Identifier
-
Mp00079:
Set partitions
—shape⟶
Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
St001513: Permutations ⟶ ℤ
Values
{{1}} => [1] => [1,0] => [1] => 0
{{1,2}} => [2] => [1,0,1,0] => [1,2] => 0
{{1},{2}} => [1,1] => [1,1,0,0] => [2,1] => 0
{{1,2,3}} => [3] => [1,0,1,0,1,0] => [1,2,3] => 0
{{1,2},{3}} => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 0
{{1,3},{2}} => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 0
{{1},{2,3}} => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 0
{{1},{2},{3}} => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 0
{{1,2,3,4}} => [4] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 0
{{1,2,3},{4}} => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 0
{{1,2,4},{3}} => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 0
{{1,2},{3,4}} => [2,2] => [1,1,1,0,0,0] => [3,2,1] => 0
{{1,2},{3},{4}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 0
{{1,3,4},{2}} => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 0
{{1,3},{2,4}} => [2,2] => [1,1,1,0,0,0] => [3,2,1] => 0
{{1,3},{2},{4}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 0
{{1,4},{2,3}} => [2,2] => [1,1,1,0,0,0] => [3,2,1] => 0
{{1},{2,3,4}} => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 0
{{1},{2,3},{4}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 0
{{1,4},{2},{3}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 0
{{1},{2,4},{3}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 0
{{1},{2},{3,4}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 0
{{1},{2},{3},{4}} => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 0
{{1,2,3,4,5}} => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 0
{{1,2,3,4},{5}} => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 0
{{1,2,3,5},{4}} => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 0
{{1,2,3},{4,5}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 0
{{1,2,3},{4},{5}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 0
{{1,2,4,5},{3}} => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 0
{{1,2,4},{3,5}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 0
{{1,2,4},{3},{5}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 0
{{1,2,5},{3,4}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 0
{{1,2},{3,4,5}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 0
{{1,2},{3,4},{5}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1,2,5},{3},{4}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 0
{{1,2},{3,5},{4}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1,2},{3},{4,5}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1,2},{3},{4},{5}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 0
{{1,3,4,5},{2}} => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 0
{{1,3,4},{2,5}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 0
{{1,3,4},{2},{5}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 0
{{1,3,5},{2,4}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 0
{{1,3},{2,4,5}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 0
{{1,3},{2,4},{5}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1,3,5},{2},{4}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 0
{{1,3},{2,5},{4}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1,3},{2},{4,5}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1,3},{2},{4},{5}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 0
{{1,4,5},{2,3}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 0
{{1,4},{2,3,5}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 0
{{1,4},{2,3},{5}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1,5},{2,3,4}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 0
{{1},{2,3,4,5}} => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 0
{{1},{2,3,4},{5}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 0
{{1,5},{2,3},{4}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1},{2,3,5},{4}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 0
{{1},{2,3},{4,5}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1},{2,3},{4},{5}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 0
{{1,4,5},{2},{3}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 0
{{1,4},{2,5},{3}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1,4},{2},{3,5}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1,4},{2},{3},{5}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 0
{{1,5},{2,4},{3}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1},{2,4,5},{3}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 0
{{1},{2,4},{3,5}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1},{2,4},{3},{5}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 0
{{1,5},{2},{3,4}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1},{2,5},{3,4}} => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
{{1},{2},{3,4,5}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 0
{{1},{2},{3,4},{5}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 0
{{1,5},{2},{3},{4}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 0
{{1},{2,5},{3},{4}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 0
{{1},{2},{3,5},{4}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 0
{{1},{2},{3},{4,5}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 0
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 0
{{1,2,3,4,5,6}} => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 0
{{1,2,3,4,5},{6}} => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 0
{{1,2,3,4,6},{5}} => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 0
{{1,2,3,4},{5,6}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
{{1,2,3,4},{5},{6}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1,2,3,5,6},{4}} => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 0
{{1,2,3,5},{4,6}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
{{1,2,3,5},{4},{6}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1,2,3,6},{4,5}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
{{1,2,3},{4,5,6}} => [3,3] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => 0
{{1,2,3},{4,5},{6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2,3,6},{4},{5}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1,2,3},{4,6},{5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2,3},{4},{5,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2,3},{4},{5},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1,2,4,5,6},{3}} => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 0
{{1,2,4,5},{3,6}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
{{1,2,4,5},{3},{6}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1,2,4,6},{3,5}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
{{1,2,4},{3,5,6}} => [3,3] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => 0
{{1,2,4},{3,5},{6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2,4,6},{3},{5}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1,2,4},{3,6},{5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2,4},{3},{5,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2,4},{3},{5},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1,2,5,6},{3,4}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
>>> Load all 3185 entries. <<<{{1,2,5},{3,4,6}} => [3,3] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => 0
{{1,2,5},{3,4},{6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2,6},{3,4,5}} => [3,3] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => 0
{{1,2},{3,4,5,6}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
