Identifier
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Images
[1,0] => [1] => [1] => [1]
[1,0,1,0] => [1,2] => [1,1] => [2]
[1,1,0,0] => [2,1] => [2] => [1,1]
[1,0,1,0,1,0] => [1,2,3] => [1,1,1] => [3]
[1,0,1,1,0,0] => [1,3,2] => [2,1] => [2,1]
[1,1,0,0,1,0] => [2,1,3] => [2,1] => [2,1]
[1,1,0,1,0,0] => [2,3,1] => [2,1] => [2,1]
[1,1,1,0,0,0] => [3,2,1] => [3] => [1,1,1]
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,1,1,1] => [4]
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [2,1,1] => [3,1]
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [2,1,1] => [3,1]
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,1,1] => [3,1]
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [3,1] => [2,1,1]
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,1] => [3,1]
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,2] => [2,2]
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,1,1] => [3,1]
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,1,1] => [3,1]
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [3,1] => [2,1,1]
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,1] => [2,1,1]
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,1] => [2,1,1]
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [3,1] => [2,1,1]
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4] => [1,1,1,1]
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,1,1,1,1] => [5]
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [2,1,1,1] => [4,1]
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [2,1,1,1] => [4,1]
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [2,1,1,1] => [4,1]
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [3,1,1] => [3,1,1]
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [2,1,1,1] => [4,1]
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [2,2,1] => [3,2]
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [2,1,1,1] => [4,1]
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,1,1,1] => [4,1]
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [3,1,1] => [3,1,1]
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [3,1,1] => [3,1,1]
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [3,1,1] => [3,1,1]
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [3,1,1] => [3,1,1]
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [4,1] => [2,1,1,1]
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,1,1] => [4,1]
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,2,1] => [3,2]
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,2,1] => [3,2]
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,2,1] => [3,2]
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [3,2] => [2,2,1]
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,1,1,1] => [4,1]
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [2,2,1] => [3,2]
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,1,1,1] => [4,1]
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,1,1,1] => [4,1]
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [3,1,1] => [3,1,1]
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,1,1] => [3,1,1]
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [3,1,1] => [3,1,1]
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [3,1,1] => [3,1,1]
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [4,1] => [2,1,1,1]
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,1,1] => [3,1,1]
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [3,2] => [2,2,1]
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,1,1] => [3,1,1]
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [3,1,1] => [3,1,1]
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [3,2] => [2,2,1]
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [3,1,1] => [3,1,1]
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [3,1,1] => [3,1,1]
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [3,1,1] => [3,1,1]
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [4,1] => [2,1,1,1]
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,1] => [2,1,1,1]
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [4,1] => [2,1,1,1]
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [4,1] => [2,1,1,1]
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [4,1] => [2,1,1,1]
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5] => [1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [6]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [2,1,1,1,1] => [5,1]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [2,1,1,1,1] => [5,1]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [2,1,1,1,1] => [5,1]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [3,1,1,1] => [4,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [2,1,1,1,1] => [5,1]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [2,2,1,1] => [4,2]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [2,1,1,1,1] => [5,1]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [2,1,1,1,1] => [5,1]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [3,1,1,1] => [4,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [3,1,1,1] => [4,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [3,1,1,1] => [4,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [3,1,1,1] => [4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [4,1,1] => [3,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [2,1,1,1,1] => [5,1]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [2,2,1,1] => [4,2]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [2,2,1,1] => [4,2]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [2,2,1,1] => [4,2]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [3,2,1] => [3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [2,1,1,1,1] => [5,1]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [2,2,1,1] => [4,2]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [2,1,1,1,1] => [5,1]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,1,1,1,1] => [5,1]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [3,1,1,1] => [4,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [3,1,1,1] => [4,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [3,1,1,1] => [4,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [3,1,1,1] => [4,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [4,1,1] => [3,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [3,1,1,1] => [4,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [3,2,1] => [3,2,1]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [3,1,1,1] => [4,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [3,1,1,1] => [4,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [3,2,1] => [3,2,1]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [3,1,1,1] => [4,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [3,1,1,1] => [4,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [3,1,1,1] => [4,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [4,1,1] => [3,1,1,1]
>>> Load all 2134 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [4,1,1] => [3,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [4,1,1] => [3,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [4,1,1] => [3,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [4,1,1] => [3,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [5,1] => [2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,1,1,1] => [5,1]
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,2,1,1] => [4,2]
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,2,1,1] => [4,2]
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,2,1,1] => [4,2]
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [3,2,1] => [3,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,2,1,1] => [4,2]
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,2,2] => [3,3]
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,2,1,1] => [4,2]
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,2,1,1] => [4,2]
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [3,2,1] => [3,2,1]
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [3,2,1] => [3,2,1]
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [3,2,1] => [3,2,1]
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [3,2,1] => [3,2,1]
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [4,2] => [2,2,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,1,1,1,1] => [5,1]
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [2,2,1,1] => [4,2]
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [2,2,1,1] => [4,2]
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [2,2,1,1] => [4,2]
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1] => [3,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,1,1,1,1] => [5,1]
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [2,2,1,1] => [4,2]
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,1,1,1,1] => [5,1]
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,1,1,1,1] => [5,1]
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [3,1,1,1] => [4,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [3,1,1,1] => [4,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [3,1,1,1] => [4,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [3,1,1,1] => [4,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [4,1,1] => [3,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [3,1,1,1] => [4,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,2,1] => [3,2,1]
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [3,1,1,1] => [4,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [3,1,1,1] => [4,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [3,2,1] => [3,2,1]
