1,7,6,4] => [2,1,1,2,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,6,7,1,2,8,3,5] => [5,3,8,2,1,7,6,4] => [1,2,1,2,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,1,8,2,3,5] => [5,3,2,8,1,7,6,4] => [1,1,2,2,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,1,2,3,5] => [5,3,2,1,8,7,6,4] => [1,1,1,2,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,1,2,3,5,7] => [7,5,3,2,1,8,6,4] => [1,1,1,1,2,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,1,2,3,5,6,8] => [8,6,5,3,2,1,7,4] => [1,1,1,1,1,2,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,1,2,3,5,8,6] => [6,8,5,3,2,1,7,4] => [2,1,1,1,2,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,1,2,3,8,5,6] => [6,5,8,3,2,1,7,4] => [1,2,1,1,2,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,1,2,8,3,5,6] => [6,5,3,8,2,1,7,4] => [1,1,2,1,2,1] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,1,8,2,3,5,6] => [6,5,3,2,8,1,7,4] => [1,1,1,2,2,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,1,2,3,5,6] => [6,5,3,2,1,8,7,4] => [1,1,1,1,2,1,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [7,6,5,3,2,1,8,4] => [1,1,1,1,1,2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,4,6,8,7] => [7,8,6,4,3,2,1,5] => [2,1,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,1,2,3,4,7,6,8] => [8,6,7,4,3,2,1,5] => [1,2,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,1,2,3,4,7,8,6] => [6,8,7,4,3,2,1,5] => [2,1,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => [7,6,8,4,3,2,1,5] => [1,2,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,2,3,6,4,7,8] => [8,7,4,6,3,2,1,5] => [1,1,2,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,1,2,3,6,4,8,7] => [7,8,4,6,3,2,1,5] => [2,2,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,2,3,6,7,4,8] => [8,4,7,6,3,2,1,5] => [1,2,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,2,3,6,7,8,4] => [4,8,7,6,3,2,1,5] => [2,1,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,2,3,6,8,4,7] => [7,4,8,6,3,2,1,5] => [1,2,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,1,2,3,7,4,6,8] => [8,6,4,7,3,2,1,5] => [1,1,2,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,1,2,3,7,4,8,6] => [6,8,4,7,3,2,1,5] => [2,2,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,1,2,3,7,8,4,6] => [6,4,8,7,3,2,1,5] => [1,2,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,1,2,3,8,4,6,7] => [7,6,4,8,3,2,1,5] => [1,1,2,1,1,2] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,2,6,3,4,7,8] => [8,7,4,3,6,2,1,5] => [1,1,1,2,1,2] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,1,2,6,3,4,8,7] => [7,8,4,3,6,2,1,5] => [2,1,2,1,2] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4,8] => [8,4,7,3,6,2,1,5] => [1,2,2,1,2] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,2,6,3,7,8,4] => [4,8,7,3,6,2,1,5] => [2,1,2,1,2] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,1,2,6,3,8,4,7] => [7,4,8,3,6,2,1,5] => [1,2,2,1,2] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,2,6,7,3,4,8] => [8,4,3,7,6,2,1,5] => [1,1,2,1,1,2] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,1,2,6,7,3,8,4] => [4,8,3,7,6,2,1,5] => [2,2,1,1,2] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,2,6,7,8,3,4] => [4,3,8,7,6,2,1,5] => [1,2,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,1,2,6,8,3,4,7] => [7,4,3,8,6,2,1,5] => [1,1,2,1,1,2] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,1,2,7,3,4,6,8] => [8,6,4,3,7,2,1,5] => [1,1,1,2,1,2] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,1,2,7,3,4,8,6] => [6,8,4,3,7,2,1,5] => [2,1,2,1,2] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,1,2,7,3,8,4,6] => [6,4,8,3,7,2,1,5] => [1,2,2,1,2] => 2
