Identifier
-
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
St000381: Integer compositions ⟶ ℤ
Values
[1,0] => [1] => [1] => [1] => 1
[1,0,1,0] => [1,2] => [1,2] => [2] => 2
[1,1,0,0] => [2,1] => [2,1] => [1,1] => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [3] => 3
[1,0,1,1,0,0] => [1,3,2] => [3,1,2] => [1,2] => 2
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [1,2] => 2
[1,1,0,1,0,0] => [2,3,1] => [2,3,1] => [2,1] => 2
[1,1,1,0,0,0] => [3,2,1] => [3,2,1] => [1,1,1] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [4] => 4
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [4,1,2,3] => [1,3] => 3
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [3,1,2,4] => [1,3] => 3
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,1,4,2] => [1,2,1] => 2
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [4,3,1,2] => [1,1,2] => 2
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [1,3] => 3
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [4,2,1,3] => [1,1,2] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,3,1,4] => [2,2] => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,3,4,1] => [3,1] => 3
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [4,2,3,1] => [1,2,1] => 2
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,2,1,4] => [1,1,2] => 2
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,2,4,1] => [1,2,1] => 2
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [2,4,3,1] => [2,1,1] => 2
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [5] => 5
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [5,1,2,3,4] => [1,4] => 4
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [4,1,2,3,5] => [1,4] => 4
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [4,1,2,5,3] => [1,3,1] => 3
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [5,4,1,2,3] => [1,1,3] => 3
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [3,1,2,4,5] => [1,4] => 4
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [5,3,1,2,4] => [1,1,3] => 3
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [3,1,4,2,5] => [1,2,2] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [3,1,4,5,2] => [1,3,1] => 3
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [5,3,1,4,2] => [1,1,2,1] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [4,3,1,2,5] => [1,1,3] => 3
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [4,3,1,5,2] => [1,1,2,1] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [5,1,3,4,2] => [1,3,1] => 3
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [5,4,3,1,2] => [1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [1,4] => 4
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [5,2,1,3,4] => [1,1,3] => 3
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [4,2,1,3,5] => [1,1,3] => 3
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [4,2,1,5,3] => [1,1,2,1] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [5,4,2,1,3] => [1,1,1,2] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,3,1,4,5] => [2,3] => 3
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [5,2,3,1,4] => [1,2,2] => 2
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,3,4,1,5] => [3,2] => 3
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,3,4,5,1] => [4,1] => 4
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [5,2,3,4,1] => [1,3,1] => 3
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [4,2,3,1,5] => [1,2,2] => 2
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [4,2,3,5,1] => [1,3,1] => 3
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [2,5,3,4,1] => [2,2,1] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [5,4,2,3,1] => [1,1,2,1] => 2
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,2,1,4,5] => [1,1,3] => 3
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [5,3,2,1,4] => [1,1,1,2] => 2
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,2,4,1,5] => [1,2,2] => 2
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [3,2,4,5,1] => [1,3,1] => 3
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [5,3,2,4,1] => [1,1,2,1] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [2,4,3,1,5] => [2,1,2] => 2
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [2,4,3,5,1] => [2,2,1] => 2
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [2,3,5,4,1] => [3,1,1] => 3
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [5,2,4,3,1] => [1,2,1,1] => 2
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [4,3,2,5,1] => [1,1,2,1] => 2
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [3,5,2,4,1] => [2,2,1] => 2
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [3,5,4,2,1] => [2,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [6] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => [1,5] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => [1,5] => 5
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [5,1,2,3,6,4] => [1,4,1] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => [1,1,4] => 4
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => [1,5] => 5
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [6,4,1,2,3,5] => [1,1,4] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [4,1,2,5,3,6] => [1,3,2] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [4,1,2,5,6,3] => [1,4,1] => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [6,4,1,2,5,3] => [1,1,3,1] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => [1,1,4] => 4
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [5,4,1,2,6,3] => [1,1,3,1] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [6,1,4,2,5,3] => [1,2,2,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => [1,1,1,3] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => [1,5] => 5
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [6,3,1,2,4,5] => [1,1,4] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [5,3,1,2,4,6] => [1,1,4] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [5,3,1,2,6,4] => [1,1,3,1] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [6,5,3,1,2,4] => [1,1,1,3] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => [1,2,3] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [6,3,1,4,2,5] => [1,1,2,2] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => [1,3,2] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => [1,4,1] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [6,3,1,4,5,2] => [1,1,3,1] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [5,3,1,4,2,6] => [1,1,2,2] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [5,3,1,4,6,2] => [1,1,3,1] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [6,1,3,4,5,2] => [1,4,1] => 4
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [6,5,3,1,4,2] => [1,1,1,2,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => [1,1,4] => 4
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [6,4,3,1,2,5] => [1,1,1,3] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [4,3,1,5,2,6] => [1,1,2,2] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [4,3,1,5,6,2] => [1,1,3,1] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [6,4,3,1,5,2] => [1,1,1,2,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [5,1,3,4,2,6] => [1,3,2] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [5,1,3,4,6,2] => [1,4,1] => 4
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [3,1,6,4,5,2] => [1,2,2,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [6,5,1,3,4,2] => [1,1,3,1] => 3
>>> Load all 1963 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => [1,1,1,3] => 3
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [5,4,3,1,6,2] => [1,1,1,2,1] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [4,6,3,1,5,2] => [2,1,2,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [6,4,1,5,3,2] => [1,1,2,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => [1,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,5] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [6,2,1,3,4,5] => [1,1,4] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [5,2,1,3,4,6] => [1,1,4] => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [5,2,1,3,6,4] => [1,1,3,1] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [6,5,2,1,3,4] => [1,1,1,3] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [4,2,1,3,5,6] => [1,1,4] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [6,4,2,1,3,5] => [1,1,1,3] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [4,2,1,5,3,6] => [1,1,2,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [4,2,1,5,6,3] => [1,1,3,1] => 3
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [6,4,2,1,5,3] => [1,1,1,2,1] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [5,4,2,1,3,6] => [1,1,1,3] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [5,4,2,1,6,3] => [1,1,1,2,1] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [6,2,4,1,5,3] => [1,2,2,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [6,5,4,2,1,3] => [1,1,1,1,2] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => [2,4] => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [6,2,3,1,4,5] => [1,2,3] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [5,2,3,1,4,6] => [1,2,3] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [5,2,3,1,6,4] => [1,2,2,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [6,5,2,3,1,4] => [1,1,2,2] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => [3,3] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [6,2,3,4,1,5] => [1,3,2] => 3
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => [4,2] => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => [5,1] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => [1,4,1] => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => [1,3,2] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [5,2,3,4,6,1] => [1,4,1] => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [2,6,3,4,5,1] => [2,3,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [6,5,2,3,4,1] => [1,1,3,1] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => [1,2,3] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [6,4,2,3,1,5] => [1,1,2,2] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [4,2,3,5,1,6] => [1,3,2] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => [1,4,1] => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [6,4,2,3,5,1] => [1,1,3,1] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [2,5,3,4,1,6] => [2,2,2] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [2,5,3,4,6,1] => [2,3,1] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [2,3,6,4,5,1] => [3,2,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [6,2,5,3,4,1] => [1,2,2,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [5,4,2,3,1,6] => [1,1,2,2] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [5,4,2,3,6,1] => [1,1,3,1] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [4,6,2,3,5,1] => [2,3,1] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [6,2,4,5,3,1] => [1,3,1,1] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => [1,1,1,2,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [1,1,4] => 4
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [6,3,2,1,4,5] => [1,1,1,3] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [5,3,2,1,4,6] => [1,1,1,3] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [5,3,2,1,6,4] => [1,1,1,2,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [6,5,3,2,1,4] => [1,1,1,1,2] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => [1,2,3] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [6,3,2,4,1,5] => [1,1,2,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => [1,3,2] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => [1,4,1] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [6,3,2,4,5,1] => [1,1,3,1] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [5,3,2,4,1,6] => [1,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [5,3,2,4,6,1] => [1,1,3,1] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [3,6,2,4,5,1] => [2,3,1] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [6,5,3,2,4,1] => [1,1,1,2,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [2,4,3,1,5,6] => [2,1,3] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [6,2,4,3,1,5] => [1,2,1,2] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [2,4,3,5,1,6] => [2,2,2] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [2,4,3,5,6,1] => [2,3,1] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [6,2,4,3,5,1] => [1,2,2,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [2,3,5,4,1,6] => [3,1,2] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,5,4,6,1] => [3,2,1] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [2,3,4,6,5,1] => [4,1,1] => 4
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [6,2,3,5,4,1] => [1,3,1,1] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [5,2,4,3,1,6] => [1,2,1,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [5,2,4,3,6,1] => [1,2,2,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [2,6,4,3,5,1] => [2,1,2,1] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [4,2,6,5,3,1] => [1,2,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [6,5,2,4,3,1] => [1,1,2,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,3] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [6,4,3,2,1,5] => [1,1,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => [1,1,2,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => [1,1,3,1] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [6,4,3,2,5,1] => [1,1,1,2,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [3,5,2,4,1,6] => [2,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,5,2,4,6,1] => [2,3,1] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [3,2,6,4,5,1] => [1,2,2,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [6,3,5,2,4,1] => [1,2,2,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [3,5,4,2,1,6] => [2,1,1,2] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [3,5,4,2,6,1] => [2,1,2,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [3,4,6,2,5,1] => [3,2,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [3,4,6,5,2,1] => [3,1,1,1] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [6,3,5,4,2,1] => [1,2,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [1,1,1,2,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [4,6,3,2,5,1] => [2,1,2,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [4,6,3,5,2,1] => [2,2,1,1] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [3,6,5,4,2,1] => [2,1,1,1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [7] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => [1,6] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => [1,6] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [6,1,2,3,4,7,5] => [1,5,1] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => [1,1,5] => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => [1,6] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [7,5,1,2,3,4,6] => [1,1,5] => 5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [5,1,2,3,6,4,7] => [1,4,2] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [5,1,2,3,6,7,4] => [1,5,1] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [7,5,1,2,3,6,4] => [1,1,4,1] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [6,5,1,2,3,4,7] => [1,1,5] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [6,5,1,2,3,7,4] => [1,1,4,1] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [7,1,5,2,3,6,4] => [1,2,3,1] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => [1,1,1,4] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => [1,6] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [7,4,1,2,3,5,6] => [1,1,5] => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [6,4,1,2,3,5,7] => [1,1,5] => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [6,4,1,2,3,7,5] => [1,1,4,1] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [7,6,4,1,2,3,5] => [1,1,1,4] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [4,1,2,5,3,6,7] => [1,3,3] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [7,4,1,2,5,3,6] => [1,1,3,2] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [4,1,2,5,6,3,7] => [1,4,2] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [4,1,2,5,6,7,3] => [1,5,1] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [7,4,1,2,5,6,3] => [1,1,4,1] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [6,4,1,2,5,3,7] => [1,1,3,2] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [6,4,1,2,5,7,3] => [1,1,4,1] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [7,1,4,2,5,6,3] => [1,2,3,1] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [7,6,4,1,2,5,3] => [1,1,1,3,1] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => [1,1,5] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [7,5,4,1,2,3,6] => [1,1,1,4] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [5,4,1,2,6,3,7] => [1,1,3,2] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [5,4,1,2,6,7,3] => [1,1,4,1] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [7,5,4,1,2,6,3] => [1,1,1,3,1] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [6,1,4,2,5,3,7] => [1,2,2,2] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [6,1,4,2,5,7,3] => [1,2,3,1] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [7,1,2,4,5,6,3] => [1,5,1] => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [7,6,1,4,2,5,3] => [1,1,2,2,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [6,5,4,1,2,3,7] => [1,1,1,4] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [6,5,4,1,2,7,3] => [1,1,1,3,1] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [5,7,4,1,2,6,3] => [2,1,3,1] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [7,5,1,6,2,4,3] => [1,1,2,2,1] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => [1,1,1,1,3] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => [1,6] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [7,3,1,2,4,5,6] => [1,1,5] => 5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [6,3,1,2,4,5,7] => [1,1,5] => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [6,3,1,2,4,7,5] => [1,1,4,1] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [7,6,3,1,2,4,5] => [1,1,1,4] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [5,3,1,2,4,6,7] => [1,1,5] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [7,5,3,1,2,4,6] => [1,1,1,4] => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [5,3,1,2,6,4,7] => [1,1,3,2] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [5,3,1,2,6,7,4] => [1,1,4,1] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [7,5,3,1,2,6,4] => [1,1,1,3,1] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [6,5,3,1,2,4,7] => [1,1,1,4] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [6,5,3,1,2,7,4] => [1,1,1,3,1] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [7,3,5,1,2,6,4] => [1,2,3,1] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [7,6,5,3,1,2,4] => [1,1,1,1,3] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [3,1,4,2,5,6,7] => [1,2,4] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [7,3,1,4,2,5,6] => [1,1,2,3] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [6,3,1,4,2,5,7] => [1,1,2,3] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [6,3,1,4,2,7,5] => [1,1,2,2,1] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [7,6,3,1,4,2,5] => [1,1,1,2,2] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [3,1,4,5,2,6,7] => [1,3,3] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [7,3,1,4,5,2,6] => [1,1,3,2] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [3,1,4,5,6,2,7] => [1,4,2] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [3,1,4,5,6,7,2] => [1,5,1] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [7,3,1,4,5,6,2] => [1,1,4,1] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [6,3,1,4,5,2,7] => [1,1,3,2] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [6,3,1,4,5,7,2] => [1,1,4,1] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [7,1,3,4,5,6,2] => [1,5,1] => 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [7,6,3,1,4,5,2] => [1,1,1,3,1] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [5,3,1,4,2,6,7] => [1,1,2,3] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [7,5,3,1,4,2,6] => [1,1,1,2,2] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [5,3,1,4,6,2,7] => [1,1,3,2] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [5,3,1,4,6,7,2] => [1,1,4,1] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [7,5,3,1,4,6,2] => [1,1,1,3,1] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [6,1,3,4,5,2,7] => [1,4,2] => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [6,1,3,4,5,7,2] => [1,5,1] => 5