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [3,1,1,1] => [4,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [3,1,1,1] => [4,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [3,1,1,1] => [4,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [4,1,1] => [3,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [4,1,1] => [3,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [4,1,1] => [3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [4,1,1] => [3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [4,1,1] => [3,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [5,1] => [2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,1,1,1] => [4,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [3,2,1] => [3,2,1]
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [3,2,1] => [3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,1] => [3,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [3,3] => [2,2,2]
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [3,1,1,1] => [4,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [3,2,1] => [3,2,1]
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [3,1,1,1] => [4,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [3,1,1,1] => [4,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [3,2,1] => [3,2,1]
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [3,2,1] => [3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [3,2,1] => [3,2,1]
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [3,2,1] => [3,2,1]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [4,2] => [2,2,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [3,1,1,1] => [4,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [3,2,1] => [3,2,1]
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [3,1,1,1] => [4,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [3,1,1,1] => [4,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [3,2,1] => [3,2,1]
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [3,1,1,1] => [4,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [3,1,1,1] => [4,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [3,1,1,1] => [4,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [4,1,1] => [3,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [4,1,1] => [3,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [4,1,1] => [3,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [4,1,1] => [3,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [4,1,1] => [3,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [5,1] => [2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,1,1] => [3,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [4,2] => [2,2,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [4,1,1] => [3,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,1,1] => [3,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [4,2] => [2,2,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [4,1,1] => [3,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [4,1,1] => [3,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [4,1,1] => [3,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [4,2] => [2,2,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [4,1,1] => [3,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [4,1,1] => [3,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [4,1,1] => [3,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [4,1,1] => [3,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [5,1] => [2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,1] => [2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [5,1] => [2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [5,1] => [2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [5,1] => [2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [5,1] => [2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6] => [1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [7]
[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] => [6,1]
[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] => [6,1]
[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] => [6,1]
[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] => [5,1,1]
[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] => [6,1]
[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] => [5,2]
[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] => [6,1]
[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] => [6,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,1,1,1]
[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] => [6,1]
[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] => [5,2]
[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] => [5,2]
[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] => [5,2]
[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] => [4,2,1]
[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] => [6,1]
[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] => [5,2]
[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] => [6,1]
[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] => [6,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,1,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [5,1,1] => [3,1,1,1,1]
[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] => [6,1]
[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] => [5,2]
[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] => [5,2]
[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] => [5,2]
[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] => [4,2,1]
[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] => [5,2]
[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] => [4,3]
[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] => [5,2]
[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] => [5,2]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [4,2,1] => [3,2,1,1]
[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] => [6,1]
[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] => [5,2]
[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] => [5,2]
[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] => [5,2]
[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] => [4,2,1]
[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] => [6,1]
[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] => [5,2]
[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] => [6,1]
[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] => [6,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,1,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [5,1,1] => [3,1,1,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [3,3,1] => [3,2,2]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [4,2,1] => [3,2,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [5,1,1] => [3,1,1,1,1]
[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] => [4,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [5,1,1] => [3,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [5,1,1] => [3,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [5,1,1] => [3,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [5,1,1] => [3,1,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [5,1,1] => [3,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [5,1,1] => [3,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [6,1] => [2,1,1,1,1,1]
[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] => [6,1]
[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] => [5,2]
[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] => [5,2]
[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] => [5,2]
[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] => [4,2,1]
[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] => [5,2]
[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] => [4,3]
[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] => [5,2]
[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] => [5,2]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [4,2,1] => [3,2,1,1]
[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] => [5,2]
[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] => [4,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,2,2,1] => [4,3]
[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] => [4,3]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [3,2,2] => [3,3,1]
[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] => [5,2]
[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] => [4,3]
[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] => [5,2]
[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] => [5,2]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [4,2,1] => [3,2,1,1]
[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] => [4,2,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [3,2,2] => [3,3,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [3,2,2] => [3,3,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [4,2,1] => [3,2,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [4,2,1] => [3,2,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [4,2,1] => [3,2,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [4,2,1] => [3,2,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [4,2,1] => [3,2,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [5,2] => [2,2,1,1,1]
[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] => [6,1]
[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] => [5,2]
