Identifier
-
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001291: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [1] => [1,0,1,0] => 2
[1,0,1,0] => [1,2] => [1,1] => [1,0,1,1,0,0] => 2
[1,1,0,0] => [2,1] => [2] => [1,1,0,0,1,0] => 3
[1,0,1,0,1,0] => [1,2,3] => [1,1,1] => [1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0] => [1,3,2] => [2,1] => [1,0,1,0,1,0] => 3
[1,1,0,0,1,0] => [2,1,3] => [2,1] => [1,0,1,0,1,0] => 3
[1,1,0,1,0,0] => [2,3,1] => [3] => [1,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,0] => [3,2,1] => [2,1] => [1,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,1] => [1,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,2] => [1,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1] => [1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,1] => [1,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,2] => [1,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2] => [1,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [3,2] => [1,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [3,2] => [1,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [3,2] => [1,1,0,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
>>> Load all 1446 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 5
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 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] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 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] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 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] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,7,5,6,8,3] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,8,6,5,7,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,8,4,6,7,5,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,8,5,4,7,6,3] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 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] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 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] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,4,5,2,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 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] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,8,4,6,5,7,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,8,4,6,7,5,2] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7,4,5,3,6,8,2] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8,5,4,3,7,6,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 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] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 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] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 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] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,7,5,6,4,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 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] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,7,5,4,6,1,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 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] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 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] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,8,6,5,7,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,3,4,7,6,8,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,3,4,8,7,6,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,6,3,5,4,7,8,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7,3,5,4,6,8,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 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] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8,3,5,6,7,4,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,8,3,7,5,6,4,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,6,4,3,5,7,8,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,6,4,3,5,8,7,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 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] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,4,5,3,7,8,1] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,7,4,5,6,3,1,8] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 5
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,7,4,6,5,3,8,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,8,5,4,3,7,6,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 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] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,5,4,6,7,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,6,4,5,3,8,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,8,7,4,5,6,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,7,5,6,8,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,8,6,7,5,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 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] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,8,7,5,6,4,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,2,3,5,1,6,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,2,3,8,5,7,6,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2,3,4,6,1,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8,2,3,5,4,7,6,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8,2,3,5,6,7,4,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8,2,3,5,7,6,4,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8,2,3,7,6,5,4,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [5,2,4,3,6,1,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8,2,4,3,7,6,5,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8,2,4,5,6,7,3,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8,2,4,5,7,6,3,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,2,4,6,5,3,8,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8,2,4,7,5,6,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [6,3,2,4,5,7,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8,3,2,4,6,5,7,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8,3,2,4,7,6,5,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 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] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8,3,2,5,6,7,4,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,3,4,2,7,6,8,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,3,5,4,2,7,8,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8,3,5,4,2,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,5,4,6,7,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8,3,7,4,5,6,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,8,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [6,4,3,2,5,8,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8,4,3,2,5,7,6,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8,4,3,2,6,5,7,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8,4,3,2,6,7,5,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8,6,3,5,4,2,7,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 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] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 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] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[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] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[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] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[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] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[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] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,10,9,8,6,7,5,4,3,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,9,8,5,6,7,4,3,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[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] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[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] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,6,4,5,3,2,1,9,8] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,10,9,5,6,7,8,4,3,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,9,8,6,7,5,4,3] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,7,6,5,4,3,2,9,1,10] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,9,8,6,5,7,4,3] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,10,9,8,7,6,5,4,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,9,5,4,6,7,8,3,2] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,9,6,7,8,5,1] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,9,5,6,7,8,4,1] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[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] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,9,8,6,5,7,4,3,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,8,7,5,6,4,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[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] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,9,8,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[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] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9,2,4,5,6,8,7,3,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [9,3,2,5,6,7,8,4,1] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [9,3,4,5,2,6,7,8,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [9,3,4,5,6,2,8,7,1] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9,3,7,6,5,4,8,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9,3,8,7,6,5,4,2,1] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [9,4,3,5,6,7,2,8,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [9,8,3,5,7,6,4,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [9,8,3,7,6,5,4,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[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] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [9,8,4,3,6,7,5,2,1] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [9,8,4,5,3,7,6,2,1] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [9,8,4,5,7,6,3,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [8,7,4,6,5,3,2,9,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [9,8,4,6,5,7,3,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[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] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[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] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[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] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [8,7,5,4,6,3,2,9,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [9,8,5,4,6,3,7,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [9,8,5,4,6,7,3,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,7,6,4,5,3,2,9,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9,8,7,4,6,5,3,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[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] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [9,7,6,5,4,3,8,2,1] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [9,8,6,5,4,3,7,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [9,8,6,5,4,7,3,2,1] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[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] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[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] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6,9,8] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,8,7,9] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2,1,7,6,5,9,8] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 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] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [10,9,8,5,7,6,4,3,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [10,9,8,6,5,7,4,3,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[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] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,8,7,5,6,4,3,2,10,1] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 4
[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] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,9,4,8,7,6,5,3,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,3,9,8,7,6,5,4,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[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] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,3,4,2,1,9,8,7,6] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[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] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,9,8,7,6] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,1,9,7,8,6,5] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,1,9,6,7,8,5,4] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,1,9,5,6,7,8,4,3] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,4,9,8,7,6,5,3] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2,6,5,4,3,1,9,8] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3,5,4,2,1,9,8,7] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,2,1,9,7,8,6,5] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[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] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [10,8,7,6,5,4,3,9,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [10,9,7,6,5,4,8,3,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[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] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,6,8,9] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,8,7,1,9] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,7,9,8,4] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,7,6,5,4,3,2,10,9,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,9,5] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,8,7,9] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,5,4,6,1,8,7,9] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7,10,9] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7,10,9] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,7,6,8,1,10,9] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,4,8,5,6,7,1,9] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,2,8,7,6,5,4,1,9] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,10,1] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,10,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,8,10,7] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,7,6,9,8,10,5] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,9,8,10,3] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,5] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,4,5,7,8,9,10,6] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7,10,9] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,7,6,8,5,10,9] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,7,6,8,5,10,9] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,7,6,8,3,10,9] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,6,5,9,8,10,7] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3,9,8,10,7] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,5,4,6,1,9,8,10,7] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,4,1,7,6,9,8,10,5] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,10,9] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,1,7,8,9,6] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3,8,10,9,7] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,5,8,10,9,7] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,8,7,5,10,9] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7,9] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,5,8,9,10,7] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,5,8,9,10,7] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7,9] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,9,8,10] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,9,8] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,9,8] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,9,8,10] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,4,6,5,8,7,9] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,10,9] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
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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
F1=q2
F2=q2+q3
F3=q2+3 q3+q4
F4=q2+8 q3+4 q4+q5
F5=q2+20 q3+15 q4+5 q5+q6
Description
The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path.
Let A be the Nakayama algebra associated to a Dyck path as given in DyckPaths/NakayamaAlgebras. This statistics is the number of indecomposable summands of D(A)⊗D(A), where D(A) is the natural dual of A.
Let A be the Nakayama algebra associated to a Dyck path as given in DyckPaths/NakayamaAlgebras. This statistics is the number of indecomposable summands of D(A)⊗D(A), where D(A) is the natural dual of A.
Map
to non-crossing permutation
Description
Sends a Dyck path D with valley at positions {(i1,j1),…,(ik,jk)} to the unique non-crossing permutation π having descents {i1,…,ik} and whose inverse has descents {j1,…,jk}.
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
cycle type
Description
The cycle type of a permutation as a partition.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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