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [3,1,7,4,5,6,2] => [1,2,3,1] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [7,6,1,3,4,5,2] => [1,1,4,1] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [6,5,3,1,4,2,7] => [1,1,1,2,2] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [6,5,3,1,4,7,2] => [1,1,1,3,1] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [5,7,3,1,4,6,2] => [2,1,3,1] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [7,5,1,3,6,4,2] => [1,1,3,1,1] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [7,6,5,3,1,4,2] => [1,1,1,1,2,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [4,3,1,2,5,6,7] => [1,1,5] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [7,4,3,1,2,5,6] => [1,1,1,4] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [6,4,3,1,2,5,7] => [1,1,1,4] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [6,4,3,1,2,7,5] => [1,1,1,3,1] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [7,6,4,3,1,2,5] => [1,1,1,1,3] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [4,3,1,5,2,6,7] => [1,1,2,3] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [7,4,3,1,5,2,6] => [1,1,1,2,2] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [4,3,1,5,6,2,7] => [1,1,3,2] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [4,3,1,5,6,7,2] => [1,1,4,1] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [7,4,3,1,5,6,2] => [1,1,1,3,1] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [6,4,3,1,5,2,7] => [1,1,1,2,2] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [6,4,3,1,5,7,2] => [1,1,1,3,1] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [4,7,3,1,5,6,2] => [2,1,3,1] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [7,6,4,3,1,5,2] => [1,1,1,1,2,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [5,1,3,4,2,6,7] => [1,3,3] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [7,5,1,3,4,2,6] => [1,1,3,2] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [5,1,3,4,6,2,7] => [1,4,2] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [5,1,3,4,6,7,2] => [1,5,1] => 5
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [7,5,1,3,4,6,2] => [1,1,4,1] => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [3,1,6,4,5,2,7] => [1,2,2,2] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [3,1,6,4,5,7,2] => [1,2,3,1] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [3,1,4,7,5,6,2] => [1,3,2,1] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [7,3,1,6,4,5,2] => [1,1,2,2,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [6,5,1,3,4,2,7] => [1,1,3,2] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [6,5,1,3,4,7,2] => [1,1,4,1] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [7,1,5,3,4,6,2] => [1,2,3,1] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [7,3,1,5,6,4,2] => [1,1,3,1,1] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [7,6,5,1,3,4,2] => [1,1,1,3,1] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [5,4,3,1,2,6,7] => [1,1,1,4] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [7,5,4,3,1,2,6] => [1,1,1,1,3] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [5,4,3,1,6,2,7] => [1,1,1,2,2] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [5,4,3,1,6,7,2] => [1,1,1,3,1] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [7,5,4,3,1,6,2] => [1,1,1,1,2,1] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [4,6,3,1,5,2,7] => [2,1,2,2] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [4,6,3,1,5,7,2] => [2,1,3,1] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [4,7,1,3,5,6,2] => [2,4,1] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [7,4,6,3,1,5,2] => [1,2,1,2,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [6,4,1,5,3,2,7] => [1,1,2,1,2] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [6,4,1,5,3,7,2] => [1,1,2,2,1] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [7,1,4,5,3,6,2] => [1,3,2,1] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [4,7,1,5,6,3,2] => [2,3,1,1] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [7,6,4,1,5,3,2] => [1,1,1,2,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [6,5,4,3,1,2,7] => [1,1,1,1,3] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [6,5,4,3,1,7,2] => [1,1,1,1,2,1] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [5,7,4,3,1,6,2] => [2,1,1,2,1] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [5,7,4,6,1,3,2] => [2,2,2,1] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [7,6,1,4,5,3,2] => [1,1,3,1,1] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [7,6,5,4,3,1,2] => [1,1,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,6] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [7,2,1,3,4,5,6] => [1,1,5] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [6,2,1,3,4,5,7] => [1,1,5] => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [6,2,1,3,4,7,5] => [1,1,4,1] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [7,6,2,1,3,4,5] => [1,1,1,4] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [5,2,1,3,4,6,7] => [1,1,5] => 5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [7,5,2,1,3,4,6] => [1,1,1,4] => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [5,2,1,3,6,4,7] => [1,1,3,2] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [5,2,1,3,6,7,4] => [1,1,4,1] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [7,5,2,1,3,6,4] => [1,1,1,3,1] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [6,5,2,1,3,4,7] => [1,1,1,4] => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [6,5,2,1,3,7,4] => [1,1,1,3,1] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [7,2,5,1,3,6,4] => [1,2,3,1] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [7,6,5,2,1,3,4] => [1,1,1,1,3] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [4,2,1,3,5,6,7] => [1,1,5] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [7,4,2,1,3,5,6] => [1,1,1,4] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [6,4,2,1,3,5,7] => [1,1,1,4] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [6,4,2,1,3,7,5] => [1,1,1,3,1] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [7,6,4,2,1,3,5] => [1,1,1,1,3] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [4,2,1,5,3,6,7] => [1,1,2,3] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [7,4,2,1,5,3,6] => [1,1,1,2,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [4,2,1,5,6,3,7] => [1,1,3,2] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [4,2,1,5,6,7,3] => [1,1,4,1] => 4
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [7,4,2,1,5,6,3] => [1,1,1,3,1] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [6,4,2,1,5,3,7] => [1,1,1,2,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [6,4,2,1,5,7,3] => [1,1,1,3,1] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [7,2,4,1,5,6,3] => [1,2,3,1] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [7,6,4,2,1,5,3] => [1,1,1,1,2,1] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [5,4,2,1,3,6,7] => [1,1,1,4] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [7,5,4,2,1,3,6] => [1,1,1,1,3] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [5,4,2,1,6,3,7] => [1,1,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [5,4,2,1,6,7,3] => [1,1,1,3,1] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [7,5,4,2,1,6,3] => [1,1,1,1,2,1] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [6,2,4,1,5,3,7] => [1,2,2,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [6,2,4,1,5,7,3] => [1,2,3,1] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [7,2,1,4,5,6,3] => [1,1,4,1] => 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [7,6,2,4,1,5,3] => [1,1,2,2,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [6,5,4,2,1,3,7] => [1,1,1,1,3] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [6,5,4,2,1,7,3] => [1,1,1,1,2,1] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [5,7,4,2,1,6,3] => [2,1,1,2,1] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [7,5,2,6,1,4,3] => [1,1,2,2,1] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [7,6,5,4,2,1,3] => [1,1,1,1,1,2] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => [2,5] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [7,2,3,1,4,5,6] => [1,2,4] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [6,2,3,1,4,5,7] => [1,2,4] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [6,2,3,1,4,7,5] => [1,2,3,1] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [7,6,2,3,1,4,5] => [1,1,2,3] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [5,2,3,1,4,6,7] => [1,2,4] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [7,5,2,3,1,4,6] => [1,1,2,3] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [5,2,3,1,6,4,7] => [1,2,2,2] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [5,2,3,1,6,7,4] => [1,2,3,1] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [7,5,2,3,1,6,4] => [1,1,2,2,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [6,5,2,3,1,4,7] => [1,1,2,3] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [6,5,2,3,1,7,4] => [1,1,2,2,1] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [7,2,5,3,1,6,4] => [1,2,1,2,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [7,6,5,2,3,1,4] => [1,1,1,2,2] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => [3,4] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [7,2,3,4,1,5,6] => [1,3,3] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [6,2,3,4,1,5,7] => [1,3,3] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [6,2,3,4,1,7,5] => [1,3,2,1] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [7,6,2,3,4,1,5] => [1,1,3,2] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => [4,3] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [7,2,3,4,5,1,6] => [1,4,2] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => [5,2] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => [6,1] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [7,2,3,4,5,6,1] => [1,5,1] => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [6,2,3,4,5,1,7] => [1,4,2] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [6,2,3,4,5,7,1] => [1,5,1] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [2,7,3,4,5,6,1] => [2,4,1] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [7,6,2,3,4,5,1] => [1,1,4,1] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [5,2,3,4,1,6,7] => [1,3,3] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [7,5,2,3,4,1,6] => [1,1,3,2] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [5,2,3,4,6,1,7] => [1,4,2] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [5,2,3,4,6,7,1] => [1,5,1] => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [7,5,2,3,4,6,1] => [1,1,4,1] => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [2,6,3,4,5,1,7] => [2,3,2] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [2,6,3,4,5,7,1] => [2,4,1] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [2,3,7,4,5,6,1] => [3,3,1] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [7,2,6,3,4,5,1] => [1,2,3,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [6,5,2,3,4,1,7] => [1,1,3,2] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [6,5,2,3,4,7,1] => [1,1,4,1] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [5,7,2,3,4,6,1] => [2,4,1] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [7,2,5,3,6,4,1] => [1,2,2,1,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [7,6,5,2,3,4,1] => [1,1,1,3,1] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [4,2,3,1,5,6,7] => [1,2,4] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [7,4,2,3,1,5,6] => [1,1,2,3] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [6,4,2,3,1,5,7] => [1,1,2,3] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [6,4,2,3,1,7,5] => [1,1,2,2,1] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [7,6,4,2,3,1,5] => [1,1,1,2,2] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [4,2,3,5,1,6,7] => [1,3,3] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [7,4,2,3,5,1,6] => [1,1,3,2] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [4,2,3,5,6,1,7] => [1,4,2] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [4,2,3,5,6,7,1] => [1,5,1] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [7,4,2,3,5,6,1] => [1,1,4,1] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [6,4,2,3,5,1,7] => [1,1,3,2] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [6,4,2,3,5,7,1] => [1,1,4,1] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [4,7,2,3,5,6,1] => [2,4,1] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [7,6,4,2,3,5,1] => [1,1,1,3,1] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [2,5,3,4,1,6,7] => [2,2,3] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [7,2,5,3,4,1,6] => [1,2,2,2] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [2,5,3,4,6,1,7] => [2,3,2] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [2,5,3,4,6,7,1] => [2,4,1] => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [7,2,5,3,4,6,1] => [1,2,3,1] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [2,3,6,4,5,1,7] => [3,2,2] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [2,3,6,4,5,7,1] => [3,3,1] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [2,3,4,7,5,6,1] => [4,2,1] => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [7,2,3,6,4,5,1] => [1,3,2,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [6,2,5,3,4,1,7] => [1,2,2,2] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [6,2,5,3,4,7,1] => [1,2,3,1] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [2,7,5,3,4,6,1] => [2,1,3,1] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [7,2,3,5,6,4,1] => [1,4,1,1] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [7,6,2,5,3,4,1] => [1,1,2,2,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [5,4,2,3,1,6,7] => [1,1,2,3] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [7,5,4,2,3,1,6] => [1,1,1,2,2] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [5,4,2,3,6,1,7] => [1,1,3,2] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [5,4,2,3,6,7,1] => [1,1,4,1] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [7,5,4,2,3,6,1] => [1,1,1,3,1] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [4,6,2,3,5,1,7] => [2,3,2] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [4,6,2,3,5,7,1] => [2,4,1] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [4,2,7,3,5,6,1] => [1,2,3,1] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [7,4,6,2,3,5,1] => [1,2,3,1] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [6,2,4,5,3,1,7] => [1,3,1,2] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [6,2,4,5,3,7,1] => [1,3,2,1] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [2,7,4,5,3,6,1] => [2,2,2,1] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [4,2,7,5,6,3,1] => [1,2,2,1,1] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [7,6,2,4,5,3,1] => [1,1,3,1,1] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [6,5,4,2,3,1,7] => [1,1,1,2,2] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [6,5,4,2,3,7,1] => [1,1,1,3,1] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [5,7,4,2,3,6,1] => [2,1,3,1] => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [5,7,4,2,6,3,1] => [2,1,2,1,1] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [7,2,6,4,5,3,1] => [1,2,2,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [7,6,5,4,2,3,1] => [1,1,1,1,2,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,5] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [7,3,2,1,4,5,6] => [1,1,1,4] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [6,3,2,1,4,5,7] => [1,1,1,4] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [6,3,2,1,4,7,5] => [1,1,1,3,1] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [7,6,3,2,1,4,5] => [1,1,1,1,3] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [5,3,2,1,4,6,7] => [1,1,1,4] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [7,5,3,2,1,4,6] => [1,1,1,1,3] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [5,3,2,1,6,4,7] => [1,1,1,2,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [5,3,2,1,6,7,4] => [1,1,1,3,1] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [7,5,3,2,1,6,4] => [1,1,1,1,2,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [6,5,3,2,1,4,7] => [1,1,1,1,3] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [6,5,3,2,1,7,4] => [1,1,1,1,2,1] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [7,3,5,2,1,6,4] => [1,2,1,2,1] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [7,6,5,3,2,1,4] => [1,1,1,1,1,2] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7] => [1,2,4] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [7,3,2,4,1,5,6] => [1,1,2,3] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [6,3,2,4,1,5,7] => [1,1,2,3] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [6,3,2,4,1,7,5] => [1,1,2,2,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [7,6,3,2,4,1,5] => [1,1,1,2,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7] => [1,3,3] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [7,3,2,4,5,1,6] => [1,1,3,2] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7] => [1,4,2] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => [1,5,1] => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [7,3,2,4,5,6,1] => [1,1,4,1] => 4
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [6,3,2,4,5,1,7] => [1,1,3,2] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [6,3,2,4,5,7,1] => [1,1,4,1] => 4
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [3,7,2,4,5,6,1] => [2,4,1] => 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [7,6,3,2,4,5,1] => [1,1,1,3,1] => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [5,3,2,4,1,6,7] => [1,1,2,3] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [7,5,3,2,4,1,6] => [1,1,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [5,3,2,4,6,1,7] => [1,1,3,2] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [5,3,2,4,6,7,1] => [1,1,4,1] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [7,5,3,2,4,6,1] => [1,1,1,3,1] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [3,6,2,4,5,1,7] => [2,3,2] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [3,6,2,4,5,7,1] => [2,4,1] => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [3,2,7,4,5,6,1] => [1,2,3,1] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [7,3,6,2,4,5,1] => [1,2,3,1] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [6,5,3,2,4,1,7] => [1,1,1,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [6,5,3,2,4,7,1] => [1,1,1,3,1] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [5,7,3,2,4,6,1] => [2,1,3,1] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [7,3,5,2,6,4,1] => [1,2,2,1,1] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [7,6,5,3,2,4,1] => [1,1,1,1,2,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [2,4,3,1,5,6,7] => [2,1,4] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [7,2,4,3,1,5,6] => [1,2,1,3] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [6,2,4,3,1,5,7] => [1,2,1,3] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [6,2,4,3,1,7,5] => [1,2,1,2,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [7,6,2,4,3,1,5] => [1,1,2,1,2] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [2,4,3,5,1,6,7] => [2,2,3] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [7,2,4,3,5,1,6] => [1,2,2,2] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [2,4,3,5,6,1,7] => [2,3,2] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [2,4,3,5,6,7,1] => [2,4,1] => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [7,2,4,3,5,6,1] => [1,2,3,1] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [6,2,4,3,5,1,7] => [1,2,2,2] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [6,2,4,3,5,7,1] => [1,2,3,1] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [2,7,4,3,5,6,1] => [2,1,3,1] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [7,6,2,4,3,5,1] => [1,1,2,2,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [2,3,5,4,1,6,7] => [3,1,3] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [7,2,3,5,4,1,6] => [1,3,1,2] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [2,3,5,4,6,1,7] => [3,2,2] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [2,3,5,4,6,7,1] => [3,3,1] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [7,2,3,5,4,6,1] => [1,3,2,1] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [2,3,4,6,5,1,7] => [4,1,2] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [2,3,4,6,5,7,1] => [4,2,1] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [2,3,4,5,7,6,1] => [5,1,1] => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [7,2,3,4,6,5,1] => [1,4,1,1] => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [6,2,3,5,4,1,7] => [1,3,1,2] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [6,2,3,5,4,7,1] => [1,3,2,1] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [2,7,3,5,4,6,1] => [2,2,2,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [5,2,3,7,6,4,1] => [1,3,1,1,1] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [7,6,2,3,5,4,1] => [1,1,3,1,1] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [5,2,4,3,1,6,7] => [1,2,1,3] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [7,5,2,4,3,1,6] => [1,1,2,1,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [5,2,4,3,6,1,7] => [1,2,2,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [5,2,4,3,6,7,1] => [1,2,3,1] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [7,5,2,4,3,6,1] => [1,1,2,2,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [2,6,4,3,5,1,7] => [2,1,2,2] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [2,6,4,3,5,7,1] => [2,1,3,1] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [2,4,7,3,5,6,1] => [3,3,1] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [7,2,6,4,3,5,1] => [1,2,1,2,1] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [4,2,6,5,3,1,7] => [1,2,1,1,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [4,2,6,5,3,7,1] => [1,2,1,2,1] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [4,2,5,7,3,6,1] => [1,3,2,1] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [4,2,5,7,6,3,1] => [1,3,1,1,1] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [7,4,2,6,5,3,1] => [1,1,2,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [6,5,2,4,3,1,7] => [1,1,2,1,2] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [6,5,2,4,3,7,1] => [1,1,2,2,1] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [5,7,2,4,3,6,1] => [2,2,2,1] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [7,2,5,4,6,3,1] => [1,2,2,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [7,2,4,6,5,3,1] => [1,3,1,1,1] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [7,6,5,2,4,3,1] => [1,1,1,2,