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,1,2,7,8,3,4,6] => [6,4,3,8,7,2,1,5] => [1,1,2,1,1,2] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,1,2,8,3,4,6,7] => [7,6,4,3,8,2,1,5] => [1,1,1,2,1,2] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7,8] => [8,7,4,3,2,6,1,5] => [1,1,1,1,2,2] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,6,2,3,4,8,7] => [7,8,4,3,2,6,1,5] => [2,1,1,2,2] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,6,2,3,7,4,8] => [8,4,7,3,2,6,1,5] => [1,2,1,2,2] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,1,6,2,3,7,8,4] => [4,8,7,3,2,6,1,5] => [2,1,1,2,2] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,1,6,2,3,8,4,7] => [7,4,8,3,2,6,1,5] => [1,2,1,2,2] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,7,3,4,8] => [8,4,3,7,2,6,1,5] => [1,1,2,2,2] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,8,4] => [4,8,3,7,2,6,1,5] => [2,2,2,2] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,6,2,7,8,3,4] => [4,3,8,7,2,6,1,5] => [1,2,1,2,2] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,8,3,4,7] => [7,4,3,8,2,6,1,5] => [1,1,2,2,2] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,1,6,7,2,3,4,8] => [8,4,3,2,7,6,1,5] => [1,1,1,2,1,2] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,6,7,2,3,8,4] => [4,8,3,2,7,6,1,5] => [2,1,2,1,2] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,6,7,2,8,3,4] => [4,3,8,2,7,6,1,5] => [1,2,2,1,2] => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,6,7,8,2,3,4] => [4,3,2,8,7,6,1,5] => [1,1,2,1,1,2] => 2
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [5,1,6,8,2,3,4,7] => [7,4,3,2,8,6,1,5] => [1,1,1,2,1,2] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,1,7,2,3,4,6,8] => [8,6,4,3,2,7,1,5] => [1,1,1,1,2,2] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,1,7,2,3,4,8,6] => [6,8,4,3,2,7,1,5] => [2,1,1,2,2] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,1,7,2,3,8,4,6] => [6,4,8,3,2,7,1,5] => [1,2,1,2,2] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,8,3,4,6] => [6,4,3,8,2,7,1,5] => [1,1,2,2,2] => 2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,1,7,8,2,3,4,6] => [6,4,3,2,8,7,1,5] => [1,1,1,2,1,2] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,1,8,2,3,4,6,7] => [7,6,4,3,2,8,1,5] => [1,1,1,1,2,2] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,1,2,3,4,7,8] => [8,7,4,3,2,1,6,5] => [1,1,1,1,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4,8,7] => [7,8,4,3,2,1,6,5] => [2,1,1,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [5,6,1,2,3,7,8,4] => [4,8,7,3,2,1,6,5] => [2,1,1,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,8,4,7] => [7,4,8,3,2,1,6,5] => [1,2,1,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,1,2,7,3,4,8] => [8,4,3,7,2,1,6,5] => [1,1,2,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,6,1,2,7,3,8,4] => [4,8,3,7,2,1,6,5] => [2,2,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,6,1,2,7,8,3,4] => [4,3,8,7,2,1,6,5] => [1,2,1,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,1,2,8,3,4,7] => [7,4,3,8,2,1,6,5] => [1,1,2,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,1,7,2,3,4,8] => [8,4,3,2,7,1,6,5] => [1,1,1,2,2,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,6,1,7,2,3,8,4] => [4,8,3,2,7,1,6,5] => [2,1,2,2,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,6,1,7,2,8,3,4] => [4,3,8,2,7,1,6,5] => [1,2,2,2,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,1,7,8,2,3,4] => [4,3,2,8,7,1,6,5] => [1,1,2,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,1,8,2,3,4,7] => [7,4,3,2,8,1,6,5] => [1,1,1,2,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,1,2,3,4,8] => [8,4,3,2,1,7,6,5] => [1,1,1,1,2,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,1,2,3,8,4] => [4,8,3,2,1,7,6,5] => [2,1,1,2,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,1,2,8,3,4] => [4,3,8,2,1,7,6,5] => [1,2,1,2,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,1,8,2,3,4] => [4,3,2,8,1,7,6,5] => [1,1,2,2,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => [1,1,1,2,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => [7,4,3,2,1,8,6,5] => [1,1,1,1,2,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,1,2,3,4,6,8] => [8,6,4,3,2,1,7,5] => [1,1,1,1,1,2,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,1,2,3,4,8,6] => [6,8,4,3,2,1,7,5] => [2,1,1,1,2,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,1,2,3,8,4,6] => [6,4,8,3,2,1,7,5] => [1,2,1,1,2,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,1,2,8,3,4,6] => [6,4,3,8,2,1,7,5] => [1,1,2,1,2,1] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,1,8,2,3,4,6] => [6,4,3,2,8,1,7,5] => [1,1,1,2,2,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => [6,4,3,2,1,8,7,5] => [1,1,1,1,2,1