[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] => [5,2]
[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] => [5,2]
[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] => [4,2,1]
[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] => [5,2]
[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] => [4,3]
[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] => [5,2]
[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] => [5,2]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [4,2,1] => [3,2,1,1]
[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] => [6,1]
[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] => [5,2]
[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] => [5,2]
[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] => [5,2]
[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] => [4,2,1]
[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] => [6,1]
[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] => [5,2]
[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] => [6,1]
[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] => [6,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,1,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [5,1,1] => [3,1,1,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [3,3,1] => [3,2,2]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [4,2,1] => [3,2,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [5,1,1] => [3,1,1,1,1]
[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] => [4,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [5,1,1] => [3,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [5,1,1] => [3,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [5,1,1] => [3,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [5,1,1] => [3,1,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [5,1,1] => [3,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [5,1,1] => [3,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [6,1] => [2,1,1,1,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [3,3,1] => [3,2,2]
[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] => [4,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [3,2,2] => [3,3,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [3,3,1] => [3,2,2]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [3,3,1] => [3,2,2]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [3,3,1] => [3,2,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [3,3,1] => [3,2,2]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [4,3] => [2,2,2,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [3,3,1] => [3,2,2]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [4,2,1] => [3,2,1,1]
[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] => [4,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [3,2,2] => [3,3,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [3,2,2] => [3,3,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [4,2,1] => [3,2,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [4,2,1] => [3,2,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [4,2,1] => [3,2,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [4,2,1] => [3,2,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [4,2,1] => [3,2,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [5,2] => [2,2,1,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [3,3,1] => [3,2,2]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[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] => [4,2,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [4,2,1] => [3,2,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,2,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [5,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [5,1,1] => [3,1,1,1,1]
[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] => [4,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [5,1,1] => [3,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [6,1] => [2,1,1,1,1,1]
[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] => [4,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [4,2,1] => [3,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [4,2,1] => [3,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [4,2,1] => [3,2,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [4,3] => [2,2,2,1]
[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] => [4,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [4,2,1] => [3,2,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [4,2,1] => [3,2,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [4,2,1] => [3,2,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [4,2,1] => [3,2,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [4,3] => [2,2,2,1]
[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] => [4,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [4,2,1] => [3,2,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [4,2,1] => [3,2,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [4,2,1] => [3,2,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [4,2,1] => [3,2,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [4,2,1] => [3,2,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [5,2] => [2,2,1,1,1]
[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] => [4,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [4,2,1] => [3,2,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[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] => [4,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [6,1] => [2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [5,2] => [2,2,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [5,2] => [2,2,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [5,2] => [2,2,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [5,2] => [2,2,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [5,1,1] => [3,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [6,1] => [2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,1] => [2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [6,1] => [2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [6,1] => [2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [6,1] => [2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [6,1] => [2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [6,1] => [2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [7] => [1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => [8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => [7,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [2,1,1,1,1,1,1] => [7,1]
[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] => [7,1]
[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] => [6,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [2,1,1,1,1,1,1] => [7,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [2,2,1,1,1,1] => [6,2]
[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] => [7,1]
[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] => [7,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [2,1,1,1,1,1,1] => [7,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [2,1,1,1,1,1,1] => [7,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [2,2,1,1,1,1] => [6,2]
[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] => [7,1]
[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] => [7,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => [7,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [2,2,1,1,1,1] => [6,2]
[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] => [5,3]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [2,1,1,1,1,1,1] => [7,1]
[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] => [6,2]
[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] => [7,1]
[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] => [7,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => [7,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [2,2,1,1,1,1] => [6,2]
[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] => [5,3]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [2,2,1,1,1,1] => [6,2]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [2,2,1,1,1,1] => [6,2]
[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] => [5,3]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [2,2,2,1,1] => [5,3]
[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] => [4,3,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [2,2,1,1,1,1] => [6,2]
[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] => [5,3]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [2,1,1,1,1,1,1] => [7,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [2,2,2,1,1] => [5,3]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [2,1,1,1,1,1,1] => [7,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,5,2,6,8,7] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [2,1,1,1,1,1,1] => [7,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [2,2,1,1,1,1] => [6,2]
[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] => [7,1]
[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] => [7,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,2]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,2]
[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] => [4,2,2]
[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] => [4,2,2]