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,4] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [7,4,3,2,1,5,6] => [1,1,1,1,3] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [6,4,3,2,1,5,7] => [1,1,1,1,3] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [6,4,3,2,1,7,5] => [1,1,1,1,2,1] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [7,6,4,3,2,1,5] => [1,1,1,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7] => [1,1,2,3] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [7,4,3,2,5,1,6] => [1,1,1,2,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1,7] => [1,1,3,2] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => [1,1,4,1] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [7,4,3,2,5,6,1] => [1,1,1,3,1] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [6,4,3,2,5,1,7] => [1,1,1,2,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [6,4,3,2,5,7,1] => [1,1,1,3,1] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [4,7,3,2,5,6,1] => [2,1,3,1] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [7,6,4,3,2,5,1] => [1,1,1,1,2,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [3,5,2,4,1,6,7] => [2,2,3] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [7,3,5,2,4,1,6] => [1,2,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [3,5,2,4,6,1,7] => [2,3,2] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [3,5,2,4,6,7,1] => [2,4,1] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [7,3,5,2,4,6,1] => [1,2,3,1] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [3,2,6,4,5,1,7] => [1,2,2,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [3,2,6,4,5,7,1] => [1,2,3,1] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [3,2,4,7,5,6,1] => [1,3,2,1] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [7,3,2,6,4,5,1] => [1,1,2,2,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [6,3,5,2,4,1,7] => [1,2,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [6,3,5,2,4,7,1] => [1,2,3,1] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [3,7,5,2,4,6,1] => [2,1,3,1] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [7,3,2,5,6,4,1] => [1,1,3,1,1] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [7,6,3,5,2,4,1] => [1,1,2,2,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [3,5,4,2,1,6,7] => [2,1,1,3] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [7,3,5,4,2,1,6] => [1,2,1,1,2] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [3,5,4,2,6,1,7] => [2,1,2,2] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [3,5,4,2,6,7,1] => [2,1,3,1] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [7,3,5,4,2,6,1] => [1,2,1,2,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [3,4,6,2,5,1,7] => [3,2,2] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [3,4,6,2,5,7,1] => [3,3,1] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [3,4,2,7,5,6,1] => [2,2,2,1] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [7,3,4,6,2,5,1] => [1,3,2,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [3,4,6,5,2,1,7] => [3,1,1,2] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [3,4,6,5,2,7,1] => [3,1,2,1] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [3,4,5,7,2,6,1] => [4,2,1] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [3,4,5,7,6,2,1] => [4,1,1,1] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [7,3,4,6,5,2,1] => [1,3,1,1,1] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [6,3,5,4,2,1,7] => [1,2,1,1,2] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [6,3,5,4,2,7,1] => [1,2,1,2,1] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [3,7,5,4,2,6,1] => [2,1,1,2,1] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [3,7,5,4,6,2,1] => [2,1,2,1,1] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [3,7,4,6,5,2,1] => [2,2,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [7,6,3,5,4,2,1] => [1,1,2,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,3] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [7,5,4,3,2,1,6] => [1,1,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1,7] => [1,1,1,2,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1] => [1,1,1,3,1] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [7,5,4,3,2,6,1] => [1,1,1,1,2,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [4,6,3,2,5,1,7] => [2,1,2,2] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [4,6,3,2,5,7,1] => [2,1,3,1] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [4,3,7,2,5,6,1] => [1,2,3,1] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [7,4,6,3,2,5,1] => [1,2,1,2,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [4,6,3,5,2,1,7] => [2,2,1,2] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [4,6,3,5,2,7,1] => [2,2,2,1] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [4,3,7,5,2,6,1] => [1,2,1,2,1] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [4,3,7,5,6,2,1] => [1,2,2,1,1] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [7,4,6,3,5,2,1] => [1,2,2,1,1] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [3,6,5,4,2,1,7] => [2,1,1,1,2] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [3,6,5,4,2,7,1] => [2,1,1,2,1] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [3,5,7,4,2,6,1] => [3,1,2,1] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [3,5,7,4,6,2,1] => [3,2,1,1] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [3,4,7,6,5,2,1] => [3,1,1,1,1] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [7,3,6,5,4,2,1] => [1,2,1,1,1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1] => [1,1,1,1,2,1] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [5,7,4,3,2,6,1] => [2,1,1,2,1] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [5,7,4,3,6,2,1] => [2,1,2,1,1] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [4,7,6,3,5,2,1] => [2,1,2,1,1] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [4,7,6,5,3,2,1] => [2,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [8] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => [1,7] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => [1,7] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [7,1,2,3,4,5,8,6] => [1,6,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [8,7,1,2,3,4,5,6] => [1,1,6] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => [1,7] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [8,6,1,2,3,4,5,7] => [1,1,6] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [6,1,2,3,4,7,5,8] => [1,5,2] => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [6,1,2,3,4,7,8,5] => [1,6,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [8,6,1,2,3,4,7,5] => [1,1,5,1] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [7,6,1,2,3,4,5,8] => [1,1,6] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [7,6,1,2,3,4,8,5] => [1,1,5,1] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => [8,1,6,2,3,4,7,5] => [1,2,4,1] => 4
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [8,7,6,1,2,3,4,5] => [1,1,1,5] => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => [1,7] => 7
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [8,5,1,2,3,4,6,7] => [1,1,6] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [7,5,1,2,3,4,6,8] => [1,1,6] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [7,5,1,2,3,4,8,6] => [1,1,5,1] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [8,7,5,1,2,3,4,6] => [1,1,1,5] => 5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [5,1,2,3,6,4,7,8] => [1,4,3] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [5,1,2,3,6,7,4,8] => [1,5,2] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [5,1,2,3,6,7,8,4] => [1,6,1] => 6
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [8,5,1,2,3,6,7,4] => [1,1,5,1] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [7,5,1,2,3,6,8,4] => [1,1,5,1] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => [8,1,5,2,3,6,7,4] => [1,2,4,1] => 4
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [8,7,5,1,2,3,6,4] => [1,1,1,4,1] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [6,5,1,2,3,4,7,8] => [1,1,6] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [8,6,5,1,2,3,4,7] => [1,1,1,5] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [6,5,1,2,3,7,8,4] => [1,1,5,1] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [8,6,5,1,2,3,7,4] => [1,1,1,4,1] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => [7,1,5,2,3,6,4,8] => [1,2,3,2] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => [7,1,5,2,3,6,8,4] => [1,2,4,1] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => [8,1,2,5,3,6,7,4] => [1,3,3,1] => 3
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => [8,7,1,5,2,3,6,4] => [1,1,2,3,1] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [7,6,5,1,2,3,4,8] => [1,1,1,5] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [7,6,5,1,2,3,8,4] => [1,1,1,4,1] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => [6,8,5,1,2,3,7,4] => [2,1,4,1] => 4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => [8,6,1,7,2,3,5,4] => [1,1,2,3,1] => 3
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [8,7,6,5,1,2,3,4] => [1,1,1,1,4] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => [1,7] => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [8,4,1,2,3,5,6,7] => [1,1,6] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [7,4,1,2,3,5,6,8] => [1,1,6] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [7,4,1,2,3,5,8,6] => [1,1,5,1] => 5
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [8,7,4,1,2,3,5,6] => [1,1,1,5] => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [6,4,1,2,3,5,7,8] => [1,1,6] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [8,6,4,1,2,3,5,7] => [1,1,1,5] => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [6,4,1,2,3,7,8,5] => [1,1,5,1] => 5
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [8,6,4,1,2,3,7,5] => [1,1,1,4,1] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,6,5,8] => [7,6,4,1,2,3,5,8] => [1,1,1,5] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [7,6,4,1,2,3,8,5] => [1,1,1,4,1] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => [8,4,6,1,2,3,7,5] => [1,2,4,1] => 4
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [8,7,6,4,1,2,3,5] => [1,1,1,1,4] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [4,1,2,5,3,6,7,8] => [1,3,4] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6,8,7] => [8,4,1,2,5,3,6,7] => [1,1,3,3] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [7,4,1,2,5,3,6,8] => [1,1,3,3] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [7,4,1,2,5,3,8,6] => [1,1,3,2,1] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [8,7,4,1,2,5,3,6] => [1,1,1,3,2] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [4,1,2,5,6,3,7,8] => [1,4,3] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [8,4,1,2,5,6,3,7] => [1,1,4,2] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [4,1,2,5,6,7,3,8] => [1,5,2] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [4,1,2,5,6,7,8,3] => [1,6,1] => 6
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [8,4,1,2,5,6,7,3] => [1,1,5,1] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,4,5,7,6,3,8] => [7,4,1,2,5,6,3,8] => [1,1,4,2] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => [8,1,4,2,5,6,7,3] => [1,2,4,1] => 4
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [8,7,4,1,2,5,6,3] => [1,1,1,4,1] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [6,4,1,2,5,3,7,8] => [1,1,3,3] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,6,5,3,8,7] => [8,6,4,1,2,5,3,7] => [1,1,1,3,2] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,5,7,3,8] => [6,4,1,2,5,7,3,8] => [1,1,4,2] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,4,6,5,7,8,3] => [6,4,1,2,5,7,8,3] => [1,1,5,1] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [8,6,4,1,2,5,7,3] => [1,1,1,4,1] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,4,7,5,6,3,8] => [7,1,4,2,5,6,3,8] => [1,2,3,2] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => [8,1,2,4,5,6,7,3] => [1,6,1] => 6
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,8,5,7,6,3] => [8,7,1,4,2,5,6,3] => [1,1,2,3,1] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,6,5,3,8] => [7,6,4,1,2,5,3,8] => [1,1,1,3,2] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [7,6,4,1,2,5,8,3] => [1,1,1,4,1] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,8,6,5,7,3] => [6,8,4,1,2,5,7,3] => [2,1,4,1] => 4
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,8,6,7,5,3] => [8,6,1,4,2,7,5,3] => [1,1,2,2,1,1] => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [8,7,6,4,1,2,5,3] => [1,1,1,1,3,1] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [5,4,1,2,3,6,7,8] => [1,1,6] => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [8,5,4,1,2,3,6,7] => [1,1,1,5] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,4,3,7,6,8] => [7,5,4,1,2,3,6,8] => [1,1,1,5] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [7,5,4,1,2,3,8,6] => [1,1,1,4,1] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [8,7,5,4,1,2,3,6] => [1,1,1,1,4] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,5,4,6,3,8,7] => [8,5,4,1,2,6,3,7] => [1,1,1,3,2] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [5,4,1,2,6,7,3,8] => [1,1,4,2] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [5,4,1,2,6,7,8,3] => [1,1,5,1] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,2,5,4,7,6,3,8] => [7,5,4,1,2,6,3,8] => [1,1,1,3,2] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [7,5,4,1,2,6,8,3] => [1,1,1,4,1] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => [5,8,4,1,2,6,7,3] => [2,1,4,1] => 4
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [8,7,5,4,1,2,6,3] => [1,1,1,1,3,1] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => [6,1,4,2,5,3,7,8] => [1,2,2,3] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => [6,1,4,2,5,7,8,3] => [1,2,4,1] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,6,4,5,8,7,3] => [8,6,1,4,2,5,7,3] => [1,1,2,3,1] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,7,4,5,6,3,8] => [7,1,2,4,5,6,3,8] => [1,5,2] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => [7,1,2,4,5,6,8,3] => [1,6,1] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => [4,1,2,8,5,6,7,3] => [1,3,3,1] => 3
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,8,4,5,7,6,3] => [8,7,1,2,4,5,6,3] => [1,1,5,1] => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,7,4,6,5,3,8] => [7,6,1,4,2,5,3,8] => [1,1,2,2,2] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,7,4,6,5,8,3] => [7,6,1,4,2,5,8,3] => [1,1,2,3,1] => 3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,8,4,6,7,5,3] => [8,6,1,2,4,7,5,3] => [1,1,4,1,1] => 4
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => [8,7,6,1,4,2,5,3] => [1,1,1,2,2,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [6,5,4,1,2,3,7,8] => [1,1,1,5] => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,5,4,3,8,7] => [8,6,5,4,1,2,3,7] => [1,1,1,1,4] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [6,5,4,1,2,7,8,3] => [1,1,1,4,1] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [8,6,5,4,1,2,7,3] => [1,1,1,1,3,1] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,7,5,4,6,8,3] => [5,7,4,1,2,6,8,3] => [2,1,4,1] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => [5,8,1,4,2,6,7,3] => [2,2,3,1] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,7,5,6,4,3,8] => [7,5,1,6,2,4,3,8] => [1,1,2,2,2] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,7,5,6,4,8,3] => [7,5,1,6,2,4,8,3] => [1,1,2,3,1] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,8,5,6,4,7,3] => [8,1,5,6,2,4,7,3] => [1,3,3,1] => 3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => [8,5,1,2,6,7,4,3] => [1,1,4,1,1] => 4
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,8,5,7,6,4,3] => [8,7,5,1,6,2,4,3] => [1,1,1,2,2,1] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [7,6,5,4,1,2,3,8] => [1,1,1,1,4] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [7,6,5,4,1,2,8,3] => [1,1,1,1,3,1] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => [6,8,5,4,1,2,7,3] => [2,1,1,3,1] => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => [6,8,5,7,1,2,4,3] => [2,2,3,1] => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => [8,7,1,5,6,2,4,3] => [1,1,3,2,1] => 3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [8,7,6,5,4,1,2,3] => [1,1,1,1,1,3] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [1,7] => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [8,3,1,2,4,5,6,7] => [1,1,6] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [7,3,1,2,4,5,6,8] => [1,1,6] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [7,3,1,2,4,5,8,6] => [1,1,5,1] => 5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [6,3,1,2,4,5,7,8] => [1,1,6] => 6
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [6,3,1,2,4,7,8,5] => [1,1,5,1] => 5
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [8,6,3,1,2,4,7,5] => [1,1,1,4,1] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [7,6,3,1,2,4,5,8] => [1,1,1,5] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [7,6,3,1,2,4,8,5] => [1,1,1,4,1] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => [8,3,6,1,2,4,7,5] => [1,2,4,1] => 4
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [8,7,6,3,1,2,4,5] => [1,1,1,1,4] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [5,3,1,2,4,6,7,8] => [1,1,6] => 6
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,4,6,8,7] => [8,5,3,1,2,4,6,7] => [1,1,1,5] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [7,5,3,1,2,4,6,8] => [1,1,1,5] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [7,5,3,1,2,4,8,6] => [1,1,1,4,1] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [8,7,5,3,1,2,4,6] => [1,1,1,1,4] => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [8,5,3,1,2,6,4,7] => [1,1,1,3,2] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [5,3,1,2,6,7,4,8] => [1,1,4,2] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [5,3,1,2,6,7,8,4] => [1,1,5,1] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [8,5,3,1,2,6,7,4] => [1,1,1,4,1] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [7,5,3,1,2,6,4,8] => [1,1,1,3,2] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [7,5,3,1,2,6,8,4] => [1,1,1,4,1] => 4
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [8,7,5,3,1,2,6,4] => [1,1,1,1,3,1] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [8,6,5,3,1,2,4,7] => [1,1,1,1,4] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [6,5,3,1,2,7,4,8] => [1,1,1,3,2] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [6,5,3,1,2,7,8,4] => [1,1,1,4,1] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [8,6,5,3,1,2,7,4] => [1,1,1,1,3,1] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,7,5,6,4,8] => [7,3,5,1,2,6,4,8] => [1,2,3,2] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,8,5,6,7,4] => [8,3,1,5,2,6,7,4] => [1,1,2,3,1] => 3
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [8,7,3,5,1,2,6,4] => [1,1,2,3,1] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [7,6,5,3,1,2,4,8] => [1,1,1,1,4] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [7,6,5,3,1,2,8,4] => [1,1,1,1,3,1] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => [6,8,5,3,1,2,7,4] => [2,1,1,3,1] => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [8,7,6,5,3,1,2,4] => [1,1,1,1,1,3] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [3,1,4,2,5,6,7,8] => [1,2,5] => 5
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [8,3,1,4,2,5,6,7] => [1,1,2,4] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [7,3,1,4,2,5,8,6] => [1,1,2,3,1] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => [8,7,3,1,4,2,5,6] => [1,1,1,2,3] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [8,6,3,1,4,2,5,7] => [1,1,1,2,3] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [6,3,1,4,2,7,5,8] => [1,1,2,2,2] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [6,3,1,4,2,7,8,5] => [1,1,2,3,1] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [8,6,3,1,4,2,7,5] => [1,1,1,2,2,1] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,4,2,7,6,5,8] => [7,6,3,1,4,2,5,8] => [1,1,1,2,3] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [7,6,3,1,4,2,8,5] => [1,1,1,2,2,1] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => [8,3,6,1,4,2,7,5] => [1,2,2,2,1] => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [8,7,6,3,1,4,2,5] => [1,1,1,1,2,2] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [3,1,4,5,2,6,7,8] => [1,3,4] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [7,3,1,4,5,2,6,8] => [1,1,3,3] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [7,3,1,4,5,2,8,6] => [1,1,3,2,1] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [8,7,3,1,4,5,2,6] => [1,1,1,3,2] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [3,1,4,5,6,2,7,8] => [1,4,3] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [3,1,4,5,6,7,2,8] => [1,5,2] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [3,1,4,5,6,7,8,2] => [1,6,1] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [8,3,1,4,5,6,7,2] => [1,1,5,1] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [7,3,1,4,5,6,2,8] => [1,1,4,2] => 4
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [7,3,1,4,5,6,8,2] => [1,1,5,1] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [8,1,3,4,5,6,7,2] => [1,6,1] => 6
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [8,7,3,1,4,5,6,2] => [1,1,1,4,1] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,3,4,6,5,2,7,8] => [6,3,1,4,5,2,7,8] => [1,1,3,3] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,3,4,6,5,2,8,7] => [8,6,3,1,4,5,2,7] => [1,1,1,3,2] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [6,3,1,4,5,7,8,2] => [1,1,5,1] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,4,6,5,8,7,2] => [8,6,3,1,4,5,7,2] => [1,1,1,4,1] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,7,5,6,8,2] => [7,1,3,4,5,6,8,2] => [1,6,1] => 6