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [7,6,4,3,2,1,8,5] => [1,1,1,1,1,2,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => [7,8,5,4,3,2,1,6] => [2,1,1,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,2,3,4,7,5,8] => [8,5,7,4,3,2,1,6] => [1,2,1,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,1,2,3,4,7,8,5] => [5,8,7,4,3,2,1,6] => [2,1,1,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,1,2,3,4,8,5,7] => [7,5,8,4,3,2,1,6] => [1,2,1,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5,8] => [8,5,4,7,3,2,1,6] => [1,1,2,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,1,2,3,7,4,8,5] => [5,8,4,7,3,2,1,6] => [2,2,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,1,2,3,7,8,4,5] => [5,4,8,7,3,2,1,6] => [1,2,1,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,1,2,3,8,4,5,7] => [7,5,4,8,3,2,1,6] => [1,1,2,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,2,7,3,4,5,8] => [8,5,4,3,7,2,1,6] => [1,1,1,2,1,2] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,1,2,7,3,4,8,5] => [5,8,4,3,7,2,1,6] => [2,1,2,1,2] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,1,2,7,3,8,4,5] => [5,4,8,3,7,2,1,6] => [1,2,2,1,2] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,1,2,7,8,3,4,5] => [5,4,3,8,7,2,1,6] => [1,1,2,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,1,2,8,3,4,5,7] => [7,5,4,3,8,2,1,6] => [1,1,1,2,1,2] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,7,2,3,4,5,8] => [8,5,4,3,2,7,1,6] => [1,1,1,1,2,2] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,1,7,2,3,4,8,5] => [5,8,4,3,2,7,1,6] => [2,1,1,2,2] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,1,7,2,3,8,4,5] => [5,4,8,3,2,7,1,6] => [1,2,1,2,2] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,1,7,2,8,3,4,5] => [5,4,3,8,2,7,1,6] => [1,1,2,2,2] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,1,7,8,2,3,4,5] => [5,4,3,2,8,7,1,6] => [1,1,1,2,1,2] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [7,5,4,3,2,8,1,6] => [1,1,1,1,2,2] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,1,2,3,4,5,8] => [8,5,4,3,2,1,7,6] => [1,1,1,1,1,2,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,1,2,3,4,8,5] => [5,8,4,3,2,1,7,6] => [2,1,1,1,2,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,1,2,3,8,4,5] => [5,4,8,3,2,1,7,6] => [1,2,1,1,2,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,1,2,8,3,4,5] => [5,4,3,8,2,1,7,6] => [1,1,2,1,2,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,1,8,2,3,4,5] => [5,4,3,2,8,1,7,6] => [1,1,1,2,2,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => [5,4,3,2,1,8,7,6] => [1,1,1,1,2,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => [7,5,4,3,2,1,8,6] => [1,1,1,1,1,2,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,8,6] => [6,8,5,4,3,2,1,7] => [2,1,1,1,1,2] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,8,5,6] => [6,5,8,4,3,2,1,7] => [1,2,1,1,1,2] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1,2,3,8,4,5,6] => [6,5,4,8,3,2,1,7] => [1,1,2,1,1,2] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1,2,8,3,4,5,6] => [6,5,4,3,8,2,1,7] => [1,1,1,2,1,2] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [6,5,4,3,2,8,1,7] => [1,1,1,1,2,2] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [6,5,4,3,2,1,8,7] => [1,1,1,1,1,2,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,1,2,3,4,5,6,7,10,9] => [9,10,7,6,5,4,3,2,1,8] => [2,1,1,1,1,1,1,2] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,3,8,9,5,7] => [7,5,9,8,3,6,1,4,2] => [1,2,1,2,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,9,10,2] => [2,10,9,8,7,6,5,4,1,3] => [2,1,1,1,1,1,1,2] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,7,4,8,9,10,5] => [5,10,9,8,4,7,6,3,2,1] => [2,1,1,2,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,8,9,10,3] => [3,10,9,8,7,6,5,2,1,4] => [2,1,1,1,1,1,1,2] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,1,6,7,8,9,10,2] => [2,10,9,8,7,6,1,5,4,3] => [2,1,1,1,1,2,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => [2,12,11,10,9,8,7,6,5,4,1,3] => [2,1,1,1,1,1,1,1,1,2] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,8,9,10,2] => [2,10,9,8,1,7,6,5,4,3] => [2,1,1,2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,9,1,10,2] => [2,10