{{1,2},{3,4,5},{6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2,6},{3,4},{5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2},{3,4,6},{5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2},{3,4},{5,6}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1,2},{3,4},{5},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,2,5,6},{3},{4}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1,2,5},{3,6},{4}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2,5},{3},{4,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2,5},{3},{4},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1,2,6},{3,5},{4}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2},{3,5,6},{4}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2},{3,5},{4,6}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1,2},{3,5},{4},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,2,6},{3},{4,5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2},{3,6},{4,5}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1,2},{3},{4,5,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,2},{3},{4,5},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,2,6},{3},{4},{5}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1,2},{3,6},{4},{5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,2},{3},{4,6},{5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,2},{3},{4},{5,6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,2},{3},{4},{5},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1,3,4,5,6},{2}} => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 0
{{1,3,4,5},{2,6}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
{{1,3,4,5},{2},{6}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1,3,4,6},{2,5}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
{{1,3,4},{2,5,6}} => [3,3] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => 0
{{1,3,4},{2,5},{6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,3,4,6},{2},{5}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1,3,4},{2,6},{5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,3,4},{2},{5,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,3,4},{2},{5},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1,3,5,6},{2,4}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
{{1,3,5},{2,4,6}} => [3,3] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => 0
{{1,3,5},{2,4},{6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,3,6},{2,4,5}} => [3,3] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => 0
{{1,3},{2,4,5,6}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
{{1,3},{2,4,5},{6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,3,6},{2,4},{5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,3},{2,4,6},{5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,3},{2,4},{5,6}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1,3},{2,4},{5},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,3,5,6},{2},{4}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1,3,5},{2,6},{4}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,3,5},{2},{4,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,3,5},{2},{4},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1,3,6},{2,5},{4}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,3},{2,5,6},{4}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,3},{2,5},{4,6}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1,3},{2,5},{4},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,3,6},{2},{4,5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,3},{2,6},{4,5}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1,3},{2},{4,5,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,3},{2},{4,5},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,3,6},{2},{4},{5}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1,3},{2,6},{4},{5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,3},{2},{4,6},{5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,3},{2},{4},{5,6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,3},{2},{4},{5},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1,4,5,6},{2,3}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
{{1,4,5},{2,3,6}} => [3,3] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => 0
{{1,4,5},{2,3},{6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,4,6},{2,3,5}} => [3,3] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => 0
{{1,4},{2,3,5,6}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
{{1,4},{2,3,5},{6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,4,6},{2,3},{5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,4},{2,3,6},{5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,4},{2,3},{5,6}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1,4},{2,3},{5},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,5,6},{2,3,4}} => [3,3] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => 0
{{1,5},{2,3,4,6}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
{{1,5},{2,3,4},{6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,6},{2,3,4,5}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 0
{{1},{2,3,4,5,6}} => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 0
{{1},{2,3,4,5},{6}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1,6},{2,3,4},{5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1},{2,3,4,6},{5}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1},{2,3,4},{5,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1},{2,3,4},{5},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1,5,6},{2,3},{4}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,5},{2,3,6},{4}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,5},{2,3},{4,6}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1,5},{2,3},{4},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,6},{2,3,5},{4}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1},{2,3,5,6},{4}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1},{2,3,5},{4,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1},{2,3,5},{4},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1,6},{2,3},{4,5}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1},{2,3,6},{4,5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1},{2,3},{4,5,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1},{2,3},{4,5},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,6},{2,3},{4},{5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2,3,6},{4},{5}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1},{2,3},{4,6},{5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2,3},{4},{5,6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2,3},{4},{5},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1,4,5,6},{2},{3}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1,4,5},{2,6},{3}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,4,5},{2},{3,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,4,5},{2},{3},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1,4,6},{2,5},{3}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,4},{2,5,6},{3}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,4},{2,5},{3,6}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1,4},{2,5},{3},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,4,6},{2},{3,5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,4},{2,6},{3,5}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1,4},{2},{3,5,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,4},{2},{3,5},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,4,6},{2},{3},{5}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1,4},{2,6},{3},{5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,4},{2},{3,6},{5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,4},{2},{3},{5,6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1,5,6},{2,4},{3}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,5},{2,4,6},{3}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,5},{2,4},{3,6}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1,5},{2,4},{3},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,6},{2,4,5},{3}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1},{2,4,5,6},{3}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1},{2,4,5},{3,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1},{2,4,5},{3},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1,6},{2,4},{3,5}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1},{2,4,6},{3,5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1},{2,4},{3,5,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1},{2,4},{3,5},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,6},{2,4},{3},{5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2,4,6},{3},{5}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1},{2,4},{3,6},{5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2,4},{3},{5,6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2,4},{3},{5},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1,5,6},{2},{3,4}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,5},{2,6},{3,4}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1,5},{2},{3,4,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1,5},{2},{3,4},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,6},{2,5},{3,4}} => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 1