[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] => [3,2,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,2]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [3,1,1,1,1,1] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [4,2,2]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,2,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [3,2,2,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [2,1,1,1,1,1,1]
[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] => [7,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[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] => [6,2]
[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] => [5,3]
[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] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [5,3]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [2,2,2,1,1] => [5,3]
[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] => [4,3,1]
[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] => [5,3]
[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] => [6,2]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[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] => [6,2]
[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] => [5,3]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [2,2,2,1,1] => [5,3]
[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] => [4,3,1]
[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] => [5,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,2,2,2] => [4,4]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,2,2,1,1] => [5,3]
[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] => [4,3,1]
[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] => [4,3,1]
[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] => [4,3,1]
[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] => [3,3,1,1]
[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] => [6,2]
[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] => [5,3]
[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] => [4,3,1]
[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] => [5,3]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [4,3,1]
[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] => [4,3,1]
[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] => [3,3,1,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[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] => [3,3,1,1]
[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] => [3,3,1,1]
[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] => [3,3,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [2,2,1,1,1,1]
[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] => [7,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [6,2]
[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] => [5,3]
[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] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[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] => [4,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [2,2,1,1,1,1] => [6,2]
[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] => [5,3]
[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] => [6,2]
[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] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [2,1,1,1,1,1,1] => [7,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [2,2,1,1,1,1] => [6,2]
[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] => [5,3]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [2,1,1,1,1,1,1] => [7,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [2,2,1,1,1,1] => [6,2]
[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] => [6,2]
[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] => [6,2]
[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] => [5,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [2,1,1,1,1,1,1] => [7,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [2,2,1,1,1,1] => [6,2]
[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] => [7,1]
[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] => [7,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,2]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [6,1,1]
[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] => [4,2,2]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [4,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [3,3,1,1] => [4,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,8,6,7,5] => [3,3,1,1] => [4,2,2]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [4,3,1] => [3,2,2,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,2]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[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] => [6,1,1]
[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] => [4,2,2]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,2,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [3,2,2,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [2,1,1,1,1,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,2]
[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] => [5,2,1]
[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] => [4,2,2]
[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] => [4,2,2]
[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] => [4,2,2]
[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] => [4,2,2]
[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] => [3,2,2,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,2]
[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] => [4,2,2]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [3,3,1,1] => [4,2,2]
[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] => [4,2,2]
[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] => [3,2,2,1]
[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] => [4,2,2]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [3,3,1,1] => [4,2,2]
[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] => [3,3,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => [3,3,1,1] => [4,2,2]
[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] => [4,2,2]
[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] => [3,2,2,1]
[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] => [3,2,2,1]
[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] => [3,2,2,1]
[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] => [3,2,2,1]
[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] => [3,2,2,1]
[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] => [2,2,2,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,2]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [3,3,1,1] => [4,2,2]
[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] => [4,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [3,3,1,1] => [4,2,2]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [4,3,1] => [3,2,2,1]
[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] => [6,1,1]
[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] => [4,2,2]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [4,3,1]
[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] => [4,3,1]
[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] => [3,3,2]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [4,3,1]
[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] => [4,3,1]
[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] => [4,3,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,3,1,1]
[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] => [4,2,1,1]
[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] => [3,3,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,3,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [2,2,1,1,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [4,2,2]
[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] => [4,2,2]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [3,3,1,1] => [4,2,2]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [4,3,1] => [3,2,2,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,2]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => [3,1,1,1,1,1] => [6,1,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [5,2,1]
[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] => [4,3,1]
[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] => [4,3,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,2]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [5,2,1]
[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] => [4,2,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,2,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [6,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,2,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,2,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [2,1,1,1,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,3,1,1]
[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] => [4,2,1,1]
[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] => [3,2,2,1]
[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] => [3,2,2,1]
[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] => [3,2,2,1]
[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] => [2,2,2,2]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [4,1,1,1,1] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [3,2,2,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,2,1]
[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] => [4,2,1,1]
[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] => [3,3,1,1]
[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] => [4,2,1,1]
[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] => [3,3,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,2,1]