,1,9,8,7,6,5,4,3] => [2,2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => [9,10,7,8,6,5,4,3,2,1] => [2,2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => [9,10,7,8,5,6,3,4,2,1] => [2,2,2,2,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [9,10,8,7,6,5,4,3,1,2] => [2,1,1,1,1,1,1,2] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => [10,9,8,7,6,5,3,4,1,2] => [1,1,1,1,1,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9,10] => [10,9,7,8,5,6,3,4,1,2] => [1,1,2,2,2,2] => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,1,10,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,10,1,9] => [1,1,1,1,1,1,2,2] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => [8,10,7,6,5,4,3,2,1,9] => [2,1,1,1,1,1,1,2] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,1,2,3,4,5,10,6,7,8] => [8,7,6,10,5,4,3,2,1,9] => [1,1,2,1,1,1,1,2] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,1,2,3,10,4,5,6,7,8] => [8,7,6,5,4,10,3,2,1,9] => [1,1,1,1,2,1,1,2] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7,9] => [9,7,8,5,6,3,1,4,2] => [1,2,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5,8,7,9] => [9,7,8,5,3,6,1,4,2] => [1,2,1,2,2,1] => 1
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [8,1,10,2,3,4,5,6,7,9] => [9,7,6,5,4,3,2,10,1,8] => [1,1,1,1,1,1,2,2] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,7,2,8,3,9,4,10,5] => [5,10,4,9,3,8,2,7,6,1] => [2,2,2,2,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => [11,1,2,3,4,5,6,7,8,9,12,10] => [10,12,9,8,7,6,5,4,3,2,1,11] => [2,1,1,1,1,1,1,1,1,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => [3,10,9,8,7,6,5,4,1,2] => [2,1,1,1,1,1,1,2] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,1,8,9,10,7] => [7,10,9,8,1,6,5,4,3,2] => [2,1,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [9,10,1,8,7,6,5,4,3,2] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,7,4,9,6,8,10] => [10,8,6,9,4,7,2,5,1,3] => [1,1,2,2,2,2] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,7,9,1,10,8] => [8,10,1,9,7,6,5,4,3,2] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,1,2,3,4,5,6,9,10,7] => [7,10,9,6,5,4,3,2,1,8] => [2,1,1,1,1,1,1,2] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,9,6,10,8] => [8,10,6,9,4,7,2,5,3,1] => [2,2,2,2,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9,10] => [10,9,8,7,6,5,2,4,1,3] => [1,1,1,1,1,1,2,2] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,4,5,7,8,9,10,6] => [6,10,9,8,7,5,4,3,1,2] => [2,1,1,1,1,1,1,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7,10,9,12,11] => [11,12,9,10,7,8,5,6,2,4,1,3] => [2,2,2,2,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,3,6,4,8,7,10,9,12,11] => [11,12,9,10,7,8,4,6,3,5,1,2] => [2,2,2,2,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,7,5,8,6,10,9,12,11] => [11,12,9,10,6,8,5,7,3,4,1,2] => [2,2,2,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,7,5,8,6,10,9,12,11] => [11,12,9,10,6,8,5,7,2,4,1,3] => [2,2,2,2,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,6,5,9,7,10,8,12,11] => [11,12,8,10,7,9,5,6,3,4,1,2] => [2,2,2,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5,9,7,10,8,12,11] => [11,12,8,10,7,9,5,6,2,4,1,3] => [2,2,2,2,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,9,7,10,8,12,11] => [11,12,8,10,7,9,4,6,3,5,1,2] => [2,2,2,2,2,2] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,1,8,2,9,3,10,4,11,5,12,6] => [6,12,5,11,4,10,3,9,2,8,1,7] => [2,2,2,2,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,8,7,11,9,12,10] => [10,12,9,11,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,6,5,8,7,11,9,12,10] => [10,12,9,11,7,8,5,6,2,4,1,3] => [2,2,2,2,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4,8,7,11,9,12,10] => [10,12,9,11,7,8,4,6,3,5,1,2] => [2,2,2,2,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,8,6,11,9,12,10] => [10,12,9,11,6,8,5,7,3,4,1,2] => [2,2,2,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,8,6,11,9,12,10] => [10,12,9,11,6,8,5,7,2,4,1,3] => [2,2,2,2,2,2] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,4,7,9,6,8] => [8,6,9,7,4,5,2,3,1] => [1,2,1,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,2,5,7,4,9,6,8] => [8,6,9,4,7,5,2,3,1] => [1,2,2,1,2,