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => [3,1,8,4,5,6,7,2] => [1,2,4,1] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [7,6,3,1,4,5,8,2] => [1,1,1,4,1] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,8,6,5,7,2] => [6,8,3,1,4,5,7,2] => [2,1,4,1] => 4
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [8,7,6,3,1,4,5,2] => [1,1,1,1,3,1] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => [5,3,1,4,2,6,7,8] => [1,1,2,4] => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [8,5,3,1,4,2,6,7] => [1,1,1,2,3] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [7,5,3,1,4,2,6,8] => [1,1,1,2,3] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [7,5,3,1,4,2,8,6] => [1,1,1,2,2,1] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,3,5,4,2,8,7,6] => [8,7,5,3,1,4,2,6] => [1,1,1,1,2,2] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,3,5,4,6,2,7,8] => [5,3,1,4,6,2,7,8] => [1,1,3,3] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,4,6,7,2,8] => [5,3,1,4,6,7,2,8] => [1,1,4,2] => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => [5,3,1,4,6,7,8,2] => [1,1,5,1] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,4,6,8,7,2] => [8,5,3,1,4,6,7,2] => [1,1,1,4,1] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [7,5,3,1,4,6,2,8] => [1,1,1,3,2] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [7,5,3,1,4,6,8,2] => [1,1,1,4,1] => 4
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [8,7,5,3,1,4,6,2] => [1,1,1,1,3,1] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => [6,1,3,4,5,7,8,2] => [1,6,1] => 6
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => [8,6,1,3,4,5,7,2] => [1,1,5,1] => 5
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,7,4,5,6,2,8] => [3,1,7,4,5,6,2,8] => [1,2,3,2] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => [3,1,7,4,5,6,8,2] => [1,2,4,1] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => [3,1,4,8,5,6,7,2] => [1,3,3,1] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,8,4,6,5,7,2] => [8,1,6,3,4,5,7,2] => [1,2,4,1] => 4
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,8,4,7,6,5,2] => [8,7,6,1,3,4,5,2] => [1,1,1,4,1] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,5,4,2,7,8] => [6,5,3,1,4,2,7,8] => [1,1,1,2,3] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [6,5,3,1,4,7,2,8] => [1,1,1,3,2] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,7,5,4,6,8,2] => [5,7,3,1,4,6,8,2] => [2,1,4,1] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => [5,8,1,3,4,6,7,2] => [2,5,1] => 5
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,7,5,6,4,2,8] => [7,5,1,3,6,4,2,8] => [1,1,3,1,2] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,8,5,6,4,7,2] => [8,1,5,3,6,4,7,2] => [1,2,2,2,1] => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => [8,3,1,5,6,7,4,2] => [1,1,4,1,1] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => [7,6,5,3,1,4,2,8] => [1,1,1,1,2,2] => 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [6,8,5,3,1,7,4,2] => [2,1,1,2,1,1] => 2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [8,7,6,5,3,1,4,2] => [1,1,1,1,1,2,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [4,3,1,2,5,6,7,8] => [1,1,6] => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [8,4,3,1,2,5,6,7] => [1,1,1,5] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [7,4,3,1,2,5,6,8] => [1,1,1,5] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [7,4,3,1,2,5,8,6] => [1,1,1,4,1] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [8,7,4,3,1,2,5,6] => [1,1,1,1,4] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,3,2,6,5,7,8] => [6,4,3,1,2,5,7,8] => [1,1,1,5] => 5
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,3,2,6,5,8,7] => [8,6,4,3,1,2,5,7] => [1,1,1,1,4] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [6,4,3,1,2,7,5,8] => [1,1,1,3,2] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [6,4,3,1,2,7,8,5] => [1,1,1,4,1] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [8,6,4,3,1,2,7,5] => [1,1,1,1,3,1] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [7,6,4,3,1,2,5,8] => [1,1,1,1,4] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [7,6,4,3,1,2,8,5] => [1,1,1,1,3,1] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,8,6,7,5] => [8,4,6,3,1,2,7,5] => [1,2,1,3,1] => 3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [8,7,6,4,3,1,2,5] => [1,1,1,1,1,3] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,3,5,2,6,8,7] => [8,4,3,1,5,2,6,7] => [1,1,1,2,3] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [7,4,3,1,5,2,6,8] => [1,1,1,2,3] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3,5,2,7,8,6] => [7,4,3,1,5,2,8,6] => [1,1,1,2,2,1] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3,5,2,8,7,6] => [8,7,4,3,1,5,2,6] => [1,1,1,1,2,2] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [4,3,1,5,6,2,7,8] => [1,1,3,3] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [4,3,1,5,6,7,8,2] => [1,1,5,1] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,3,5,6,8,7,2] => [8,4,3,1,5,6,7,2] => [1,1,1,4,1] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [7,4,3,1,5,6,2,8] => [1,1,1,3,2] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,3,5,7,6,8,2] => [7,4,3,1,5,6,8,2] => [1,1,1,4,1] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [4,8,3,1,5,6,7,2] => [2,1,4,1] => 4
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [8,7,4,3,1,5,6,2] => [1,1,1,1,3,1] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [6,4,3,1,5,2,7,8] => [1,1,1,2,3] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [6,4,3,1,5,7,2,8] => [1,1,1,3,2] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [6,4,3,1,5,7,8,2] => [1,1,1,4,1] => 4
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [8,6,4,3,1,5,7,2] => [1,1,1,1,3,1] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,3,7,5,6,2,8] => [4,7,3,1,5,6,2,8] => [2,1,3,2] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [4,8,1,3,5,6,7,2] => [2,5,1] => 5
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => [8,4,7,3,1,5,6,2] => [1,2,1,3,1] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,3,7,6,5,2,8] => [7,6,4,3,1,5,2,8] => [1,1,1,1,2,2] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => [6,8,4,3,1,5,7,2] => [2,1,1,3,1] => 3
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => [8,4,6,3,1,7,5,2] => [1,2,1,2,1,1] => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [8,7,6,4,3,1,5,2] => [1,1,1,1,1,2,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => [5,1,3,4,2,6,7,8] => [1,3,4] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,5,3,4,2,7,6,8] => [7,5,1,3,4,2,6,8] => [1,1,3,3] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => [7,5,1,3,4,2,8,6] => [1,1,3,2,1] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => [8,7,5,1,3,4,2,6] => [1,1,1,3,2] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,5,3,4,6,2,7,8] => [5,1,3,4,6,2,7,8] => [1,4,3] => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,3,4,6,2,8,7] => [8,5,1,3,4,6,2,7] => [1,1,4,2] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,5,3,4,6,7,2,8] => [5,1,3,4,6,7,2,8] => [1,5,2] => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [5,1,3,4,6,7,8,2] => [1,6,1] => 6
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,5,3,4,8,6,7,2] => [8,1,5,3,4,6,7,2] => [1,2,4,1] => 4
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,5,3,4,8,7,6,2] => [8,7,5,1,3,4,6,2] => [1,1,1,4,1] => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => [3,1,6,4,5,2,7,8] => [1,2,2,3] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,6,3,4,5,7,2,8] => [3,1,6,4,5,7,2,8] => [1,2,3,2] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,6,3,4,5,7,8,2] => [3,1,6,4,5,7,8,2] => [1,2,4,1] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => [3,1,4,7,5,6,2,8] => [1,3,2,2] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [3,1,4,5,8,6,7,2] => [1,4,2,1] => 4
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8,3,4,5,7,6,2] => [8,3,1,4,7,5,6,2] => [1,1,3,2,1] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,7,3,4,6,5,2,8] => [7,3,1,6,4,5,2,8] => [1,1,2,2,2] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => [8,3,1,4,6,7,5,2] => [1,1,4,1,1] => 4
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => [8,7,3,1,6,4,5,2] => [1,1,1,2,2,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => [6,5,1,3,4,2,7,8] => [1,1,3,3] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,6,3,5,4,7,2,8] => [6,5,1,3,4,7,2,8] => [1,1,4,2] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,6,3,5,4,7,8,2] => [6,5,1,3,4,7,8,2] => [1,1,5,1] => 5
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => [8,6,5,1,3,4,7,2] => [1,1,1,4,1] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => [5,1,8,3,4,6,7,2] => [1,2,4,1] => 4
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,8,3,5,4,7,6,2] => [8,7,1,5,3,4,6,2] => [1,1,2,3,1] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => [8,1,3,5,6,4,7,2] => [1,4,2,1] => 4
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8,3,5,6,7,4,2] => [5,3,1,8,6,7,4,2] => [1,1,2,2,1,1] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,7,3,6,5,4,2,8] => [7,6,5,1,3,4,2,8] => [1,1,1,3,2] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => [7,6,5,1,3,4,8,2] => [1,1,1,4,1] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => [6,8,5,1,3,4,7,2] => [2,1,4,1] => 4
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,8,3,6,5,7,4,2] => [8,6,1,5,3,7,4,2] => [1,1,2,2,1,1] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => [8,7,1,3,5,6,4,2] => [1,1,4,1,1] => 4
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => [8,7,6,5,1,3,4,2] => [1,1,1,1,3,1] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [5,4,3,1,2,6,7,8] => [1,1,1,5] => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,4,3,2,6,8,7] => [8,5,4,3,1,2,6,7] => [1,1,1,1,4] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [7,5,4,3,1,2,8,6] => [1,1,1,1,3,1] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [8,7,5,4,3,1,2,6] => [1,1,1,1,1,3] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [5,4,3,1,6,2,7,8] => [1,1,1,2,3] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [5,4,3,1,6,7,2,8] => [1,1,1,3,2] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [5,4,3,1,6,7,8,2] => [1,1,1,4,1] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [8,5,4,3,1,6,7,2] => [1,1,1,1,3,1] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,4,3,7,6,8,2] => [7,5,4,3,1,6,8,2] => [1,1,1,1,3,1] => 3
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [8,7,5,4,3,1,6,2] => [1,1,1,1,1,2,1] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => [4,6,3,1,5,2,7,8] => [2,1,2,3] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => [8,4,6,3,1,5,7,2] => [1,2,1,3,1] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [4,3,1,8,5,6,7,2] => [1,1,2,3,1] => 3
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => [8,4,7,1,3,5,6,2] => [1,2,4,1] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => [4,8,6,3,1,5,7,2] => [2,1,1,3,1] => 3
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,8,4,3,6,7,5,2] => [8,4,6,1,3,7,5,2] => [1,2,3,1,1] => 3
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,8,4,3,7,6,5,2] => [8,7,4,6,3,1,5,2] => [1,1,2,1,2,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => [6,4,1,5,3,2,7,8] => [1,1,2,1,3] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => [8,6,4,1,5,3,2,7] => [1,1,1,2,1,2] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7,4,5,3,6,8,2] => [7,1,4,5,3,6,8,2] => [1,3,3,1] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [4,1,8,5,3,6,7,2] => [1,2,1,3,1] => 3
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,8,4,5,3,7,6,2] => [8,7,1,4,5,3,6,2] => [1,1,3,2,1] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,7,4,5,6,3,2,8] => [4,7,1,5,6,3,2,8] => [2,3,1,2] => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [4,5,1,8,6,7,3,2] => [2,2,2,1,1] => 2
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,8,4,5,7,6,3,2] => [8,4,7,1,5,6,3,2] => [1,2,3,1,1] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => [7,6,4,1,5,3,2,8] => [1,1,1,2,1,2] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,7,4,6,5,3,8,2] => [7,6,4,1,5,3,8,2] => [1,1,1,2,2,1] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => [6,8,4,1,5,3,7,2] => [2,1,2,2,1] => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => [8,7,6,4,1,5,3,2] => [1,1,1,1,2,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [6,5,4,3,1,2,7,8] => [1,1,1,1,4] => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [8,6,5,4,3,1,2,7] => [1,1,1,1,1,3] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,5,4,3,7,2,8] => [6,5,4,3,1,7,2,8] => [1,1,1,1,2,2] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [6,5,4,3,1,7,8,2] => [1,1,1,1,3,1] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [8,6,5,4,3,1,7,2] => [1,1,1,1,1,2,1] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,7,5,4,3,6,2,8] => [5,7,4,3,1,6,2,8] => [2,1,1,2,2] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7,5,4,3,6,8,2] => [5,7,4,3,1,6,8,2] => [2,1,1,3,1] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => [5,4,8,3,1,6,7,2] => [1,2,1,3,1] => 3
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8,5,4,3,7,6,2] => [8,5,7,4,3,1,6,2] => [1,2,1,1,2,1] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,7,5,4,6,3,8,2] => [5,7,4,6,1,3,8,2] => [2,2,3,1] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => [5,4,8,6,1,3,7,2] => [1,2,1,3,1] => 3
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [5,8,4,1,6,7,3,2] => [2,1,3,1,1] => 3
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => [8,5,7,4,6,1,3,2] => [1,2,2,2,1] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => [7,6,1,4,5,3,2,8] => [1,1,3,1,2] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,7,6,4,5,3,8,2] => [7,6,1,4,5,3,8,2] => [1,1,3,2,1] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => [8,1,6,4,5,3,7,2] => [1,2,2,2,1] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => [6,8,1,4,5,7,3,2] => [2,4,1,1] => 4
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => [4,8,1,7,5,6,3,2] => [2,2,2,1,1] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => [8,7,6,1,4,5,3,2] => [1,1,1,3,1,1] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [7,6,5,4,3,1,2,8] => [1,1,1,1,1,3] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [7,6,5,4,3,1,8,2] => [1,1,1,1,1,2,1] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [6,8,5,4,3,1,7,2] => [2,1,1,1,2,1] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [6,8,5,4,7,1,3,2] => [2,1,2,2,1] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => [5,8,7,4,6,1,3,2] => [2,1,2,2,1] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [8,7,5,1,6,4,3,2] => [1,1,1,2,1,1,1] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [1,7] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [8,2,1,3,4,5,6,7] => [1,1,6] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [7,2,1,3,4,5,6,8] => [1,1,6] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [7,2,1,3,4,5,8,6] => [1,1,5,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [8,7,2,1,3,4,5,6] => [1,1,1,5] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [6,2,1,3,4,5,7,8] => [1,1,6] => 6
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [6,2,1,3,4,7,8,5] => [1,1,5,1] => 5
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,4,6,8,7,5] => [8,6,2,1,3,4,7,5] => [1,1,1,4,1] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [7,6,2,1,3,4,8,5] => [1,1,1,4,1] => 4
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [8,7,6,2,1,3,4,5] => [1,1,1,1,4] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [5,2,1,3,4,6,7,8] => [1,1,6] => 6
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [8,5,2,1,3,4,6,7] => [1,1,1,5] => 5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6,8] => [7,5,2,1,3,4,6,8] => [1,1,1,5] => 5
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [8,7,5,2,1,3,4,6] => [1,1,1,1,4] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [5,2,1,3,6,7,8,4] => [1,1,5,1] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,6,8,4] => [7,5,2,1,3,6,8,4] => [1,1,1,4,1] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => [8,2,5,1,3,6,7,4] => [1,2,4,1] => 4
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,3,5,8,7,6,4] => [8,7,5,2,1,3,6,4] => [1,1,1,1,3,1] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,6,5,4,7,8] => [6,5,2,1,3,4,7,8] => [1,1,1,5] => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [8,6,5,2,1,3,4,7] => [1,1,1,1,4] => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,6,5,7,8,4] => [6,5,2,1,3,7,8,4] => [1,1,1,4,1] => 4
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,7,5,6,8,4] => [7,2,5,1,3,6,8,4] => [1,2,4,1] => 4
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => [8,7,2,5,1,3,6,4] => [1,1,2,3,1] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,7,6,5,4,8] => [7,6,5,2,1,3,4,8] => [1,1,1,1,4] => 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,7,6,5,8,4] => [7,6,5,2,1,3,8,4] => [1,1,1,1,3,1] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,8,6,5,7,4] => [6,8,5,2,1,3,7,4] => [2,1,1,3,1] => 3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => [8,6,2,7,1,3,5,4] => [1,1,2,3,1] => 3
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [8,7,6,5,2,1,3,4] => [1,1,1,1,1,3] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [4,2,1,3,5,6,7,8] => [1,1,6] => 6
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [8,4,2,1,3,5,6,7] => [1,1,1,5] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [7,4,2,1,3,5,8,6] => [1,1,1,4,1] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [8,7,4,2,1,3,5,6] => [1,1,1,1,4] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [6,4,2,1,3,5,7,8] => [1,1,1,5] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [8,6,4,2,1,3,5,7] => [1,1,1,1,4] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [6,4,2,1,3,7,5,8] => [1,1,1,3,2] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [6,4,2,1,3,7,8,5] => [1,1,1,4,1] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [8,6,4,2,1,3,7,5] => [1,1,1,1,3,1] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,7,6,5,8] => [7,6,4,2,1,3,5,8] => [1,1,1,1,4] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [7,6,4,2,1,3,8,5] => [1,1,1,1,3,1] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [8,4,6,2,1,3,7,5] => [1,2,1,3,1] => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [8,7,6,4,2,1,3,5] => [1,1,1,1,1,3] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [4,2,1,5,3,6,7,8] => [1,1,2,4] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [8,4,2,1,5,3,6,7] => [1,1,1,2,3] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3,7,8,6] => [7,4,2,1,5,3,8,6] => [1,1,1,2,2,1] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [8,7,4,2,1,5,3,6] => [1,1,1,1,2,2] => 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] => [8,4,2,1,5,6,3,7] => [1,1,1,3,2] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [4,2,1,5,6,7,3,8] => [1,1,4,2] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [4,2,1,5,6,7,8,3] => [1,1,5,1] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [8,4,2,1,5,6,7,3] => [1,1,1,4,1] => 4
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,4,5,7,6,3,8] => [7,4,2,1,5,6,3,8] => [1,1,1,3,2] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,6,8,3] => [7,4,2,1,5,6,8,3] => [1,1,1,4,1] => 4
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [8,2,4,1,5,6,7,3] => [1,2,4,1] => 4
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [8,7,4,2,1,5,6,3] => [1,1,1,1,3,1] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [6,4,2,1,5,3,7,8] => [1,1,1,2,3] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [8,6,4,2,1,5,3,7] => [1,1,1,1,2,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,4,6,5,7,3,8] => [6,4,2,1,5,7,3,8] => [1,1,1,3,2] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,5,7,8,3] => [6,4,2,1,5,7,8,3] => [1,1,1,4,1] => 4
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [8,6,4,2,1,5,7,3] => [1,1,1,1,3,1] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,7,5,6,8,3] => [7,2,4,1,5,6,8,3] => [1,2,4,1] => 4
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [8,2,1,4,5,6,7,3] => [1,1,5,1] => 5
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => [8,7,2,4,1,5,6,3] => [1,1,2,3,1] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,4,7,6,5,3,8] => [7,6,4,2,1,5,3,8] => [1,1,1,1,2,2] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [7,6,4,2,1,5,8,3] => [1,1,1,1,3,1] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [6,8,4,2,1,5,7,3] => [2,1,1,3,1] => 3
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => [8,6,2,4,1,7,5,3] => [1,1,2,2,1,1] => 2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [8,7,6,4,2,1,5,3] => [1,1,1,1,1,2,1] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [5,4,2,1,3,6,7,8] => [1,1,1,5] => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [8,5,4,2,1,3,6,7] => [1,1,1,1,4] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,5,4,3,7,8,6] => [7,5,4,2,1,3,8,6] => [1,1,1,1,3,1] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [8,7,5,4,2,1,3,6] => [1,1,1,1,1,3] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,4,6,3,7,8] => [5,4,2,1,6,3,7,8] => [1,1,1,2,3] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [8,5,4,2,1,6,3,7] => [1,1,1,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [5,4,2,1,6,7,8,3] => [1,1,1,4,1] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [8,5,4,2,1,6,7,3] => [1,1,1,1,3,1] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,4,7,6,3,8] => [7,5,4,2,1,6,3,8] => [1,1,1,1,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [7,5,4,2,1,6,8,3] => [1,1,1,1,3,1] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [5,8,4,2,1,6,7,3] => [2,1,1,3,1] => 3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [8,7,5,4,2,1,6,3] => [1,1,1,1,1,2,1] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,4,5,3,7,8] => [6,2,4,1,5,3,7,8] => [1,2,2,3] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [8,6,2,4,1,5,3,7] => [1,1,2,2,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => [6,2,4,1,5,7,8,3] => [1,2,4,1] => 4