[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] => [3,2,2,1]
[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] => [3,2,2,1]
[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] => [2,2,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,2,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[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] => [3,3,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,3,1,1]
[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] => [4,2,1,1]
[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] => [3,3,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [2,2,1,1,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [3,2,2,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [4,2,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [5,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [2,1,1,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [2,2,2,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [2,2,2,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [2,2,2,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [3,2,1,1,1]
[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] => [2,2,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,2,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [2,1,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [2,2,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [2,2,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [2,2,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [2,2,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [2,2,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [3,1,1,1,1,1]
[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] => [2,1,1,1,1,1,1]
[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] => [2,1,1,1,1,1,1]
[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] => [2,1,1,1,1,1,1]
[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] => [2,1,1,1,1,1,1]
[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] => [2,1,1,1,1,1,1]
[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] => [2,1,1,1,1,1,1]
[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] => [2,1,1,1,1,1,1]
[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] => [2,1,1,1,1,1,1]
[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] => [1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [8,1] => [2,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,7,6,4,5,3,2,1,9] => [7,1,1] => [3,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,9,8,7,5,6,4,3,2] => [7,1,1] => [3,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,1] => [2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,8,7,5,6,4,3,2,1,10] => [8,1,1] => [3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,7,5,4,6,3,2,1,9] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,7,4,6,5,3,2,1,9] => [7,1,1] => [3,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,9,8,6,5,7,4,3,2] => [7,1,1] => [3,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,9,8,5,7,6,4,3,2] => [7,1,1] => [3,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,10,9,8,6,7,5,4,3,2] => [8,1,1] => [3,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [10,1] => [2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1,12] => [11,1] => [2,1,1,1,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,9,8,5,6,7,4,3,2] => [6,1,1,1] => [4,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,10,9,8,5,6,7,4,3,2] => [7,1,1,1] => [4,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,9,8,5,4,6,7,3,2] => [6,1,1,1] => [4,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,10,9,6,5,8,7,4,3,2] => [7,2,1] => [3,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,6,5,4,3,2,8,1,9] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [7,1,1] => [3,1,1,1,1,1,1]
[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] => [2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,9,8,4,5,6,7,3,2] => [5,1,1,1,1] => [5,1,1,1,1]
[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] => [2,2,1,1,1,1,1]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [7,1,1] => [3,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [7,1,1] => [3,1,1,1,1,1,1]
[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] => [3,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,10,9,5,6,7,8,4,3,2] => [6,1,1,1,1] => [5,1,1,1,1,1]
[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] => [3,2,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,7,6,5,4,3,2,9,1,10] => [8,1,1] => [3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [8,2] => [2,2,1,1,1,1,1,1]
[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] => [3,2,1,1,1,1]
[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] => [3,2,1,1,1,1]
[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] => [3,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [8,2] => [2,2,1,1,1,1,1,1]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,10,9,8,7,6,5,4,2] => [8,1,1] => [3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [8,1,1] => [3,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [8,1,1] => [3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,4,5,3,2,1,10,9] => [7,2,1] => [3,2,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,9,5,4,6,7,8,3,2] => [5,1,1,1,1] => [5,1,1,1,1]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,10,9,8,6,7,5,4,3] => [7,2,1] => [3,2,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [8,1,1] => [3,1,1,1,1,1,1,1]
[] => [] => [] => []
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [2,1,1,1,1,1,1,1] => [8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,9,7,8,1] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,1] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,5,8,6,7,9,1] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,9,6,7,8,1] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,5,9,6,8,7,1] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,5,8,7,6,9,1] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,5,9,7,6,8,1] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,9,7,8,6,1] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,9,5,6,7,8,1] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,4,9,6,5,7,8,1] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,9,6,7,8,5,1] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,9,4,5,6,7,8,1] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,9,5,4,6,7,8,1] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,9,5,6,7,8,4,1] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,9,3,4,5,6,7,8,1] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,9,4,3,5,6,7,8,1] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,9,4,5,6,7,8,3,1] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,8,7,5,6,4,3,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => [7,1,1]
[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] => [4,4,1]
[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] => [6,2,1]
[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] => [2,2,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => [7,1,1]
[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] => [6,2,1]
[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] => [6,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9,2,4,5,6,8,7,3,1] => [5,1,1,1,1] => [5,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [9,2,7,4,5,6,3,8,1] => [5,1,1,1,1] => [5,1,1,1,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9,2,7,6,5,4,3,8,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9,2,8,7,6,5,4,3,1] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,3,2,4,5,6,7,8,1] => [4,1,1,1,1,1] => [6,1,1,1]
[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] => [5,2,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9,3,4,2,5,6,7,8,1] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [9,3,4,5,2,6,7,8,1] => [4,1,1,1,1,1] => [6,1,1,1]
[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] => [5,2,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,3,4,5,6,7,8,2,1] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9,3,4,5,6,8,7,2,1] => [5,1,1,1,1] => [5,1,1,1,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9,3,7,6,5,4,8,2,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9,3,8,7,6,5,4,2,1] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => [5,1,1,1,1] => [5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [9,4,3,2,5,6,7,8,1] => [5,1,1,1,1] => [5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [9,4,3,5,6,7,2,8,1] => [5,1,1,1,1] => [5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [9,4,3,5,6,7,8,2,1] => [5,1,1,1,1] => [5,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [9,8,3,4,5,7,6,2,1] => [6,1,1,1] => [4,1,1,1,1,1]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [9,8,3,5,7,6,4,2,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [9,8,3,6,5,4,7,2,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [9,8,3,7,6,5,4,2,1] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,1] => [6,1,1,1] => [4,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [9,8,4,3,5,6,7,2,1] => [6,1,1,1] => [4,1,1,1,1,1]
[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] => [3,2,1,1,1,1]
[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] => [3,2,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [9,8,4,5,7,6,3,2,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [8,7,4,6,5,3,2,9,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [9,8,4,6,5,7,3,2,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [9,8,4,7,6,5,3,2,1] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,1] => [7,1,1] => [3,1,1,1,1,1,1]
