Identifier
-
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St000676: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [1] => [1,0] => 1
[1,0,1,0] => [1,2] => [1,1] => [1,1,0,0] => 1
[1,1,0,0] => [2,1] => [2] => [1,0,1,0] => 2
[1,0,1,0,1,0] => [1,2,3] => [1,1,1] => [1,1,0,1,0,0] => 1
[1,0,1,1,0,0] => [1,3,2] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,0,0,1,0] => [2,1,3] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,0,1,0,0] => [2,3,1] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,1,0,0,0] => [3,2,1] => [3] => [1,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,2] => [1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
>>> Load all 1740 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 4
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,7,5,6,8,3] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,8,6,5,7,3] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,6,4,5,8,7,3] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,8,4,6,7,5,3] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,8,5,6,4,7,3] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,5,2,6,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,8,6,5,7,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,3,5,4,6,2,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,4,6,7,2,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,7,4,5,6,2,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,8,4,6,5,7,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[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] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3,5,2,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3,5,2,8,7,6] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,5,3,4,6,2,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,5,3,4,6,7,2,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,5,3,4,7,6,2,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,5,3,4,8,6,7,2] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,8,4,3,6,7,5,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,7,4,5,6,3,2,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,7,5,4,3,6,2,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7,5,4,3,6,8,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8,5,4,3,7,6,2] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,4,6,7,5,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,8,6,5,7,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 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] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,8,6,7,4] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,7,5,6,8,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,4,5,7,8,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,4,5,8,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,7,5,4,6,1,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,7,5,4,6,8,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,8,5,6,4,7,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,8,5,7,6,4,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[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] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,8,6,7,5] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 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] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,4,3,5,8,7,6,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,8,5,7,6,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,8,6,5,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,3,8,6,7,5,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,3,4,7,6,8,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,7,3,4,5,6,1,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,8,3,4,5,7,6,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,6,3,5,4,1,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,6,3,5,4,8,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7,3,5,4,6,8,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8,3,5,6,7,4,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,8,3,7,5,6,4,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[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] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,4,5,3,1,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,6,4,5,3,8,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,8,4,5,3,6,7,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,7,4,5,6,3,1,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,7,4,6,5,3,1,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,7,4,6,5,3,8,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,8,5,4,3,7,6,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,6,4,5,3,8,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,5,6,7,4,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 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] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 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] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 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] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,7,5,6,8,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,8,6,7,5,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,2,6,4,5,7,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,8,6,5,7,4,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,2,3,5,8,7,6,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,2,3,6,5,1,7,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,2,3,6,5,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,2,3,7,5,6,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,2,3,8,5,7,6,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,2,3,7,6,5,8,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,2,3,8,6,7,5,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,2,3,8,7,6,5,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,2,3,4,6,5,1,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8,2,3,4,7,6,5,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [6,2,3,5,4,7,1,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,2,3,5,4,7,8,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8,2,3,5,7,6,4,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8,2,3,7,6,5,4,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [5,2,4,3,6,1,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,2,4,3,8,7,6,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2,4,5,3,1,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,2,4,5,3,8,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8,2,4,5,6,3,7,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8,2,4,5,7,6,3,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8,2,4,7,5,6,3,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,2,5,4,3,1,7,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,2,5,4,3,7,8,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8,2,5,4,3,6,7,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,2,5,4,6,3,8,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,6,4,5,3,1,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,2,6,5,4,3,1,8] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,6,5,4,3,8,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 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] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[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] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 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] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 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] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8,3,2,4,7,6,5,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,3,2,5,4,8,7,1] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,3,2,5,6,4,8,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,3,5,4,2,7,8,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,3,5,4,2,8,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8,3,5,4,2,6,7,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8,3,5,4,2,7,6,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,5,4,6,2,1,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [8,3,6,4,5,7,2,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8,3,7,4,5,6,2,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8,3,7,5,4,6,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [6,4,3,2,5,8,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8,4,3,2,5,7,6,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,4,3,2,6,5,1,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8,4,3,2,6,5,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8,4,3,2,6,7,5,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8,4,3,5,2,7,6,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8,4,3,7,6,5,2,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,3,4,2,7,8,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8,6,3,4,5,2,7,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8,6,3,5,4,2,7,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8,6,3,5,4,7,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8,6,4,5,3,7,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[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] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[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] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[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] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,6,4,3,5,2,1,9,8] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [7,6,3,5,4,2,1,9,8] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[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] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[] => [] => [] => [] => 0
[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] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,9,4,5,6,7,8,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,2,3,4,9,6,7,8,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [7,2,3,4,5,6,9,8,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[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] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[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] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[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] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[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] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,8,7] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[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] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[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] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[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] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 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] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[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] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[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] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[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] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => [6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,9,8,10] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,2,3,4,5,6,1,9,8] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,9,4,5,6,7,8,3] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,2,3,1,9,8,7,6,5] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[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] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,5,3,4,2,1,9,8,7] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[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] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[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] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[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] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[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] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[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] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,2,1,9,5,8,7,6,4] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[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] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[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] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 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] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,3,2,1,9,7,8,6] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,1,9,8,6,7,5,4] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[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] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[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] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [10,5,4,3,2,9,8,7,6,1] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,9,4] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,9,5] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[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] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,10,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,9,8,1,10] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,2,1,7,8,9,6] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[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] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,2,1,10,7,6,9,8,5] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,8,7,9,2] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,5] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,6,5,7,10,8,9,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,9,8,3] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,10,9,2] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7,10,9,12,11] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7,10,9,12,11] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7,10,9,12,11] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,7,6,8,5,10,9,12,11] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,4,7,6,8,3,10,9,12,11] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,5,4,7,6,8,1,10,9,12,11] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,6,5,9,8,10,7,12,11] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,7,6,9,8,10,5,12,11] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,7,6,9,8,10,3,12,11] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,7,6,9,8,10,1,12,11] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,8,7,11,10,12,9] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,8,11,10,12,7] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,7,6,9,8,11,10,12,5] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,9,8,11,10,12,3] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,11,10,12,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10,3,2,5,4,7,6,9,8,1] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[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] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,7,10,12,11,9] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,5,8,10,9,7,12,11] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9,12,11] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9,12,11] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9,12,11] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,12,11,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[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] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[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] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[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] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[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] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,9,8] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[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] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7,10,9] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 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] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
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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 1,7,5,1 1,15,18,7,1 1,31,57,33,9,1 1,63,169,132,52,11,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + 3\ q^{2} + q^{3}$
$F_{4} = q + 7\ q^{2} + 5\ q^{3} + q^{4}$
$F_{5} = q + 15\ q^{2} + 18\ q^{3} + 7\ q^{4} + q^{5}$
$F_{6} = q + 31\ q^{2} + 57\ q^{3} + 33\ q^{4} + 9\ q^{5} + q^{6}$
$F_{7} = q + 63\ q^{2} + 169\ q^{3} + 132\ q^{4} + 52\ q^{5} + 11\ q^{6} + q^{7}$
Description
The number of odd rises of a Dyck path.
This is the number of ones at an odd position, with the initial position equal to 1.
The number of Dyck paths of semilength $n$ with $k$ up steps in odd positions and $k$ returns to the main diagonal are counted by the binomial coefficient $\binom{n-1}{k-1}$ [3,4].
This is the number of ones at an odd position, with the initial position equal to 1.
The number of Dyck paths of semilength $n$ with $k$ up steps in odd positions and $k$ returns to the main diagonal are counted by the binomial coefficient $\binom{n-1}{k-1}$ [3,4].
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
LLPS
Description
The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
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