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => [8,6,2,4,1,5,7,3] => [1,1,2,3,1] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,7,4,5,6,3,8] => [7,2,1,4,5,6,3,8] => [1,1,4,2] => 4
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [4,2,1,8,5,6,7,3] => [1,1,2,3,1] => 3
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => [8,7,2,1,4,5,6,3] => [1,1,1,4,1] => 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [7,6,2,4,1,5,8,3] => [1,1,2,3,1] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [8,2,6,4,1,5,7,3] => [1,2,1,3,1] => 3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => [8,6,2,1,4,7,5,3] => [1,1,1,3,1,1] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [8,6,5,4,2,1,3,7] => [1,1,1,1,1,3] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,6,5,4,7,3,8] => [6,5,4,2,1,7,3,8] => [1,1,1,1,2,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,5,4,7,8,3] => [6,5,4,2,1,7,8,3] => [1,1,1,1,3,1] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [8,6,5,4,2,1,7,3] => [1,1,1,1,1,2,1] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => [5,8,2,4,1,6,7,3] => [2,2,3,1] => 3
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [8,5,7,4,2,1,6,3] => [1,2,1,1,2,1] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => [7,5,2,6,1,4,8,3] => [1,1,2,3,1] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [8,2,5,6,1,4,7,3] => [1,3,3,1] => 3
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => [8,5,2,1,6,7,4,3] => [1,1,1,3,1,1] => 3
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [8,7,5,2,6,1,4,3] => [1,1,1,2,2,1] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [7,6,5,4,2,1,3,8] => [1,1,1,1,1,3] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [7,6,5,4,2,1,8,3] => [1,1,1,1,1,2,1] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [6,8,5,4,2,1,7,3] => [2,1,1,1,2,1] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [6,8,5,7,2,1,4,3] => [2,2,1,2,1] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [8,7,2,5,6,1,4,3] => [1,1,3,2,1] => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,2] => 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] => [2,3,1,4,5,6,7,8] => [2,6] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [8,2,3,1,4,5,6,7] => [1,2,5] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [7,2,3,1,4,5,6,8] => [1,2,5] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [7,2,3,1,4,5,8,6] => [1,2,4,1] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,7,6] => [8,7,2,3,1,4,5,6] => [1,1,2,4] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [8,6,2,3,1,4,5,7] => [1,1,2,4] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [6,2,3,1,4,7,8,5] => [1,2,4,1] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,3,1,4,6,8,7,5] => [8,6,2,3,1,4,7,5] => [1,1,2,3,1] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [7,6,2,3,1,4,8,5] => [1,1,2,3,1] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,8,6,7,5] => [8,2,6,3,1,4,7,5] => [1,2,1,3,1] => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [8,7,6,2,3,1,4,5] => [1,1,1,2,3] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [5,2,3,1,4,6,7,8] => [1,2,5] => 5
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [7,5,2,3,1,4,6,8] => [1,1,2,4] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,4,7,8,6] => [7,5,2,3,1,4,8,6] => [1,1,2,3,1] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,6,4,8,7] => [8,5,2,3,1,6,4,7] => [1,1,2,2,2] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [5,2,3,1,6,7,4,8] => [1,2,3,2] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [5,2,3,1,6,7,8,4] => [1,2,4,1] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,7,4] => [8,5,2,3,1,6,7,4] => [1,1,2,3,1] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [7,5,2,3,1,6,8,4] => [1,1,2,3,1] => 3
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,3,1,5,8,7,6,4] => [8,7,5,2,3,1,6,4] => [1,1,1,2,2,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [6,5,2,3,1,4,7,8] => [1,1,2,4] => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [8,6,5,2,3,1,4,7] => [1,1,1,2,3] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [6,5,2,3,1,7,4,8] => [1,1,2,2,2] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,5,7,8,4] => [6,5,2,3,1,7,8,4] => [1,1,2,3,1] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [8,6,5,2,3,1,7,4] => [1,1,1,2,2,1] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,7,5,6,4,8] => [7,2,5,3,1,6,4,8] => [1,2,1,2,2] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,7,5,6,8,4] => [7,2,5,3,1,6,8,4] => [1,2,1,3,1] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [8,2,3,5,1,6,7,4] => [1,3,3,1] => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,8,5,7,6,4] => [8,7,2,5,3,1,6,4] => [1,1,2,1,2,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,7,6,5,4,8] => [7,6,5,2,3,1,4,8] => [1,1,1,2,3] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,8,6,5,7,4] => [6,8,5,2,3,1,7,4] => [2,1,2,2,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [8,6,2,7,3,1,5,4] => [1,1,2,1,2,1] => 2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [8,7,6,5,2,3,1,4] => [1,1,1,1,2,2] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => [3,5] => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [8,2,3,4,1,5,6,7] => [1,3,4] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [7,2,3,4,1,5,6,8] => [1,3,4] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [7,2,3,4,1,5,8,6] => [1,3,3,1] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [8,7,2,3,4,1,5,6] => [1,1,3,3] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [6,2,3,4,1,5,7,8] => [1,3,4] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [8,6,2,3,4,1,5,7] => [1,1,3,3] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [6,2,3,4,1,7,5,8] => [1,3,2,2] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [6,2,3,4,1,7,8,5] => [1,3,3,1] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [8,6,2,3,4,1,7,5] => [1,1,3,2,1] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [7,6,2,3,4,1,5,8] => [1,1,3,3] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [7,6,2,3,4,1,8,5] => [1,1,3,2,1] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [8,2,6,3,4,1,7,5] => [1,2,2,2,1] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [8,7,6,2,3,4,1,5] => [1,1,1,3,2] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7,8] => [4,4] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [8,2,3,4,5,1,6,7] => [1,4,3] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [7,2,3,4,5,1,6,8] => [1,4,3] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [7,2,3,4,5,1,8,6] => [1,4,2,1] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [8,7,2,3,4,5,1,6] => [1,1,4,2] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7,8] => [5,3] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [8,2,3,4,5,6,1,7] => [1,5,2] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1,8] => [6,2] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1] => [7,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [8,2,3,4,5,6,7,1] => [1,6,1] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [7,2,3,4,5,6,1,8] => [1,5,2] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [7,2,3,4,5,6,8,1] => [1,6,1] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => [2,8,3,4,5,6,7,1] => [2,5,1] => 5
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [8,7,2,3,4,5,6,1] => [1,1,5,1] => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [6,2,3,4,5,1,7,8] => [1,4,3] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [6,2,3,4,5,7,1,8] => [1,5,2] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [6,2,3,4,5,7,8,1] => [1,6,1] => 6
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [8,6,2,3,4,5,7,1] => [1,1,5,1] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => [2,7,3,4,5,6,1,8] => [2,4,2] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,7,5,6,8,1] => [2,7,3,4,5,6,8,1] => [2,5,1] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => [2,3,8,4,5,6,7,1] => [3,4,1] => 4
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => [8,2,7,3,4,5,6,1] => [1,2,4,1] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [7,6,2,3,4,5,1,8] => [1,1,4,2] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [7,6,2,3,4,5,8,1] => [1,1,5,1] => 5
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => [6,8,2,3,4,5,7,1] => [2,5,1] => 5
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => [8,2,6,3,4,7,5,1] => [1,2,3,1,1] => 3
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [8,7,6,2,3,4,5,1] => [1,1,1,4,1] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [5,2,3,4,1,6,7,8] => [1,3,4] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [8,5,2,3,4,1,6,7] => [1,1,3,3] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [7,5,2,3,4,1,6,8] => [1,1,3,3] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,3,5,4,1,7,8,6] => [7,5,2,3,4,1,8,6] => [1,1,3,2,1] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [8,7,5,2,3,4,1,6] => [1,1,1,3,2] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [5,2,3,4,6,1,7,8] => [1,4,3] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [5,2,3,4,6,7,1,8] => [1,5,2] => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [5,2,3,4,6,7,8,1] => [1,6,1] => 6
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,3,5,4,7,6,1,8] => [7,5,2,3,4,6,1,8] => [1,1,4,2] => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [7,5,2,3,4,6,8,1] => [1,1,5,1] => 5
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => [5,8,2,3,4,6,7,1] => [2,5,1] => 5
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => [2,6,3,4,5,1,7,8] => [2,3,3] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [8,2,6,3,4,5,1,7] => [1,2,3,2] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,4,5,7,8,1] => [2,6,3,4,5,7,8,1] => [2,5,1] => 5
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,4,5,8,7,1] => [8,2,6,3,4,5,7,1] => [1,2,4,1] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,7,4,5,6,1,8] => [2,3,7,4,5,6,1,8] => [3,3,2] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => [2,3,7,4,5,6,8,1] => [3,4,1] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [2,3,4,8,5,6,7,1] => [4,3,1] => 4
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,8,4,5,7,6,1] => [8,2,3,7,4,5,6,1] => [1,3,3,1] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,7,4,6,5,1,8] => [7,2,6,3,4,5,1,8] => [1,2,3,2] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => [7,2,6,3,4,5,8,1] => [1,2,4,1] => 4
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,8,4,6,5,7,1] => [2,8,6,3,4,5,7,1] => [2,1,4,1] => 4
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => [8,2,3,6,4,7,5,1] => [1,3,2,1,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [6,5,2,3,4,1,7,8] => [1,1,3,3] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [8,6,5,2,3,4,1,7] => [1,1,1,3,2] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [6,5,2,3,4,7,8,1] => [1,1,5,1] => 5
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,7,5,4,6,8,1] => [5,7,2,3,4,6,8,1] => [2,5,1] => 5
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => [5,2,8,3,4,6,7,1] => [1,2,4,1] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => [7,2,5,3,6,4,1,8] => [1,2,2,1,2] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => [7,2,5,3,6,4,8,1] => [1,2,2,2,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,8,5,6,4,7,1] => [2,8,5,3,6,4,7,1] => [2,1,2,2,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => [8,2,3,5,6,7,4,1] => [1,5,1,1] => 5
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,8,5,7,6,4,1] => [8,7,2,5,3,6,4,1] => [1,1,2,2,1,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [7,6,5,2,3,4,1,8] => [1,1,1,3,2] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [7,6,5,2,3,4,8,1] => [1,1,1,4,1] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => [6,8,5,2,3,4,7,1] => [2,1,4,1] => 4
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,8,6,5,7,4,1] => [6,8,5,2,3,7,4,1] => [2,1,3,1,1] => 3
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,8,7,5,6,4,1] => [8,2,7,5,3,6,4,1] => [1,2,1,2,1,1] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [8,7,6,5,2,3,4,1] => [1,1,1,1,3,1] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [1,2,5] => 5
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,4,3,1,5,7,6,8] => [7,4,2,3,1,5,6,8] => [1,1,2,4] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [8,6,4,2,3,1,5,7] => [1,1,1,2,3] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [6,4,2,3,1,7,8,5] => [1,1,2,3,1] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [8,6,4,2,3,1,7,5] => [1,1,1,2,2,1] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [7,6,4,2,3,1,8,5] => [1,1,1,2,2,1] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,8,6,7,5] => [8,4,6,2,3,1,7,5] => [1,2,2,2,1] => 2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [8,7,6,4,2,3,1,5] => [1,1,1,1,2,2] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [4,2,3,5,1,6,7,8] => [1,3,4] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [8,4,2,3,5,1,6,7] => [1,1,3,3] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [7,4,2,3,5,1,6,8] => [1,1,3,3] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [7,4,2,3,5,1,8,6] => [1,1,3,2,1] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [8,7,4,2,3,5,1,6] => [1,1,1,3,2] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,4,3,5,6,1,7,8] => [4,2,3,5,6,1,7,8] => [1,4,3] => 4
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [8,4,2,3,5,6,1,7] => [1,1,4,2] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,3,5,6,7,1,8] => [4,2,3,5,6,7,1,8] => [1,5,2] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [4,2,3,5,6,7,8,1] => [1,6,1] => 6
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [8,4,2,3,5,6,7,1] => [1,1,5,1] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,4,3,5,7,6,1,8] => [7,4,2,3,5,6,1,8] => [1,1,4,2] => 4
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [7,4,2,3,5,6,8,1] => [1,1,5,1] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => [4,8,2,3,5,6,7,1] => [2,5,1] => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [6,4,2,3,5,1,7,8] => [1,1,3,3] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [8,6,4,2,3,5,1,7] => [1,1,1,3,2] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [6,4,2,3,5,7,1,8] => [1,1,4,2] => 4
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [6,4,2,3,5,7,8,1] => [1,1,5,1] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [8,6,4,2,3,5,7,1] => [1,1,1,4,1] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,4,3,7,5,6,1,8] => [4,7,2,3,5,6,1,8] => [2,4,2] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => [4,7,2,3,5,6,8,1] => [2,5,1] => 5
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => [4,2,8,3,5,6,7,1] => [1,2,4,1] => 4
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,8,5,7,6,1] => [8,4,7,2,3,5,6,1] => [1,2,4,1] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,4,3,7,6,5,1,8] => [7,6,4,2,3,5,1,8] => [1,1,1,3,2] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [7,6,4,2,3,5,8,1] => [1,1,1,4,1] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,8,6,5,7,1] => [6,8,4,2,3,5,7,1] => [2,1,4,1] => 4
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,3,8,6,7,5,1] => [8,4,6,2,3,7,5,1] => [1,2,3,1,1] => 3
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [8,7,6,4,2,3,5,1] => [1,1,1,1,3,1] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => [2,5,3,4,1,6,7,8] => [2,2,4] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,5,3,4,1,7,6,8] => [7,2,5,3,4,1,6,8] => [1,2,2,3] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,5,3,4,1,7,8,6] => [7,2,5,3,4,1,8,6] => [1,2,2,2,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => [8,7,2,5,3,4,1,6] => [1,1,2,2,2] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,5,3,4,6,1,8,7] => [8,2,5,3,4,6,1,7] => [1,2,3,2] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => [2,5,3,4,6,7,1,8] => [2,4,2] => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => [2,5,3,4,6,7,8,1] => [2,5,1] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => [8,2,5,3,4,6,7,1] => [1,2,4,1] => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,5,3,4,7,6,1,8] => [7,2,5,3,4,6,1,8] => [1,2,3,2] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => [2,8,5,3,4,6,7,1] => [2,1,4,1] => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => [2,3,6,4,5,1,7,8] => [3,2,3] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,6,3,4,5,1,8,7] => [8,2,3,6,4,5,1,7] => [1,3,2,2] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => [2,3,6,4,5,7,8,1] => [3,4,1] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,7,3,4,5,6,1,8] => [2,3,4,7,5,6,1,8] => [4,2,2] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,7,3,4,5,6,8,1] => [2,3,4,7,5,6,8,1] => [4,3,1] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => [2,3,4,5,8,6,7,1] => [5,2,1] => 5
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,8,3,4,5,7,6,1] => [8,2,3,4,7,5,6,1] => [1,4,2,1] => 4
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,8,3,4,6,7,5,1] => [8,2,3,4,6,7,5,1] => [1,5,1,1] => 5
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,6,3,5,4,1,7,8] => [6,2,5,3,4,1,7,8] => [1,2,2,3] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => [8,6,2,5,3,4,1,7] => [1,1,2,2,2] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,6,3,5,4,8,7,1] => [8,6,2,5,3,4,7,1] => [1,1,2,3,1] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,7,3,5,4,6,1,8] => [2,7,5,3,4,6,1,8] => [2,1,3,2] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7,3,5,4,6,8,1] => [2,7,5,3,4,6,8,1] => [2,1,4,1] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,8,3,5,4,6,7,1] => [2,5,8,3,4,6,7,1] => [3,4,1] => 4
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => [8,2,7,5,3,4,6,1] => [1,2,1,3,1] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,7,3,5,6,4,1,8] => [7,2,3,5,6,4,1,8] => [1,4,1,2] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,7,3,5,6,4,8,1] => [7,2,3,5,6,4,8,1] => [1,4,2,1] => 4
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8,3,5,6,7,4,1] => [5,2,3,8,6,7,4,1] => [1,3,2,1,1] => 3
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => [8,7,2,3,5,6,4,1] => [1,1,4,1,1] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => [7,6,2,5,3,4,1,8] => [1,1,2,2,2] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,8,3,6,5,4,7,1] => [6,8,2,5,3,4,7,1] => [2,2,3,1] => 3
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,8,3,6,5,7,4,1] => [8,2,6,5,3,7,4,1] => [1,2,1,2,1,1] => 2
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => [8,7,6,2,5,3,4,1] => [1,1,1,2,2,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [5,4,2,3,1,6,7,8] => [1,1,2,4] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [8,5,4,2,3,1,6,7] => [1,1,1,2,3] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [7,5,4,2,3,1,6,8] => [1,1,1,2,3] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [7,5,4,2,3,1,8,6] => [1,1,1,2,2,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [8,7,5,4,2,3,1,6] => [1,1,1,1,2,2] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,5,4,3,6,1,7,8] => [5,4,2,3,6,1,7,8] => [1,1,3,3] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [8,5,4,2,3,6,1,7] => [1,1,1,3,2] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [5,4,2,3,6,7,1,8] => [1,1,4,2] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [5,4,2,3,6,7,8,1] => [1,1,5,1] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [8,5,4,2,3,6,7,1] => [1,1,1,4,1] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,5,4,3,7,6,1,8] => [7,5,4,2,3,6,1,8] => [1,1,1,3,2] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [7,5,4,2,3,6,8,1] => [1,1,1,4,1] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => [5,8,4,2,3,6,7,1] => [2,1,4,1] => 4
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [8,7,5,4,2,3,6,1] => [1,1,1,1,3,1] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,6,4,3,5,1,7,8] => [4,6,2,3,5,1,7,8] => [2,3,3] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => [8,4,6,2,3,5,1,7] => [1,2,3,2] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,6,4,3,5,7,8,1] => [4,6,2,3,5,7,8,1] => [2,5,1] => 5
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,6,4,3,5,8,7,1] => [8,4,6,2,3,5,7,1] => [1,2,4,1] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => [4,2,7,3,5,6,8,1] => [1,2,4,1] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => [4,2,3,8,5,6,7,1] => [1,3,3,1] => 3
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => [8,4,2,7,3,5,6,1] => [1,1,2,3,1] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,7,4,3,6,5,1,8] => [7,4,6,2,3,5,1,8] => [1,2,3,2] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => [7,4,6,2,3,5,8,1] => [1,2,4,1] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => [4,8,6,2,3,5,7,1] => [2,1,4,1] => 4
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => [8,4,2,6,3,7,5,1] => [1,1,2,2,1,1] => 2