[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] => [2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [8,7,5,4,6,3,2,9,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [9,8,5,4,6,3,7,2,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [9,8,5,4,6,7,3,2,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,7,6,4,5,3,2,9,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [9,8,7,4,5,6,3,2,1] => [7,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9,8,7,4,6,5,3,2,1] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9,7,6,5,4,3,2,8,1] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [9,7,6,5,4,3,8,2,1] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [9,8,6,5,4,3,7,2,1] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [9,8,6,5,4,7,3,2,1] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [9,8,7,5,4,6,3,2,1] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,8,7,5,6,4,3,2,1] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [9] => [1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => [9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [2,1,1,1,1,1,1,1] => [8,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [2,1,1,1,1,1,1,1] => [8,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [2,1,1,1,1,1,1,1] => [8,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [2,1,1,1,1,1,1,1] => [8,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [2,1,1,1,1,1,1,1] => [8,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [2,1,1,1,1,1,1,1] => [8,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [2,1,1,1,1,1,1,1] => [8,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => [10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [3,1,1,1,1,1,1] => [7,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [3,1,1,1,1,1,1] => [7,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,6,8,9,5] => [3,1,1,1,1,1,1] => [7,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,5,7,8,9,4] => [3,1,1,1,1,1,1] => [7,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => [3,1,1,1,1,1,1] => [7,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [3,1,1,1,1,1,1] => [7,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1] => [11]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [2,1,1,1,1,1,1,1,1,1] => [10,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [2,1,1,1,1,1,1,1,1,1] => [10,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,9,7,8,6] => [3,1,1,1,1,1,1] => [7,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => [2,1,1,1,1,1,1,1,1,1] => [10,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => [3,1,1,1,1,1,1,1,1] => [9,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,6,10,8,9,7] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,9,6,7,8,5] => [3,1,1,1,1,1,1] => [7,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [4,1,1,1,1,1,1] => [7,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,2,7,4,5,6,8,9,3] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,10,1] => [4,1,1,1,1,1,1] => [7,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,11,1] => [3,1,1,1,1,1,1,1,1] => [9,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,12,2] => [2,1,1,1,1,1,1,1,1,1,1] => [11,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,5,10,7,8,9,6] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,9,5,6,7,8,4] => [3,1,1,1,1,1,1] => [7,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [5,1,1,1,1] => [5,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,4,10,6,7,8,9,5] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,9,4,5,6,7,8,3] => [3,1,1,1,1,1,1] => [7,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [5,1,1,1,1,1] => [6,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,8,3,4,5,6,7,9,2] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,2,3,4,5,7,8,9,10,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,10,1] => [5,1,1,1,1,1] => [6,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,3,10,5,6,7,8,9,4] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9,3,4,5,6,7,8,2] => [3,1,1,1,1,1,1] => [7,1,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [6,1,1,1] => [4,1,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,9,4,5,6,7,8,3,2] => [4,1,1,1,1,1] => [6,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,10,4,5,6,7,8,9,3] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [6,1,1,1,1] => [5,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,10,1] => [6,1,1,1,1] => [5,1,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,10,3,4,5,6,7,8,9,2] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,10,4,5,6,7,8,9,3,2] => [4,1,1,1,1,1,1] => [7,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [2,2,1,1,1,1,1] => [7,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => [2,2,1,1,1,1,1] => [7,2]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[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] => [6,3]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[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] => [6,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [2,2,1,1,1,1,1] => [7,2]
[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] => [6,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => [2,2,1,1,1,1,1] => [7,2]
[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] => [5,4]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [3,1,1,1,1,1,1] => [7,1,1]
[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] => [3,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [2,2,1,1,1,1,1] => [7,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [2,2,1,1,1,1,1] => [7,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [2,2,1,1,1,1,1] => [7,2]
[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] => [5,4]
[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] => [3,2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [3,1,1,1,1,1,1] => [7,1,1]
[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] => [4,4,1]
[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] => [2,2,2,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [4,1,1,1,1,1] => [6,1,1,1]
[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] => [2,2,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [5,1,1,1,1] => [5,1,1,1,1]
[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] => [2,2,2,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [6,1,1,1] => [4,1,1,1,1,1]
[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] => [2,2,2,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [2,2,2,1,1,1,1] => [7,3]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [7,1,1,1] => [4,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[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] => [6,4]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [2,2,1,1,1,1,1,1] => [8,2]
[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] => [5,5]
[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] => [4,4,1,1]
[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] => [3,3,2,2]
[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] => [3,3,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => [8,1,1]
[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] => [5,4,1]
[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] => [2,2,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [4,1,1,1,1,1,1] => [7,1,1,1]
[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] => [4,4,1,1]
[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] => [3,3,2,2]
[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] => [3,3,2,2]
[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] => [2,2,2,2,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [5,1,1,1,1,1] => [6,1,1,1,1]
[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] => [2,2,2,2,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [6,1,1,1,1] => [5,1,1,1,1,1]
[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] => [2,2,2,2,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [7,1,1,1] => [4,1,1,1,1,1,1]
[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] => [2,2,2,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [10] => [1,1,1,1,1,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [10,9,3,4,5,6,8,7,2,1] => [6,1,1,1,1] => [5,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [10,9,4,3,5,6,7,8,2,1] => [6,1,1,1,1] => [5,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [11,10,3,4,5,6,7,9,8,2,1] => [6,1,1,1,1,1] => [6,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [10,3,4,5,6,7,9,8,2,1] => [5,1,1,1,1,1] => [6,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10,4,3,5,6,7,8,9,2,1] => [5,1,1,1,1,1] => [6,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [11,10,4,3,5,6,7,8,9,2,1] => [6,1,1,1,1,1] => [6,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,1,1,1,1,1,1,1,1] => [10,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [2,2,1,1,1,1,1] => [7,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [10,9,8,5,7,6,4,3,2,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [10,9,8,6,5,7,4,3,2,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,5,7,6,4,3,2,1] => [10,1] => [2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [10,9,8,4,5,7,6,3,2,1] => [8,1,1] => [3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [10,9,8,5,4,6,7,3,2,1] => [8,1,1] => [3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [11,10,9,8,6,5,7,4,3,2,1] => [10,1] => [2,1,1,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,7,9,10,8] => [2,2,1,1,1,1,1,1] => [8,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,6,8,9,7] => [2,2,1,1,1,1,1] => [7,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,6,8,9,7] => [2,2,1,1,1,1,1] => [7,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [2,2,1,1,1,1,1] => [7,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,2,3,4,5,6,7,1,9] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,2,3,4,5,6,1,8,9] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [10,1] => [2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,8,7,5,6,4,3,2,10,1] => [8,1,1] => [3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,5,4,3,2,7,1,8,9] => [6,1,1,1] => [4,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,4,3,2,6,1,7,8,9] => [5,1,1,1,1] => [5,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8,9] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,9,8,7,5,6,4,3,2,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [10,9,8,4,7,6,5,3,2,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,9,4,8,7,6,5,3,2,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,9,3,8,7,6,5,4,2,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,3,9,8,7,6,5,4,2,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,2,9,8,7,6,5,4,3,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[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] => [6,2,1]