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,3,8,5,7,10,9] => [9,10,7,5,8,3,6,4,1,2] => [2,1,2,2,1,2] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,8,10,5,7,9] => [9,7,5,10,8,3,1,6,4,2] => [1,1,2,1,1,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,3,6,5,8,10,12,7,9,11] => [11,9,7,12,10,8,5,6,3,4,1,2] => [1,1,2,1,1,2,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,1,4,3,6,8,10,5,7,9,12,11] => [11,12,9,7,5,10,8,6,3,4,1,2] => [2,1,1,2,1,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,1,4,3,6,8,10,5,12,7,9,11] => [11,9,7,12,5,10,8,6,3,4,1,2] => [1,1,2,2,1,1,2,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,3,5,8,10,7,9,12,11] => [11,12,9,7,10,8,5,3,6,4,1,2] => [2,1,2,1,1,2,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,8,3,5,7,10,9,12,11] => [11,12,9,10,7,5,3,8,6,4,1,2] => [2,2,1,1,2,1,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [2,1,4,6,8,3,10,5,7,9,12,11] => [11,12,9,7,5,10,3,8,6,4,1,2] => [2,1,1,2,2,1,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,3,8,5,10,12,7,9,11] => [11,9,7,12,10,5,8,3,6,4,1,2] => [1,1,2,1,2,2,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [2,1,4,6,8,3,10,5,12,7,9,11] => [11,9,7,12,5,10,3,8,6,4,1,2] => [1,1,2,2,2,1,1,2] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,1,4,6,8,10,12,3,5,7,9,11] => [11,9,7,5,3,12,10,8,6,4,1,2] => [1,1,1,1,2,1,1,1,1,2] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,6,1,3,5,8,7,10,9,12,11] => [11,12,9,10,7,8,5,3,1,6,4,2] => [2,2,2,1,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,8,10,12,7,9,11] => [11,9,7,12,10,8,5,3,1,6,4,2] => [1,1,2,1,1,1,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [2,4,6,1,8,3,5,7,10,9,12,11] => [11,12,9,10,7,5,3,8,1,6,4,2] => [2,2,1,1,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,6,1,3,8,5,10,7,9,12,11] => [11,12,9,7,10,5,8,3,1,6,4,2] => [2,1,2,2,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,1,8,3,10,5,7,9,12,11] => [11,12,9,7,5,10,3,8,1,6,4,2] => [2,1,1,2,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [2,4,6,8,10,1,3,5,7,9,12,11] => [11,12,9,7,5,3,1,10,8,6,4,2] => [2,1,1,1,1,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,1,8,3,10,5,12,7,9,11] => [11,9,7,12,5,10,3,8,1,6,4,2] => [1,1,2,2,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,4,6,1,8,10,12,3,5,7,9,11] => [11,9,7,5,3,12,10,8,1,6,4,2] => [1,1,1,1,2,1,1,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0] => [2,4,6,8,10,1,3,5,12,7,9,11] => [11,9,7,12,5,3,1,10,8,6,4,2] => [1,1,2,1,1,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [2,4,6,8,10,1,12,3,5,7,9,11] => [11,9,7,5,3,12,1,10,8,6,4,2] => [1,1,1,1,2,2,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,1,8,9,10,11,12,2,3,4,5,6] => [6,5,4,3,2,12,11,10,9,8,1,7] => [1,1,1,1,2,1,1,1,1,2] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,10,9] => [9,10,7,8,5,6,1,4,3,2] => [2,2,2,2,1,1] => 1
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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 3,2 9,5 28,14 90,42 297,132
F1=q
F2=q+q2
F3=3 q+2 q2
F4=9 q+5 q2
F5=28 q+14 q2
F6=90 q+42 q2
F7=297 q+132 q2
Description
The last part of an integer composition.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation π of length n is the integer composition of n whose descent set equals the descent set of π. The descent set of a permutation π is {i∣1≤i<n,π(i)>π(i+1)}. The descent set of a composition c=(i1,i2,…,ik) is the set {i1,i1+i2,i1+i2+i3,…,i1+i2+⋯+ik−1}.
The descent composition of a permutation π of length n is the integer composition of n whose descent set equals the descent set of π. The descent set of a permutation π is {i∣1≤i<n,π(i)>π(i+1)}. The descent set of a composition c=(i1,i2,…,ik) is the set {i1,i1+i2,i1+i2+i3,…,i1+i2+⋯+ik−1}.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation σ of length n is given by τ with τ(i)=σ(n+1−i).
The reverse of a permutation σ of length n is given by τ with τ(i)=σ(n+1−i).
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength n in an n×n square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Draw the path of semilength n in an n×n square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
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