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => [8,7,4,6,2,3,5,1] => [1,1,2,3,1] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,4,5,3,1,7,8] => [6,2,4,5,3,1,7,8] => [1,3,1,3] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,4,5,3,1,8,7] => [8,6,2,4,5,3,1,7] => [1,1,3,1,2] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,4,5,3,7,8,1] => [6,2,4,5,3,7,8,1] => [1,3,3,1] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,6,4,5,3,8,7,1] => [8,6,2,4,5,3,7,1] => [1,1,3,2,1] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,7,4,5,3,6,1,8] => [2,7,4,5,3,6,1,8] => [2,2,2,2] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,8,4,5,3,6,7,1] => [2,4,8,5,3,6,7,1] => [3,1,3,1] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,7,4,5,6,3,1,8] => [4,2,7,5,6,3,1,8] => [1,2,2,1,2] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => [4,2,7,5,6,3,8,1] => [1,2,2,2,1] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => [4,2,5,8,6,3,7,1] => [1,3,1,2,1] => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => [4,2,5,8,6,7,3,1] => [1,3,2,1,1] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,7,4,6,5,3,1,8] => [7,6,2,4,5,3,1,8] => [1,1,3,1,2] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,7,4,6,5,3,8,1] => [7,6,2,4,5,3,8,1] => [1,1,3,2,1] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => [6,8,2,4,5,3,7,1] => [2,3,2,1] => 3
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,8,4,6,5,7,3,1] => [8,2,6,4,5,7,3,1] => [1,2,3,1,1] => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,8,4,7,5,6,3,1] => [8,2,4,7,5,6,3,1] => [1,3,2,1,1] => 3
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => [8,7,6,2,4,5,3,1] => [1,1,1,3,1,1] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [8,6,5,4,2,3,1,7] => [1,1,1,1,2,2] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [6,5,4,2,3,7,8,1] => [1,1,1,4,1] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [8,6,5,4,2,3,7,1] => [1,1,1,1,3,1] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => [5,7,4,2,3,6,8,1] => [2,1,4,1] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => [5,4,8,2,3,6,7,1] => [1,2,4,1] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => [5,7,4,2,6,3,8,1] => [2,1,2,2,1] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,5,4,6,3,7,1] => [5,4,8,2,6,3,7,1] => [1,2,2,2,1] => 2
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,5,4,6,7,3,1] => [5,8,2,4,6,7,3,1] => [2,4,1,1] => 4
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => [8,5,7,4,2,6,3,1] => [1,2,1,2,1,1] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,6,4,5,3,8,1] => [7,2,6,4,5,3,8,1] => [1,2,2,2,1] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,8,6,4,5,3,7,1] => [2,8,6,4,5,3,7,1] => [2,1,2,2,1] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,8,6,4,5,7,3,1] => [6,2,8,4,5,7,3,1] => [1,2,3,1,1] => 3
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,8,7,4,5,6,3,1] => [4,2,8,7,5,6,3,1] => [1,2,1,2,1,1] => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => [8,7,2,6,4,5,3,1] => [1,1,2,2,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [7,6,5,4,2,3,1,8] => [1,1,1,1,2,2] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [7,6,5,4,2,3,8,1] => [1,1,1,1,3,1] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,8,6,5,4,3,7,1] => [6,8,5,4,2,3,7,1] => [2,1,1,3,1] => 3
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,8,6,5,4,7,3,1] => [6,8,5,4,2,7,3,1] => [2,1,1,2,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => [5,8,7,4,2,6,3,1] => [2,1,1,2,1,1] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => [8,7,2,5,6,4,3,1] => [1,1,3,1,1,1] => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [8,7,6,5,4,2,3,1] => [1,1,1,1,1,2,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [1,1,6] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [8,3,2,1,4,5,6,7] => [1,1,1,5] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [7,3,2,1,4,5,6,8] => [1,1,1,5] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [7,3,2,1,4,5,8,6] => [1,1,1,4,1] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [8,7,3,2,1,4,5,6] => [1,1,1,1,4] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,2,1,4,6,5,7,8] => [6,3,2,1,4,5,7,8] => [1,1,1,5] => 5
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,2,1,4,6,5,8,7] => [8,6,3,2,1,4,5,7] => [1,1,1,1,4] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,2,1,4,6,7,5,8] => [6,3,2,1,4,7,5,8] => [1,1,1,3,2] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [6,3,2,1,4,7,8,5] => [1,1,1,4,1] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [8,6,3,2,1,4,7,5] => [1,1,1,1,3,1] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [7,6,3,2,1,4,5,8] => [1,1,1,1,4] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [7,6,3,2,1,4,8,5] => [1,1,1,1,3,1] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [8,3,6,2,1,4,7,5] => [1,2,1,3,1] => 3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [8,7,6,3,2,1,4,5] => [1,1,1,1,1,3] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [5,3,2,1,4,6,7,8] => [1,1,1,5] => 5
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,5,4,6,8,7] => [8,5,3,2,1,4,6,7] => [1,1,1,1,4] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [7,5,3,2,1,4,6,8] => [1,1,1,1,4] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,1,5,4,7,8,6] => [7,5,3,2,1,4,8,6] => [1,1,1,1,3,1] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,1,5,4,8,7,6] => [8,7,5,3,2,1,4,6] => [1,1,1,1,1,3] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [5,3,2,1,6,4,7,8] => [1,1,1,2,3] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,5,6,4,8,7] => [8,5,3,2,1,6,4,7] => [1,1,1,1,2,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,5,6,7,4,8] => [5,3,2,1,6,7,4,8] => [1,1,1,3,2] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [5,3,2,1,6,7,8,4] => [1,1,1,4,1] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [8,5,3,2,1,6,7,4] => [1,1,1,1,3,1] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [7,5,3,2,1,6,4,8] => [1,1,1,1,2,2] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [7,5,3,2,1,6,8,4] => [1,1,1,1,3,1] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => [8,3,5,2,1,6,7,4] => [1,2,1,3,1] => 3
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [8,7,5,3,2,1,6,4] => [1,1,1,1,1,2,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [6,5,3,2,1,4,7,8] => [1,1,1,1,4] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [8,6,5,3,2,1,4,7] => [1,1,1,1,1,3] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,2,1,6,5,7,4,8] => [6,5,3,2,1,7,4,8] => [1,1,1,1,2,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [6,5,3,2,1,7,8,4] => [1,1,1,1,3,1] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [8,6,5,3,2,1,7,4] => [1,1,1,1,1,2,1] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => [7,3,5,2,1,6,4,8] => [1,2,1,2,2] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => [7,3,5,2,1,6,8,4] => [1,2,1,3,1] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => [8,3,2,5,1,6,7,4] => [1,1,2,3,1] => 3
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => [8,7,3,5,2,1,6,4] => [1,1,2,1,2,1] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [7,6,5,3,2,1,4,8] => [1,1,1,1,1,3] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [7,6,5,3,2,1,8,4] => [1,1,1,1,1,2,1] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => [6,8,5,3,2,1,7,4] => [2,1,1,1,2,1] => 2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => [8,6,3,7,2,1,5,4] => [1,1,2,1,2,1] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [8,7,6,5,3,2,1,4] => [1,1,1,1,1,1,2] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => [1,2,5] => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [8,3,2,4,1,5,6,7] => [1,1,2,4] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [7,3,2,4,1,5,6,8] => [1,1,2,4] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [7,3,2,4,1,5,8,6] => [1,1,2,3,1] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [8,7,3,2,4,1,5,6] => [1,1,1,2,3] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [6,3,2,4,1,5,7,8] => [1,1,2,4] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [8,6,3,2,4,1,5,7] => [1,1,1,2,3] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [6,3,2,4,1,7,5,8] => [1,1,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [6,3,2,4,1,7,8,5] => [1,1,2,3,1] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [8,6,3,2,4,1,7,5] => [1,1,1,2,2,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [7,6,3,2,4,1,5,8] => [1,1,1,2,3] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [7,6,3,2,4,1,8,5] => [1,1,1,2,2,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [8,3,6,2,4,1,7,5] => [1,2,2,2,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [8,7,6,3,2,4,1,5] => [1,1,1,1,2,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [3,2,4,5,1,6,7,8] => [1,3,4] => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,2,4,5,1,7,8,6] => [7,3,2,4,5,1,8,6] => [1,1,3,2,1] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [8,7,3,2,4,5,1,6] => [1,1,1,3,2] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [3,2,4,5,6,1,7,8] => [1,4,3] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1,8] => [1,5,2] => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,8,1] => [1,6,1] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [8,3,2,4,5,6,7,1] => [1,1,5,1] => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,2,4,5,7,6,1,8] => [7,3,2,4,5,6,1,8] => [1,1,4,2] => 4
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [7,3,2,4,5,6,8,1] => [1,1,5,1] => 5
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => [3,8,2,4,5,6,7,1] => [2,5,1] => 5
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,2,4,6,5,1,8,7] => [8,6,3,2,4,5,1,7] => [1,1,1,3,2] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,2,4,6,5,7,1,8] => [6,3,2,4,5,7,1,8] => [1,1,4,2] => 4
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,7,5,6,1,8] => [3,7,2,4,5,6,1,8] => [2,4,2] => 4
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,7,5,6,8,1] => [3,7,2,4,5,6,8,1] => [2,5,1] => 5
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => [3,2,8,4,5,6,7,1] => [1,2,4,1] => 4
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,2,4,8,5,7,6,1] => [8,3,7,2,4,5,6,1] => [1,2,4,1] => 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,2,4,7,6,5,1,8] => [7,6,3,2,4,5,1,8] => [1,1,1,3,2] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [7,6,3,2,4,5,8,1] => [1,1,1,4,1] => 4
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,2,4,8,6,5,7,1] => [6,8,3,2,4,5,7,1] => [2,1,4,1] => 4
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [8,7,6,3,2,4,5,1] => [1,1,1,1,3,1] => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [5,3,2,4,1,6,7,8] => [1,1,2,4] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [8,5,3,2,4,1,6,7] => [1,1,1,2,3] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [7,5,3,2,4,1,6,8] => [1,1,1,2,3] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [7,5,3,2,4,1,8,6] => [1,1,1,2,2,1] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [8,7,5,3,2,4,1,6] => [1,1,1,1,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,5,4,6,1,7,8] => [5,3,2,4,6,1,7,8] => [1,1,3,3] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [8,5,3,2,4,6,1,7] => [1,1,1,3,2] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,5,4,6,7,1,8] => [5,3,2,4,6,7,1,8] => [1,1,4,2] => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [5,3,2,4,6,7,8,1] => [1,1,5,1] => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [7,5,3,2,4,6,1,8] => [1,1,1,3,2] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [7,5,3,2,4,6,8,1] => [1,1,1,4,1] => 4
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [8,3,6,2,4,5,1,7] => [1,2,3,2] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,2,6,4,5,7,1,8] => [3,6,2,4,5,7,1,8] => [2,4,2] => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => [3,2,7,4,5,6,1,8] => [1,2,3,2] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => [3,2,4,8,5,6,7,1] => [1,3,3,1] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => [7,3,6,2,4,5,1,8] => [1,2,3,2] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => [7,3,6,2,4,5,8,1] => [1,2,4,1] => 4
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => [3,8,6,2,4,5,7,1] => [2,1,4,1] => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [8,6,5,3,2,4,1,7] => [1,1,1,1,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [6,5,3,2,4,7,1,8] => [1,1,1,3,2] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [8,6,5,3,2,4,7,1] => [1,1,1,1,3,1] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => [5,7,3,2,4,6,1,8] => [2,1,3,2] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => [5,3,8,2,4,6,7,1] => [1,2,4,1] => 4
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => [8,5,7,3,2,4,6,1] => [1,2,1,3,1] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [7,3,5,2,6,4,1,8] => [1,2,2,1,2] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => [7,3,5,2,6,4,8,1] => [1,2,2,2,1] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => [3,8,5,2,6,4,7,1] => [2,1,2,2,1] => 2
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,8,5,6,7,4,1] => [8,3,2,5,6,7,4,1] => [1,1,4,1,1] => 4
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => [8,7,3,5,2,6,4,1] => [1,1,2,2,1,1] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [7,6,5,3,2,4,1,8] => [1,1,1,1,2,2] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,2,8,6,5,4,7,1] => [6,8,5,3,2,4,7,1] => [2,1,1,3,1] => 3
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,8,6,5,7,4,1] => [6,8,5,3,2,7,4,1] => [2,1,1,2,1,1] => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,8,7,5,6,4,1] => [8,3,7,5,2,6,4,1] => [1,2,1,2,1,1] => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [8,7,6,5,3,2,4,1] => [1,1,1,1,1,2,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => [2,4,3,1,5,6,7,8] => [2,1,5] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,2,3,1,5,6,8,7] => [8,2,4,3,1,5,6,7] => [1,2,1,4] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,2,3,1,5,7,6,8] => [7,2,4,3,1,5,6,8] => [1,2,1,4] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,2,3,1,5,7,8,6] => [7,2,4,3,1,5,8,6] => [1,2,1,3,1] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,2,3,1,5,8,7,6] => [8,7,2,4,3,1,5,6] => [1,1,2,1,3] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,3,1,6,5,7,8] => [6,2,4,3,1,5,7,8] => [1,2,1,4] => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [8,6,2,4,3,1,5,7] => [1,1,2,1,3] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,2,3,1,6,7,5,8] => [6,2,4,3,1,7,5,8] => [1,2,1,2,2] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [6,2,4,3,1,7,8,5] => [1,2,1,3,1] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [8,6,2,4,3,1,7,5] => [1,1,2,1,2,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,2,3,1,7,6,5,8] => [7,6,2,4,3,1,5,8] => [1,1,2,1,3] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [7,6,2,4,3,1,8,5] => [1,1,2,1,2,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [8,2,6,4,3,1,7,5] => [1,2,1,1,2,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [8,7,6,2,4,3,1,5] => [1,1,1,2,1,2] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => [2,4,3,5,1,6,7,8] => [2,2,4] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => [7,2,4,3,5,1,8,6] => [1,2,2,2,1] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => [8,7,2,4,3,5,1,6] => [1,1,2,2,2] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => [2,4,3,5,6,1,7,8] => [2,3,3] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => [8,2,4,3,5,6,1,7] => [1,2,3,2] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => [2,4,3,5,6,7,1,8] => [2,4,2] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => [2,4,3,5,6,7,8,1] => [2,5,1] => 5
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => [8,2,4,3,5,6,7,1] => [1,2,4,1] => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [4,2,3,5,7,6,8,1] => [7,2,4,3,5,6,8,1] => [1,2,4,1] => 4
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,2,3,5,8,7,6,1] => [8,7,2,4,3,5,6,1] => [1,1,2,3,1] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,2,3,6,5,1,8,7] => [8,6,2,4,3,5,1,7] => [1,1,2,2,2] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [2,7,4,3,5,6,8,1] => [2,1,4,1] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => [2,4,8,3,5,6,7,1] => [3,4,1] => 4
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,2,3,8,5,7,6,1] => [8,2,7,4,3,5,6,1] => [1,2,1,3,1] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [4,2,3,7,6,5,1,8] => [7,6,2,4,3,5,1,8] => [1,1,2,2,2] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,2,3,7,6,5,8,1] => [7,6,2,4,3,5,8,1] => [1,1,2,3,1] => 3
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,2,3,8,6,7,5,1] => [8,2,6,4,3,7,5,1] => [1,2,1,2,1,1] => 2
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,2,3,8,7,6,5,1] => [8,7,6,2,4,3,5,1] => [1,1,1,2,2,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [2,3,5,4,1,6,7,8] => [3,1,4] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => [8,2,3,5,4,1,6,7] => [1,3,1,3] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,3,4,1,7,6,8] => [7,2,3,5,4,1,6,8] => [1,3,1,3] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [7,2,3,5,4,1,8,6] => [1,3,1,2,1] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => [8,7,2,3,5,4,1,6] => [1,1,3,1,2] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => [2,3,5,4,6,1,7,8] => [3,2,3] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => [2,3,5,4,6,7,1,8] => [3,3,2] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [2,3,5,4,6,7,8,1] => [3,4,1] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,2,3,4,6,8,7,1] => [8,2,3,5,4,6,7,1] => [1,3,3,1] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => [7,2,3,5,4,6,1,8] => [1,3,2,2] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => [2,8,3,5,4,6,7,1] => [2,2,3,1] => 3
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => [8,7,2,3,5,4,6,1] => [1,1,3,2,1] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => [2,3,4,6,5,1,7,8] => [4,1,3] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => [2,3,4,6,5,7,1,8] => [4,2,2] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => [2,3,4,6,5,7,8,1] => [4,3,1] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => [8,2,3,4,6,5,7,1] => [1,4,2,1] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [2,3,4,5,7,6,1,8] => [5,1,2] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [2,3,4,5,7,6,8,1] => [5,2,1] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,8,7,1] => [6,1,1] => 6
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => [8,2,3,4,5,7,6,1] => [1,5,1,1] => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,2,3,4,6,5,1,8] => [7,2,3,4,6,5,1,8] => [1,4,1,2] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,2,3,4,6,5,8,1] => [7,2,3,4,6,5,8,1] => [1,4,2,1] => 4
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [8,2,3,4,6,7,5,1] => [6,2,3,4,8,7,5,1] => [1,4,1,1,1] => 4
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8,2,3,4,7,6,5,1] => [8,7,2,3,4,6,5,1] => [1,1,4,1,1] => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => [6,2,3,5,4,1,7,8] => [1,3,1,3] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => [8,6,2,3,5,4,1,7] => [1,1,3,1,2] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [6,2,3,5,4,7,1,8] => [6,2,3,5,4,7,1,8] => [1,3,2,2] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,2,3,5,4,7,8,1] => [6,2,3,5,4,7,8,1] => [1,3,3,1] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => [2,7,3,5,4,6,1,8] => [2,2,2,2] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => [2,3,8,5,4,6,7,1] => [3,1,3,1] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => [5,2,3,7,6,4,1,8] => [1,3,1,1,2] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [8,2,3,5,6,4,7,1] => [5,2,3,6,8,4,7,1] => [1,4,2,1] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => [7,6,2,3,5,4,1,8] => [1,1,3,1,2] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8,2,3,6,5,4,7,1] => [6,8,2,3,5,4,7,1] => [2,3,2,1] => 3
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [8,2,3,6,5,7,4,1] => [8,2,6,3,5,7,4,1] => [1,2,3,1,1] => 3
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => [8,2,5,3,7,6,4,1] => [1,2,2,1,1,1] => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8,2,3,7,6,5,4,1] => [8,7,6,2,3,5,4,1] => [1,1,1,3,1,1] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => [5,2,4,3,1,6,7,8] => [1,2,1,4] => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => [8,5,2,4,3,1,6,7] => [1,1,2,1,3] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => [7,5,2,4,3,1,6,8] => [1,1,2,1,3] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [5,2,4,3,1,7,8,6] => [7,5,2,4,3,1,8,6] => [1,1,2,1,2,1] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => [8,7,5,2,4,3,1,6] => [1,1,1,2,1,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [5,2,4,3,6,1,7,8] => [5,2,4,3,6,1,7,8] => [1,2,2,3] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [8,5,2,4,3,6,1,7] => [1,1,2,2,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [5,2,4,3,6,7,1,8] => [5,2,4,3,6,7,1,8] => [1,2,3,2] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [5,2,4,3,6,7,8,1] => [5,2,4,3,6,7,8,1] => [1,2,4,1] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [5,2,4,3,7,6,1,8] => [7,5,2,4,3,6,1,8] => [1,1,2,2,2] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => [7,5,2,4,3,6,8,1] => [1,1,2,3,1] => 3
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,2,4,3,8,7,6,1] => [8,7,5,2,4,3,6,1] => [1,1,1,2,2,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [8,2,6,4,3,5,1,7] => [1,2,1,2,2] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,2,4,3,5,6,8,1] => [2,4,7,3,5,6,8,1] => [3,4,1] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [8,2,4,3,5,6,7,1] => [2,4,3,8,5,6,7,1] => [2,2,3,1] => 3