[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] => [6,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,8,3,4,5,6,7,1,9] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,10,3,4,5,6,7,8,9,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,6,7,5,4,3,2,1] => [10,1] => [2,1,1,1,1,1,1,1,1,1]
[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] => [3,2,1,1,1,1]
[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] => [3,2,2,1,1]
[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] => [3,2,2,2]
[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] => [3,2,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,9,6,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6,7,9,8] => [2,2,1,1,1,1,1] => [7,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8,9] => [2,2,1,1,1,1,1] => [7,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,6,3,4,5,7,8,9,10,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,6,4,5,7,8,9,10,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,10,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,10,9,4,5,6,7,8,3,2] => [5,1,1,1,1,1] => [6,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,9,4,3,5,6,7,8,2] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [3,1,1,1,1,1,1] => [7,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [2,2,1,1,1,1,1] => [7,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [2,2,1,1,1,1,1] => [7,2]
[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] => [6,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => [4,1,1,1,1,1,1] => [7,1,1,1]
[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] => [5,2,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,6,10,8,9,7,1] => [4,1,1,1,1,1,1] => [7,1,1,1]
[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] => [5,2,1,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,10,7,8,9,6,1] => [4,1,1,1,1,1,1] => [7,1,1,1]
[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] => [5,2,1,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,10,6,7,8,9,5,1] => [4,1,1,1,1,1,1] => [7,1,1,1]
[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] => [5,2,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,10,5,6,7,8,9,4,1] => [4,1,1,1,1,1,1] => [7,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,10,4,5,6,7,8,9,3,1] => [4,1,1,1,1,1,1] => [7,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10,3,4,5,6,7,8,9,2,1] => [4,1,1,1,1,1,1] => [7,1,1,1]
[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] => [3,2,1,1,1,1]
[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] => [3,2,1,1,1,1]
[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] => [3,2,2,1,1]
[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] => [3,2,2,1,1]
[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] => [3,2,2,2]
[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] => [3,2,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [10,8,7,6,5,4,3,2,9,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[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] => [3,2,2,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [10,8,7,6,5,4,3,9,2,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [10,9,7,6,5,4,3,8,2,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[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] => [3,2,2,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [10,9,7,6,5,4,8,3,2,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [10,9,8,6,5,4,7,3,2,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,3,5,7,8,9,6] => [2,2,1,1,1,1,1] => [7,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,5,10,6,7,8,9,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,9] => [2,2,1,1,1,1,1] => [7,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,6,8,9] => [2,2,1,1,1,1,1] => [7,2]
[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] => [5,3,1]
[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] => [5,4]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9] => [3,2,2,2,1] => [5,4,1]
[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] => [5,4,1]
[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] => [6,4]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,7,10,8,9,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,10,7,8,9,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,10,5,6,7,8,9,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,10,4,5,6,7,8,9,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,2,3,4,5,6,7,8,9,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,9,11,10,1] => [3,1,1,1,1,1,1,1,1] => [9,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,3,2,4,5,6,7,8,9,1] => [4,1,1,1,1,1,1] => [7,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [11,2,3,4,5,6,7,8,9,10,1] => [3,1,1,1,1,1,1,1,1] => [9,1,1]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [10,9,8,5,4,7,6,3,2,1] => [8,2] => [2,2,1,1,1,1,1,1]
[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] => [2,2,2,2,1,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => [11] => [1,1,1,1,1,1,1,1,1,1,1]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,11,10,9,8,7,6,5,4,3] => [9,2] => [2,2,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1,10] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10,11] => [2,1,1,1,1,1,1,1,1,1] => [10,1]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [6,1,1,1] => [4,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => [5,1,1,1,1] => [5,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => [4,1,1,1,1,1] => [6,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [3,1,1,1,1,1,1] => [7,1,1]
[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] => [6,2,1]
[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] => [5,2,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,8,7,6,5,4,3,2,1,11,10] => [9,2] => [2,2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [10,7,6,5,4,3,2,9,8,1] => [8,2] => [2,2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => [2,2,1,1,1,1,1,1] => [8,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => [2,2,1,1,1,1,1] => [7,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [2,1,1,1,1,1,1,1,1,1] => [10,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,1,8,9,10,7] => [2,2,1,1,1,1,1,1] => [8,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,7,9,8,4] => [3,1,1,1,1,1,1] => [7,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,6,8,9,7,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => [2,1,1,1,1,1,1,1,1,1] => [10,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [2,1,1,1,1,1,1,1] => [8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,7,6,5,4,3,2,10,9,1] => [8,2] => [2,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,5,7,6,8,1,9] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [11,3,4,5,6,7,8,9,10,2,1] => [4,1,1,1,1,1,1,1] => [8,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,9,4] => [2,2,1,1,1,1,1] => [7,2]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,9,4,5,6,7,8,2] => [3,1,1,1,1,1,1] => [7,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [2,2,1,1,1,1,1,1] => [8,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => [2,2,1,1,1,1,1] => [7,2]
[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] => [6,5]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1,10,11] => [9,1,1] => [3,1,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,2,3,4,5,6,7,8,9,11,1] => [3,1,1,1,1,1,1,1,1] => [9,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,3,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,9,5] => [2,2,1,1,1,1,1] => [7,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,6,8,10,9,7] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,7,8,4,9,10] => [2,1,1,1,1,1,1,1,1] => [9,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,7,10,9,8,5] => [4,1,1,1,1,1,1] => [7,1,1,1]
[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] => [5,3,1]
[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] => [5,3,1]
[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] => [5,4,1]
[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] => [5,4,1]
[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] => [5,4,1]