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [8,2,4,3,5,7,6,1] => [8,2,4,7,3,5,6,1] => [1,3,3,1] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => [7,2,6,4,3,5,1,8] => [1,2,1,2,2] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [7,2,6,4,3,5,8,1] => [1,2,1,3,1] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [2,8,6,4,3,5,7,1] => [2,1,1,3,1] => 3
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => [8,2,4,6,3,7,5,1] => [1,3,2,1,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2,4,5,3,1,8,7] => [8,4,2,6,5,3,1,7] => [1,1,2,1,1,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [6,2,4,5,3,7,8,1] => [4,2,6,5,3,7,8,1] => [1,2,1,3,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,2,4,5,3,8,7,1] => [8,4,2,6,5,3,7,1] => [1,1,2,1,2,1] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => [4,2,5,7,3,6,1,8] => [1,3,2,2] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => [4,2,5,7,3,6,8,1] => [1,3,3,1] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [8,2,4,5,3,6,7,1] => [4,2,5,3,8,6,7,1] => [1,2,2,2,1] => 2
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [8,4,2,5,7,3,6,1] => [1,1,3,2,1] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,2,4,5,6,3,1,8] => [4,2,5,7,6,3,1,8] => [1,3,1,1,2] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [7,2,4,5,6,3,8,1] => [4,2,5,7,6,3,8,1] => [1,3,1,2,1] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8,2,4,5,6,3,7,1] => [4,2,5,6,8,3,7,1] => [1,4,2,1] => 4
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8,2,4,5,7,6,3,1] => [8,4,2,5,7,6,3,1] => [1,1,3,1,1,1] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => [7,4,2,6,5,3,1,8] => [1,1,2,1,1,2] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,2,4,6,5,3,8,1] => [7,4,2,6,5,3,8,1] => [1,1,2,1,2,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [8,2,4,6,5,3,7,1] => [4,8,2,6,5,3,7,1] => [2,2,1,2,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [8,2,4,6,5,7,3,1] => [8,2,4,6,5,7,3,1] => [1,3,2,1,1] => 3
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8,2,4,7,5,6,3,1] => [8,2,4,5,7,6,3,1] => [1,4,1,1,1] => 4
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => [8,7,4,2,6,5,3,1] => [1,1,1,2,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,2,5,4,3,1,7,8] => [6,5,2,4,3,1,7,8] => [1,1,2,1,3] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => [8,6,5,2,4,3,1,7] => [1,1,1,2,1,2] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => [6,5,2,4,3,7,1,8] => [1,1,2,2,2] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,2,5,4,3,7,8,1] => [6,5,2,4,3,7,8,1] => [1,1,2,3,1] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,2,5,4,3,8,7,1] => [8,6,5,2,4,3,7,1] => [1,1,1,2,2,1] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => [5,7,2,4,3,6,1,8] => [2,2,2,2] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,2,5,4,3,6,8,1] => [5,7,2,4,3,6,8,1] => [2,2,3,1] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8,2,5,4,3,6,7,1] => [5,2,8,4,3,6,7,1] => [1,2,1,3,1] => 3
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => [8,5,7,2,4,3,6,1] => [1,2,2,2,1] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,2,5,4,6,3,1,8] => [7,2,5,4,6,3,1,8] => [1,2,2,1,2] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,2,5,4,6,3,8,1] => [7,2,5,4,6,3,8,1] => [1,2,2,2,1] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [8,2,5,4,6,3,7,1] => [2,8,5,4,6,3,7,1] => [2,1,2,2,1] => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [8,2,5,4,6,7,3,1] => [5,2,8,4,6,7,3,1] => [1,2,3,1,1] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,6,4,5,3,1,8] => [7,2,4,6,5,3,1,8] => [1,3,1,1,2] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => [7,2,4,6,5,3,8,1] => [1,3,1,2,1] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => [2,8,4,6,5,3,7,1] => [2,2,1,2,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => [4,2,8,6,5,7,3,1] => [1,2,1,2,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => [4,2,8,5,7,6,3,1] => [1,2,2,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => [8,7,2,4,6,5,3,1] => [1,1,3,1,1,1] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,2,6,5,4,3,1,8] => [7,6,5,2,4,3,1,8] => [1,1,1,2,1,2] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,6,5,4,3,8,1] => [7,6,5,2,4,3,8,1] => [1,1,1,2,2,1] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => [6,8,5,2,4,3,7,1] => [2,1,2,2,1] => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => [8,2,7,5,4,6,3,1] => [1,2,1,2,1,1] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => [8,7,6,5,2,4,3,1] => [1,1,1,1,2,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [1,1,1,5] => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [8,4,3,2,1,5,6,7] => [1,1,1,1,4] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [7,4,3,2,1,5,6,8] => [1,1,1,1,4] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [7,4,3,2,1,5,8,6] => [1,1,1,1,3,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [8,7,4,3,2,1,5,6] => [1,1,1,1,1,3] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [6,4,3,2,1,5,7,8] => [1,1,1,1,4] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [8,6,4,3,2,1,5,7] => [1,1,1,1,1,3] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [6,4,3,2,1,7,5,8] => [1,1,1,1,2,2] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [6,4,3,2,1,7,8,5] => [1,1,1,1,3,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [8,6,4,3,2,1,7,5] => [1,1,1,1,1,2,1] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [7,6,4,3,2,1,5,8] => [1,1,1,1,1,3] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [7,6,4,3,2,1,8,5] => [1,1,1,1,1,2,1] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [8,4,6,3,2,1,7,5] => [1,2,1,1,2,1] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [8,7,6,4,3,2,1,5] => [1,1,1,1,1,1,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [4,3,2,5,1,6,7,8] => [1,1,2,4] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,3,2,5,1,7,6,8] => [7,4,3,2,5,1,6,8] => [1,1,1,2,3] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [7,4,3,2,5,1,8,6] => [1,1,1,2,2,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [8,7,4,3,2,5,1,6] => [1,1,1,1,2,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [4,3,2,5,6,1,7,8] => [1,1,3,3] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [8,4,3,2,5,6,1,7] => [1,1,1,3,2] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [4,3,2,5,6,7,1,8] => [1,1,4,2] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [4,3,2,5,6,7,8,1] => [1,1,5,1] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [8,4,3,2,5,6,7,1] => [1,1,1,4,1] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [7,4,3,2,5,6,1,8] => [1,1,1,3,2] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [7,4,3,2,5,6,8,1] => [1,1,1,4,1] => 4
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [8,7,4,3,2,5,6,1] => [1,1,1,1,3,1] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [6,4,3,2,5,1,7,8] => [1,1,1,2,3] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [8,6,4,3,2,5,1,7] => [1,1,1,1,2,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [8,6,4,3,2,5,7,1] => [1,1,1,1,3,1] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,3,2,7,5,6,1,8] => [4,7,3,2,5,6,1,8] => [2,1,3,2] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => [4,7,3,2,5,6,8,1] => [2,1,4,1] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => [4,3,8,2,5,6,7,1] => [1,2,4,1] => 4
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => [8,4,7,3,2,5,6,1] => [1,2,1,3,1] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,2,7,6,5,1,8] => [7,6,4,3,2,5,1,8] => [1,1,1,1,2,2] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [7,6,4,3,2,5,8,1] => [1,1,1,1,3,1] => 3
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => [8,4,6,3,2,7,5,1] => [1,2,1,2,1,1] => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [8,7,6,4,3,2,5,1] => [1,1,1,1,1,2,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => [3,5,2,4,1,6,7,8] => [2,2,4] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => [8,3,5,2,4,1,6,7] => [1,2,2,3] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => [7,3,5,2,4,1,6,8] => [1,2,2,3] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,3,2,4,1,7,8,6] => [7,3,5,2,4,1,8,6] => [1,2,2,2,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => [8,7,3,5,2,4,1,6] => [1,1,2,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => [8,3,5,2,4,6,1,7] => [1,2,3,2] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => [3,5,2,4,6,7,8,1] => [2,5,1] => 5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => [7,3,5,2,4,6,1,8] => [1,2,3,2] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,3,2,4,8,6,7,1] => [3,8,5,2,4,6,7,1] => [2,1,4,1] => 4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,3,2,4,8,7,6,1] => [8,7,3,5,2,4,6,1] => [1,1,2,3,1] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,3,2,4,5,1,8,7] => [8,3,2,6,4,5,1,7] => [1,1,2,2,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [6,3,2,4,5,7,1,8] => [3,2,6,4,5,7,1,8] => [1,2,3,2] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,3,2,4,5,6,1,8] => [3,2,4,7,5,6,1,8] => [1,3,2,2] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [3,2,4,7,5,6,8,1] => [1,3,3,1] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [3,2,4,5,8,6,7,1] => [1,4,2,1] => 4
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [8,3,2,4,5,7,6,1] => [8,3,2,4,7,5,6,1] => [1,1,3,2,1] => 3
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => [8,3,2,4,6,7,5,1] => [1,1,4,1,1] => 4
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8,3,2,4,7,6,5,1] => [8,7,3,2,6,4,5,1] => [1,1,1,2,2,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [8,6,3,5,2,4,1,7] => [1,1,2,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => [6,3,5,2,4,7,1,8] => [1,2,3,2] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => [6,3,5,2,4,7,8,1] => [1,2,4,1] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [3,7,5,2,4,6,1,8] => [2,1,3,2] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [7,3,2,5,4,6,8,1] => [3,7,5,2,4,6,8,1] => [2,1,4,1] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [8,3,2,5,4,6,7,1] => [3,5,8,2,4,6,7,1] => [3,4,1] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [8,3,7,5,2,4,6,1] => [1,2,1,3,1] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,3,2,5,6,4,8,1] => [7,3,2,5,6,4,8,1] => [1,1,3,2,1] => 3
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8,3,2,5,6,7,4,1] => [5,3,2,8,6,7,4,1] => [1,1,2,2,1,1] => 2
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => [8,7,3,2,5,6,4,1] => [1,1,1,3,1,1] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [7,3,2,6,5,4,8,1] => [7,6,3,5,2,4,8,1] => [1,1,2,3,1] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [8,3,2,6,5,4,7,1] => [6,8,3,5,2,4,7,1] => [2,2,3,1] => 3
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => [8,3,6,5,2,7,4,1] => [1,2,1,2,1,1] => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [8,7,6,3,5,2,4,1] => [1,1,1,2,2,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => [3,5,4,2,1,6,7,8] => [2,1,1,4] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => [8,3,5,4,2,1,6,7] => [1,2,1,1,3] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,3,4,2,1,7,6,8] => [7,3,5,4,2,1,6,8] => [1,2,1,1,3] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [7,3,5,4,2,1,8,6] => [1,2,1,1,2,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => [8,7,3,5,4,2,1,6] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,3,4,2,6,1,7,8] => [3,5,4,2,6,1,7,8] => [2,1,2,3] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => [8,3,5,4,2,6,1,7] => [1,2,1,2,2] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,3,4,2,6,7,1,8] => [3,5,4,2,6,7,1,8] => [2,1,3,2] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => [3,5,4,2,6,7,8,1] => [2,1,4,1] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => [7,3,5,4,2,6,1,8] => [1,2,1,2,2] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,3,4,2,7,6,8,1] => [7,3,5,4,2,6,8,1] => [1,2,1,3,1] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => [3,8,5,4,2,6,7,1] => [2,1,1,3,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [6,3,4,2,5,1,7,8] => [3,4,6,2,5,1,7,8] => [3,2,3] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [6,3,4,2,5,7,1,8] => [3,4,6,2,5,7,1,8] => [3,3,2] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [7,3,4,2,5,6,8,1] => [3,4,2,7,5,6,8,1] => [2,2,3,1] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [3,4,2,5,8,6,7,1] => [2,3,2,1] => 3
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [8,3,4,2,5,7,6,1] => [8,3,4,2,7,5,6,1] => [1,2,2,2,1] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,2,6,5,1,8] => [7,3,4,6,2,5,1,8] => [1,3,2,2] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => [7,3,4,6,2,5,8,1] => [1,3,3,1] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8,3,4,2,6,5,7,1] => [3,8,4,6,2,5,7,1] => [2,2,3,1] => 3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [8,3,4,2,6,7,5,1] => [8,3,4,2,6,7,5,1] => [1,2,3,1,1] => 3
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [8,3,4,2,7,6,5,1] => [8,7,3,4,6,2,5,1] => [1,1,3,2,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => [8,3,4,6,5,2,1,7] => [1,3,1,1,2] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [3,4,6,5,2,7,1,8] => [3,1,2,2] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => [3,4,6,5,2,7,8,1] => [3,1,3,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => [8,3,4,6,5,2,7,1] => [1,3,1,2,1] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,3,4,5,2,6,8,1] => [3,4,5,7,2,6,8,1] => [4,3,1] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [3,4,5,2,8,6,7,1] => [3,2,2,1] => 3
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [8,3,4,5,7,2,6,1] => [1,4,2,1] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [3,4,5,7,6,2,8,1] => [4,1,2,1] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => [3,4,5,6,8,2,7,1] => [5,2,1] => 5
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [3,4,5,6,8,7,2,1] => [5,1,1,1] => 5
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => [8,3,4,5,7,6,2,1] => [1,4,1,1,1] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,3,4,6,5,2,1,8] => [7,3,4,6,5,2,1,8] => [1,3,1,1,2] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [7,3,4,6,5,2,8,1] => [7,3,4,6,5,2,8,1] => [1,3,1,2,1] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [8,3,4,6,5,2,7,1] => [3,8,4,6,5,2,7,1] => [2,2,1,2,1] => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [8,3,4,6,5,7,2,1] => [3,8,4,6,5,7,2,1] => [2,2,2,1,1] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [8,3,4,7,5,6,2,1] => [3,8,4,5,7,6,2,1] => [2,3,1,1,1] => 3
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => [8,7,3,4,6,5,2,1] => [1,1,3,1,1,1] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [6,3,5,4,2,1,7,8] => [6,3,5,4,2,1,7,8] => [1,2,1,1,3] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => [8,6,3,5,4,2,1,7] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => [6,3,5,4,2,7,1,8] => [1,2,1,2,2] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,3,5,4,2,7,8,1] => [6,3,5,4,2,7,8,1] => [1,2,1,3,1] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,3,5,4,2,8,7,1] => [8,6,3,5,4,2,7,1] => [1,1,2,1,2,1] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => [3,7,5,4,2,6,1,8] => [2,1,1,2,2] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,3,5,4,2,6,8,1] => [3,7,5,4,2,6,8,1] => [2,1,1,3,1] => 3
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8,3,5,4,2,7,6,1] => [8,3,7,5,4,2,6,1] => [1,2,1,1,2,1] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,5,4,6,2,1,8] => [3,7,5,4,6,2,1,8] => [2,1,2,1,2] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => [3,7,5,4,6,2,8,1] => [2,1,2,2,1] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [8,3,5,4,6,2,7,1] => [3,5,8,4,6,2,7,1] => [3,2,2,1] => 3
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,5,4,6,7,2,1] => [3,5,8,4,6,7,2,1] => [3,3,1,1] => 3
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [8,3,7,5,4,6,2,1] => [1,2,1,2,1,1] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => [3,7,4,6,5,2,8,1] => [2,2,1,2,1] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [3,4,8,6,5,2,7,1] => [3,1,1,2,1] => 3
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [8,3,6,4,5,7,2,1] => [3,4,8,6,5,7,2,1] => [3,1,2,1,1] => 3
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => [8,3,7,4,6,5,2,1] => [1,2,2,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => [7,6,3,5,4,2,1,8] => [1,1,2,1,1,2] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => [7,6,3,5,4,2,8,1] => [1,1,2,1,2,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => [6,8,3,5,4,7,2,1] => [2,2,2,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8,3,7,5,4,6,2,1] => [3,8,7,5,4,6,2,1] => [2,1,1,2,1,1] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => [8,3,5,7,6,4,2,1] => [1,3,1,1,1,1] => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => [8,7,6,3,5,4,2,1] => [1,1,1,2,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => [1,1,1,1,4] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [8,5,4,3,2,1,6,7] => [1,1,1,1,1,3] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [7,5,4,3,2,1,6,8] => [1,1,1,1,1,3] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [7,5,4,3,2,1,8,6] => [1,1,1,1,1,2,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [8,7,5,4,3,2,1,6] => [1,1,1,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7,8] => [1,1,1,2,3] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [8,5,4,3,2,6,1,7] => [1,1,1,1,2,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [5,4,3,2,6,7,1,8] => [1,1,1,3,2] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [5,4,3,2,6,7,8,1] => [1,1,1,4,1] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [8,5,4,3,2,6,7,1] => [1,1,1,1,3,1] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [7,5,4,3,2,6,1,8] => [1,1,1,1,2,2] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [7,5,4,3,2,6,8,1] => [1,1,1,1,3,1] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,8,6,7,1] => [5,8,4,3,2,6,7,1] => [2,1,1,3,1] => 3
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [8,7,5,4,3,2,6,1] => [1,1,1,1,1,2,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => [4,6,3,2,5,1,7,8] => [2,1,2,3] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1,8] => [4,3,7,2,5,6,1,8] => [1,2,3,2] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [4,3,7,2,5,6,8,1] => [1,2,4,1] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => [4,3,2,8,5,6,7,1] => [1,1,2,3,1] => 3
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8,4,3,2,5,7,6,1] => [8,4,3,7,2,5,6,1] => [1,1,2,3,1] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,4,3,2,6,5,1,8] => [7,4,6,3,2,5,1,8] => [1,2,1,2,2] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => [8,7,4,6,3,2,5,1] => [1,1,2,1,2,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => [8,4,6,3,5,2,1,7] => [1,2,2,1,2] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,4,3,5,2,7,1,8] => [4,6,3,5,2,7,1,8] => [2,2,2,2] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,4,3,5,2,8,7,1] => [8,4,6,3,5,2,7,1] => [1,2,2,2,1] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => [4,3,7,5,2,6,1,8] => [1,2,1,2,2] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8,4,3,5,2,7,6,1] => [8,4,3,7,5,2,6,1] => [1,1,2,1,2,1] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => [4,3,5,8,6,2,7,1] => [1,3,1,2,1] => 3
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => [4,3,5,8,6,7,2,1] => [1,3,2,1,1] => 3
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => [8,4,3,7,5,6,2,1] => [1,1,2,2,1,1] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => [7,4,6,3,5,2,1,8] => [1,2,2,1,2] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => [7,4,6,3,5,2,8,1] => [1,2,2,2,1] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [8,4,3,6,5,7,2,1] => [4,8,6,3,5,7,2,1] => [2,1,3,1,1] => 3
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => [4,8,3,7,5,6,2,1] => [2,2,2,1,1] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8,4,3,7,6,5,2,1] => [8,7,4,6,3,5,2,1] => [1,1,2,2,1,1] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => [3,6,5,4,2,1,7,8] => [2,1,1,1,3] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => [8,3,6,5,4,2,1,7] => [1,2,1,1,1,2] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,3,4,2,7,8,1] => [3,6,5,4,2,7,8,1] => [2,1,1,3,1] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [6,5,3,4,2,8,7,1] => [8,3,6,5,4,2,7,1] => [1,2,1,1,2,1] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => [3,5,7,4,2,6,1,8] => [3,1,2,2] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,8,1] => [3,5,7,4,2,6,8,1] => [3,1,3,1] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => [3,5,4,8,2,6,7,1] => [2,2,3,1] => 3
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => [8,3,5,7,4,2,6,1] => [1,3,1,2,1] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [3,5,7,4,6,2,8,1] => [3,2,2,1] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [8,5,3,4,6,2,7,1] => [3,5,4,8,6,2,7,1] => [2,2,1,2,1] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => [8,3,5,7,4,6,2,1] => [1,3,2,1,1] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => [3,4,7,6,5,2,1,8] => [3,1,1,1,2] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => [3,4,7,6,5,2,8,1] => [3,1,1,2,1] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8,6,3,4,5,2,7,1] => [3,4,6,8,5,2,7,1] => [4,1,2,1] => 4
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [8,6,3,4,5,7,2,1] => [3,4,6,8,5,7,2,1] => [4,2,1,1] => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => [3,4,5,8,7,6,2,1] => [4,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => [8,3,4,7,6,5,2,1] => [1,3,1,1,1,1] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => [7,3,6,5,4,2,1,8] => [1,2,1,1,1,2] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => [7,3,6,5,4,2,8,1] => [1,2,1,1,2,1] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8,6,3,5,4,2,7,1] => [3,8,6,5,4,2,7,1] => [2,1,1,1,2,1] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [3,8,5,7,4,6,2,1] => [2,2,2,1,1] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [5,3,8,7,6,4,2,1] => [1,2,1,1,1,1,1] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => [8,7,3,6,5,4,2,1] => [1,1,2,1,1,1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => [1,1,1,1,1,3] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [8,6,5,4,3,2,1,7] => [1,1,1,1,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [6,5,4,3,2,7,1,8] => [1,1,1,1,2,2] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [6,5,4,3,2,7,8,1] => [1,1,1,1,3,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [8,6,5,4,3,2,7,1] => [1,1,1,1,1,2,1] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => [5,7,4,3,2,6,1,8] => [2,1,1,2,2] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => [5,4,8,3,2,6,7,1] => [1,2,1,3,1] => 3
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [8,5,7,4,3,2,6,1] => [1,2,1,1,2,1] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => [5,7,4,3,6,2,1,8] => [2,1,2,1,2] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [5,7,4,3,6,2,8,1] => [2,1,2,2,1] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => [5,4,8,3,6,2,7,1] => [1,2,2,2,1] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => [5,4,8,3,6,7,2,1] => [1,2,3,1,1] => 3
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => [8,5,7,4,3,6,2,1] => [1,2,1,2,1,1] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => [4,7,6,3,5,2,1,8] => [2,1,2,1,2] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => [4,7,6,3,5,2,8,1] => [2,1,2,2,1] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => [4,6,8,3,5,2,7,1] => [3,2,2,1] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => [4,6,8,3,5,7,2,1] => [3,3,1,1] => 3
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => [4,3,8,7,5,6,2,1] => [1,2,1,2,1,1] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [8,4,7,6,3,5,2,1] => [1,2,1,2,1,1] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => [4,7,6,5,3,2,1,8] => [2,1,1,1,1,2] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => [4,7,6,5,3,2,8,1] => [2,1,1,1,2,1] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => [4,6,8,5,3,2,7,1] => [3,1,1,2,1] => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8,6,4,5,3,7,2,1] => [4,6,8,5,3,7,2,1] => [3,1,2,1,1] => 3
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => [4,5,8,7,3,6,2,1] => [3,1,2,1,1] => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [4,5,8,7,6,3,2,1] => [3,1,1,1,1,1] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => [8,4,7,6,5,3,2,1] => [1,2,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,2] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,8,1] => [1,1,1,1,1,2,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => [6,8,5,4,3,2,7,1] => [2,1,1,1,2,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => [6,8,5,4,3,7,2,1] => [2,1,1,2,1,1] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => [5,8,7,4,3,6,2,1] => [2,1,1,2,1,1] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => [5,8,7,4,6,3,2,1] => [2,1,2,1,1,1] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [4,8,7,6,5,3,2,1] => [2,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [1,1,1,1,1,1,1,2] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,2] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,7,6,4,5,3,2,1,9] => [4,8,7,6,5,3,2,1,9] => [2,1,1,1,1,1,2] => 2
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,9,8,7,5,6,4,3,2] => [9,8,7,1,5,6,4,3,2] => [1,1,1,3,1,1,1] => 3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,8,7,5,6,4,3,2,1,10] => [5,9,8,7,6,4,3,2,1,10] => [2,1,1,1,1,1,1,2] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,7,5,4,6,3,2,1,9] => [5,8,7,4,6,3,2,1,9] => [2,1,2,1,1,2] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,7,4,6,5,3,2,1,9] => [8,4,7,6,5,3,2,1,9] => [1,2,1,1,1,1,2] => 2
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,9,8,6,5,7,4,3,2] => [6,9,8,5,7,4,1,3,2] => [2,1,2,1,2,1] => 2
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,9,8,5,7,6,4,3,2] => [9,8,7,5,1,6,4,3,2] => [1,1,1,1,2,1,1,1] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,7,3,6,5,4,2,1,9] => [8,7,3,6,5,4,2,1,9] => [1,1,2,1,1,1,2] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,3,7,6,5,4,2,1,9] => [8,7,6,3,5,4,2,1,9] => [1,1,1,2,1,1,2] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,6,5,4,3,2,8,1,9] => [7,6,5,4,3,2,8,1,9] => [1,1,1,1,1,2,2] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [9,7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,2] => 2
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [9,8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,2] => 2
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [9,8,7,6,5,3,1,4,2] => [1,1,1,1,1,1,2,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => [1,1,1,1,1,1,3] => 3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,3] => 3
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,3] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [9,2,3,4,5,6,7,8,1] => [1,7,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [8,2,3,4,5,6,7,9,1] => [1,7,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,9,7,8,1] => [2,9,3,4,5,6,7,8,1] => [2,6,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => [9,8,2,3,4,5,6,7,1] => [1,1,6,1] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,5,8,6,7,9,1] => [2,8,3,4,5,6,7,9,1] => [2,6,1] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,9,6,7,8,1] => [2,3,9,4,5,6,7,8,1] => [3,5,1] => 5
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,5,9,7,6,8,1] => [7,9,2,3,4,5,6,8,1] => [2,6,1] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,9,5,6,7,8,1] => [2,3,4,9,5,6,7,8,1] => [4,4,1] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,3,7,4,5,6,8,9,1] => [2,3,7,4,5,6,8,9,1] => [3,5,1] => 5
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,9,4,5,6,7,8,1] => [2,3,4,5,9,6,7,8,1] => [5,3,1] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => [4,2,3,5,6,7,8,9,1] => [1,7,1] => 7
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [2,8,3,4,5,6,7,9,1] => [2,3,4,5,8,6,7,9,1] => [5,3,1] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,9,3,4,5,6,7,8,1] => [2,3,4,5,6,9,7,8,1] => [6,2,1] => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => [8,7,6,5,4,2,3,9,1] => [1,1,1,1,1,3,1] => 3
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [9,8,7,6,5,4,2,3,1] => [1,1,1,1,1,1,2,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,9,1] => [1,7,1] => 7
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,9,8,7,6,5,4,1] => [9,8,7,6,5,3,2,4,1] => [1,1,1,1,1,1,2,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,1] => [2,4,3,5,6,7,8,9,1] => [2,6,1] => 6
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,2,3,4,9,6,7,8,1] => [2,3,9,5,4,6,7,8,1] => [3,1,4,1] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [2,3,4,5,6,8,7,9,1] => [6,2,1] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,9,8,1] => [7,1,1] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9,2,3,4,5,6,8,7,1] => [9,2,3,4,5,6,8,7,1] => [1,6,1,1] => 6
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9,2,8,7,6,5,4,3,1] => [9,8,7,6,5,2,4,3,1] => [1,1,1,1,1,2,1,1] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [4,3,2,5,6,7,8,9,1] => [1,1,6,1] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9,3,4,5,6,8,7,2,1] => [9,3,4,5,6,8,7,2,1] => [1,5,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => [5,4,3,2,6,7,8,9,1] => [1,1,1,5,1] => 5
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [8,7,3,6,5,4,2,9,1] => [8,7,3,6,5,4,2,9,1] => [1,1,2,1,1,2,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,1] => [6,5,4,3,2,7,8,9,1] => [1,1,1,1,4,1] => 4
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [9,8,4,7,6,5,3,2,1] => [9,8,4,7,6,5,3,2,1] => [1,1,2,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,1] => [7,6,5,4,3,2,8,9,1] => [1,1,1,1,1,3,1] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,6,5,4,3,2,9,8,1] => [9,7,6,5,4,3,2,8,1] => [1,1,1,1,1,1,2,1] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [8,7,6,5,4,3,2,9,1] => [1,1,1,1,1,1,2,1] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9,7,6,5,4,3,2,8,1] => [7,9,6,5,4,3,2,8,1] => [2,1,1,1,1,2,1] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [9,8,7,5,4,6,3,2,1] => [5,9,8,7,4,6,3,2,1] => [2,1,1,2,1,1,1] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,8,7,5,6,4,3,2,1] => [5,9,8,7,6,4,3,2,1] => [2,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [9] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [9,1,2,3,4,5,6,7,8] => [1,8] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [8,1,2,3,4,5,6,9,7] => [1,7,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [7,1,2,3,4,5,8,9,6] => [1,7,1] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [6,1,2,3,4,7,8,9,5] => [1,7,1] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [5,1,2,3,6,7,8,9,4] => [1,7,1] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [4,1,2,5,6,7,8,9,3] => [1,7,1] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [3,1,4,5,6,7,8,9,2] => [1,7,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [10,1,2,3,4,5,6,7,8,9] => [1,9] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [9,8,1,2,3,4,5,6,7] => [1,1,7] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [9,1,2,3,4,5,6,7,10,8] => [1,8,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [8,7,1,2,3,4,5,9,6] => [1,1,6,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [8,1,2,3,4,5,6,9,10,7] => [1,8,1] => 8
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,6,8,9,5] => [7,6,1,2,3,4,8,9,5] => [1,1,6,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [7,1,2,3,4,5,8,9,10,6] => [1,8,1] => 8
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,5,7,8,9,4] => [6,5,1,2,3,7,8,9,4] => [1,1,6,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [6,1,2,3,4,7,8,9,10,5] => [1,8,1] => 8
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => [5,4,1,2,6,7,8,9,3] => [1,1,6,1] => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [5,1,2,3,6,7,8,9,10,4] => [1,8,1] => 8
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [4,3,1,5,6,7,8,9,2] => [1,1,6,1] => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [4,1,2,5,6,7,8,9,10,3] => [1,8,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [3,1,4,5,6,7,8,9,10,2] => [1,8,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,10,1] => [9,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [11,1,2,3,4,5,6,7,8,9,10] => [1,10] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,9,7,8,6] => [9,1,7,2,3,4,5,8,6] => [1,2,5,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [9,8,7,1,2,3,4,5,6] => [1,1,1,6] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,10,2] => [4,3,1,5,6,7,8,9,10,2] => [1,1,7,1] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [3,2,4,5,6,7,8,9,10,1] => [1,8,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [2,3,4,5,6,7,8,9,10,11,1] => [10,1] => 10
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,10,1] => [4,3,2,5,6,7,8,9,10,1] => [1,1,7,1] => 7
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [9,8,7,6,1,2,3,4,5] => [1,1,1,1,5] => 5
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,4] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,10,1] => [6,5,4,3,2,7,8,9,10,1] => [1,1,1,1,5,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [8,1,2,3,4,5,6,7,9] => [1,8] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [7,1,2,3,4,5,6,8,9] => [1,8] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [9,7,1,2,3,4,5,6,8] => [1,1,7] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [6,1,2,3,4,5,7,8,9] => [1,8] => 8
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,4,6,5,7,9,8] => [9,6,1,2,3,4,5,7,8] => [1,1,7] => 7
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [1,8] => 8
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [1,8] => 8
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,7,9,8] => [9,4,1,2,3,5,6,7,8] => [1,1,7] => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,6,9,8,7] => [9,8,4,1,2,3,5,6,7] => [1,1,1,6] => 6
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,8,7,6,5,4,3,9] => [8,7,6,5,4,1,2,3,9] => [1,1,1,1,1,4] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [1,8] => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [9,3,1,2,4,5,6,7,8] => [1,1,7] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,6,8,9] => [7,5,3,1,2,4,6,8,9] => [1,1,1,6] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,5] => 5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [4,3,1,2,5,6,7,8,9] => [1,1,7] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,7,6,5,4,3,2,8,9] => [7,6,5,4,3,1,2,8,9] => [1,1,1,1,1,4] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,6,5,4,3,2,9,8] => [9,7,6,5,4,3,1,2,8] => [1,1,1,1,1,1,3] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [1,8] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [9,2,1,3,4,5,6,7,8] => [1,1,7] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [8,2,1,3,4,5,6,7,9] => [1,1,7] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,9,8,7] => [9,8,2,1,3,4,5,6,7] => [1,1,1,6] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [8,6,4,2,1,3,5,7,9] => [1,1,1,1,5] => 5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => [8,7,6,5,4,2,1,3,9] => [1,1,1,1,1,1,3] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [1,1,7] => 7
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [9,8,7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,2] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [1,1,1,6] => 6
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,8,7,6,5,9] => [8,7,6,4,3,2,1,5,9] => [1,1,1,1,1,1,3] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [9,8,7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,2] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [1,1,1,1,5] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,4,3,2,1,8,7,6,9] => [8,7,5,4,3,2,1,6,9] => [1,1,1,1,1,1,3] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [9,8,7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,2] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => [1,1,1,1,1,4] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,5,4,3,2,1,8,7,9] => [8,6,5,4,3,2,1,7,9] => [1,1,1,1,1,1,3] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [9,8,6,5,4,3,2,1,7] => [1,1,1,1,1,1,1,2] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [9,1,2,3,4,5,6,7,8,10] => [1,9] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => [1,9] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [1,9] => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [1,9] => 9
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [1,9] => 9
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [1,9] => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [1,9] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [1,9] => 9
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [2,7] => 7
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [3,6] => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [4,5] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [2,3,4,5,6,1,7,8,9] => [5,4] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [2,3,4,5,6,7,1,8,9] => [6,3] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [2,3,4,5,6,7,8,1,9] => [7,2] => 7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [1,2,6] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => [1,3,5] => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,4,6,5,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => [1,4,4] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [5,5] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,5,7,6,1,8,9] => [7,2,3,4,5,6,1,8,9] => [1,5,3] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [8,2,3,4,5,6,7,1,9] => [1,6,2] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [1,10] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [8,2,1,3,4,5,6,9,7] => [1,1,6,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [10,2,3,4,5,6,7,8,9,1] => [1,8,1] => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,6,8,9,7] => [8,2,3,1,4,5,6,9,7] => [1,2,5,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,6,8,9,7] => [8,3,1,2,4,5,6,9,7] => [1,1,6,1] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [9,2,3,1,4,5,6,7,8] => [1,2,6] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,2,3,4,5,6,7,1,9] => [2,3,4,5,6,8,7,1,9] => [6,1,2] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,2,3,4,5,6,1,8,9] => [2,3,4,5,7,6,1,8,9] => [5,1,3] => 5
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,2,3,4,5,1,7,8,9] => [2,3,4,6,5,1,7,8,9] => [4,1,4] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8,9] => [2,3,5,4,1,6,7,8,9] => [3,1,5] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8,9] => [2,4,3,1,5,6,7,8,9] => [2,1,6] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,5,4,3,2,7,1,8,9] => [6,5,4,3,2,7,1,8,9] => [1,1,1,1,2,3] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,4,3,2,6,1,7,8,9] => [5,4,3,2,6,1,7,8,9] => [1,1,1,2,4] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8,9] => [4,3,2,5,1,6,7,8,9] => [1,1,2,5] => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => [1,2,6] => 6
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => [9,8,7,6,5,2,3,1,4] => [1,1,1,1,1,2,2] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8,9] => [4,1,2,5,3,6,7,8,9] => [1,3,5] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6,7,9,8] => [9,2,3,4,5,1,6,7,8] => [1,4,4] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8,9] => [4,2,1,5,3,6,7,8,9] => [1,1,2,5] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,10,1] => [6,2,3,4,5,7,8,9,10,1] => [1,8,1] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [3,2,4,5,6,7,8,1,9] => [1,6,2] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [9,3,1,4,5,6,7,8,2] => [1,1,6,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [9,2,3,4,5,6,7,1,8] => [1,6,2] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => [9,8,2,3,4,5,6,1,7] => [1,1,5,2] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => [10,9,2,3,4,5,6,7,8,1] => [1,1,7,1] => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,5,4,3,2,1,8,9,7] => [8,6,5,4,3,2,1,9,7] => [1,1,1,1,1,1,2,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,3,5,7,8,9,6] => [7,4,1,2,3,5,8,9,6] => [1,1,6,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,6,7,5,8,9] => [6,1,2,3,4,7,5,8,9] => [1,5,3] => 5
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [9,7,5,2,3,1,4,6,8] => [1,1,1,2,4] => 4
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,1] => [10,8,6,4,2,3,5,7,9,1] => [1,1,1,1,5,1] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,10,9,1] => [8,1,1] => 8
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,3,10,5,4,6,7,8,9,1] => [5,2,3,4,10,6,7,8,9,1] => [1,4,4,1] => 4
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => [2,11,4,9,6,7,5,8,3,10,1,12] => [2,11,4,9,6,7,5,8,3,10,1,12] => [2,2,2,2,2,2] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [3,1,4,2,5,6,7,8,9] => [1,2,6] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [10,2,3,4,5,6,7,9,8,1] => [10,2,3,4,5,6,7,9,8,1] => [1,7,1,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [10,1,2,3,4,5,6,7,8,9,11] => [1,10] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [7,1,2,3,4,5,8,6,9] => [1,6,2] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [3,1,4,5,6,7,8,2,9] => [1,6,2] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10,11] => [3,1,2,4,5,6,7,8,9,10,11] => [1,10] => 10
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,5,8,7,6,1,9] => [8,7,2,3,4,5,6,1,9] => [1,1,5,2] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => [10,3,1,4,5,6,7,8,9,2] => [1,1,7,1] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,9,4] => [5,3,1,2,6,7,8,9,4] => [1,1,6,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,9,8,5] => [9,6,1,2,3,4,7,8,5] => [1,1,6,1] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [11,2,3,4,5,6,7,8,10,9,1] => [11,2,3,4,5,6,7,8,10,9,1] => [1,8,1,1] => 8
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,10,4,5,6,7,8,9,1] => [3,2,4,5,6,10,7,8,9,1] => [1,5,3,1] => 5
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10,3,2,5,4,7,6,9,8,1] => [10,3,9,7,5,2,4,6,8,1] => [1,2,1,1,4,1] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,7,8,10,9,1] => [10,3,2,4,5,6,7,8,9,1] => [1,1,7,1] => 7
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,1 1,8,4,1 1,20,15,5,1 1,50,52,22,6,1 1,122,181,86,31,7,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + 3\ q^{2} + q^{3}$
$F_{4} = q + 8\ q^{2} + 4\ q^{3} + q^{4}$
$F_{5} = q + 20\ q^{2} + 15\ q^{3} + 5\ q^{4} + q^{5}$
$F_{6} = q + 50\ q^{2} + 52\ q^{3} + 22\ q^{4} + 6\ q^{5} + q^{6}$
$F_{7} = q + 122\ q^{2} + 181\ q^{3} + 86\ q^{4} + 31\ q^{5} + 7\ q^{6} + q^{7}$
Description
The largest part of an integer composition.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
- If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
- If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
- $1$
- $|1|4 \to 14$
- $|14|2 \to 412$
- $|4|1|2|5 \to 4125$
- $|4|125|3 \to 45123.$
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
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