[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] => [5,4,1]
[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] => [5,4,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,4,8,5,6,7,1,9] => [3,1,1,1,1,1,1] => [7,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,9,5,4,6,7,8,3] => [4,1,1,1,1,1] => [6,1,1,1]
[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] => [4,2,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,6,8,7,9,2] => [3,1,1,1,1,1,1] => [7,1,1]
[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] => [3,2,1,1,1,1]
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10,3,2,9,8,7,6,5,4,1] => [8,2] => [2,2,1,1,1,1,1,1]
[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] => [3,3,2,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,8,3,9] => [2,2,1,1,1,1,1] => [7,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,10,1] => [8,1,1] => [3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,10,1] => [7,1,1,1] => [4,1,1,1,1,1,1]
[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] => [5,3,1]
[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] => [5,4,1]
[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] => [5,4,1]
[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] => [5,4,1]
[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] => [6,4]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,4,9,7,6,8,5] => [4,1,1,1,1,1] => [6,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,3,9,6,5,7,8,4] => [4,1,1,1,1,1] => [6,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => [8,1,1]
[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] => [6,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => [2,1,1,1,1,1,1,1] => [8,1]
[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] => [6,3,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,7,9,8,1,10] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,9,8,5] => [3,1,1,1,1,1,1] => [7,1,1]
[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] => [5,3,1]
[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] => [5,4,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,4,5,7,8,9,10,6] => [2,2,1,1,1,1,1,1] => [8,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [8,2,3,4,5,6,7,10,9,1] => [3,2,1,1,1,1,1] => [7,2,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,10,4,5,6,7,8,9,1] => [3,2,1,1,1,1,1] => [7,2,1]
[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] => [5,4,1]
[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] => [5,4,1]
[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] => [5,3,2]
[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] => [5,4,1]
[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] => [5,3,2]
[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] => [5,3,2]
[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] => [5,3,2]
[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] => [5,3,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,2,2,2,2,2] => [6,6]
[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] => [6,5,1]
[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] => [6,5,1]
[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] => [6,5,1]
[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] => [6,5,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,7,6,8,5,10,9,12,11] => [3,3,2,2,1,1] => [6,4,2]
[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] => [6,5,1]
[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] => [6,5,1]
[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] => [6,5,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5,9,8,10,7,12,11] => [3,3,2,2,1,1] => [6,4,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,9,8,10,7,12,11] => [3,3,2,2,1,1] => [6,4,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,9,8,10,7,12,11] => [3,3,2,2,1,1] => [6,4,2]
[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] => [6,5,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,7,6,9,8,10,5,12,11] => [3,3,2,2,1,1] => [6,4,2]
[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] => [6,5,1]
[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] => [6,5,1]
[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] => [6,5,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,6,5,8,7,11,10,12,9] => [3,3,2,2,1,1] => [6,4,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3,8,7,11,10,12,9] => [3,3,2,2,1,1] => [6,4,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,2,5,4,6,1,8,7,11,10,12,9] => [3,3,2,2,1,1] => [6,4,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5,11,10,12,9] => [3,3,2,2,1,1] => [6,4,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5,11,10,12,9] => [3,3,3,1,1,1] => [6,3,3]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3,11,10,12,9] => [3,3,2,2,1,1] => [6,4,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1,11,10,12,9] => [3,3,2,2,1,1] => [6,4,2]
[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] => [6,5,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,4,1,6,5,9,8,11,10,12,7] => [3,3,2,2,1,1] => [6,4,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,6,3,9,8,11,10,12,7] => [3,3,2,2,1,1] => [6,4,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1,9,8,11,10,12,7] => [3,3,2,2,1,1] => [6,4,2]
[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] => [6,5,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,4,1,7,6,9,8,11,10,12,5] => [3,3,2,2,1,1] => [6,4,2]
[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] => [6,5,1]
[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] => [6,5,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8,10] => [2,2,1,1,1,1,1,1] => [8,2]
[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] => [4,4,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => [10,2] => [2,2,1,1,1,1,1,1,1,1]
[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] => [6,4]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,11,10] => [2,2,1,1,1,1,1,1,1] => [9,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,1,7,8,9,6] => [2,2,1,1,1,1,1] => [7,2]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,4,6,10,7,8,9,1] => [3,2,1,1,1,1,1] => [7,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,7,8,10,9,1] => [3,2,1,1,1,1,1] => [7,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,5,4,3,2,1,9,10,8] => [7,2,1] => [3,2,1,1,1,1,1]
[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] => [5,4,1]
[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] => [5,4,1]
[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] => [5,4,1]
[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] => [5,3,2]
[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] => [5,3,2]
[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] => [5,3,2]
[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] => [6,5,1]
[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] => [6,5,1]
[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] => [6,5,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5,10,12,11,9] => [3,3,2,2,1,1] => [6,4,2]
[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] => [6,5,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3,8,7,10,12,11,9] => [3,3,2,2,1,1] => [6,4,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,10,9,7,12,11] => [3,3,2,2,1,1] => [6,4,2]
[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] => [6,5,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,5,8,7,10,12,11,9] => [3,3,2,2,1,1] => [6,4,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5,8,10,9,7,12,11] => [3,3,2,2,1,1] => [6,4,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,8,7,5,10,9,12,11] => [3,3,2,2,1,1] => [6,4,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5,10,12,11,9] => [3,3,3,1,1,1] => [6,3,3]
[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] => [6,5,1]
[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] => [6,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,7,1,9,10,8] => [2,2,1,1,1,1,1,1] => [8,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,5,8,9,10,7] => [2,2,2,1,1,1,1] => [7,3]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,8,10,9,5] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,5,7,8,10,9,6] => [3,1,1,1,1,1,1,1] => [8,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,10,5] => [2,2,2,1,1,1,1] => [7,3]
[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] => [6,4]
[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] => [6,3]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,9,8,10] => [2,2,2,1,1,1,1] => [7,3]
[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] => [6,3]
[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] => [6,3]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,9,8,10] => [2,2,2,1,1,1,1] => [7,3]
[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] => [6,3]
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [10,9,6,5,4,3,8,7,2,1] => [8,2] => [2,2,1,1,1,1,1,1]
[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] => [4,4,1,1]
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,10,9,8,7,6,5,3] => [7,1,1,1] => [4,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7,10,9] => [2,2,2,1,1,1,1] => [7,3]
[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] => [6,4]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,12,10] => [2,2,2,2,2,1,1] => [7,5]
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
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
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
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