{{1},{2,5,6},{3,4}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1},{2,5},{3,4,6}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1},{2,5},{3,4},{6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,6},{2},{3,4,5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1},{2,6},{3,4,5}} => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 0
{{1},{2},{3,4,5,6}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 0
{{1},{2},{3,4,5},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1,6},{2},{3,4},{5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2,6},{3,4},{5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2},{3,4,6},{5}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1},{2},{3,4},{5,6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2},{3,4},{5},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1,5,6},{2},{3},{4}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1,5},{2,6},{3},{4}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,5},{2},{3,6},{4}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,5},{2},{3},{4,6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1,6},{2,5},{3},{4}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2,5,6},{3},{4}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1},{2,5},{3,6},{4}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2,5},{3},{4,6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2,5},{3},{4},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1,6},{2},{3,5},{4}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2,6},{3,5},{4}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2},{3,5,6},{4}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1},{2},{3,5},{4,6}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2},{3,5},{4},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1,6},{2},{3},{4,5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2,6},{3},{4,5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2},{3,6},{4,5}} => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
{{1},{2},{3},{4,5,6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 0
{{1},{2},{3},{4,5},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1},{2,6},{3},{4},{5}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1},{2},{3,6},{4},{5}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1},{2},{3},{4,6},{5}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1},{2},{3},{4},{5,6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 0
{{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 0
{{1,2,3,4,5,6,7}} => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 0
{{1,2,3,4,5,6},{7}} => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 0
{{1,2,3,4,5,7},{6}} => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 0
{{1,2,3,4,5},{6,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,2,3,4,5},{6},{7}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,2,3,4,6,7},{5}} => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 0
{{1,2,3,4,6},{5,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,2,3,4,6},{5},{7}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,2,3,4,7},{5,6}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,2,3,4},{5,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2,3,4},{5,6},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,3,4,7},{5},{6}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,2,3,4},{5,7},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,3,4},{5},{6,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,3,4},{5},{6},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,2,3,5,6,7},{4}} => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 0
{{1,2,3,5,6},{4,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,2,3,5,6},{4},{7}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,2,3,5,7},{4,6}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,2,3,5},{4,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2,3,5},{4,6},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,3,5,7},{4},{6}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,2,3,5},{4,7},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,3,5},{4},{6,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,3,5},{4},{6},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,2,3,6,7},{4,5}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,2,3,6},{4,5,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2,3,6},{4,5},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,3,7},{4,5,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2,3},{4,5,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2,3},{4,5,6},{7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,3,7},{4,5},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,3},{4,5,7},{6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,3},{4,5},{6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2,3},{4,5},{6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,3,6,7},{4},{5}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,2,3,6},{4,7},{5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,3,6},{4},{5,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,2,3,7},{4,6},{5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,3},{4,6,7},{5}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,3},{4,6},{5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2,3},{4,6},{5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,3,7},{4},{5,6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,3},{4,7},{5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2,3},{4},{5,6,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,3},{4},{5,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,2,3},{4,7},{5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,3},{4},{5,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,3},{4},{5},{6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,3},{4},{5},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,2,4,5,6,7},{3}} => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 0
{{1,2,4,5,6},{3,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,2,4,5,6},{3},{7}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,2,4,5,7},{3,6}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,2,4,5},{3,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2,4,5},{3,6},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,4,5,7},{3},{6}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,2,4,5},{3,7},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,4,5},{3},{6,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,4,5},{3},{6},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,2,4,6,7},{3,5}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,2,4,6},{3,5,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2,4,6},{3,5},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,4,7},{3,5,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2,4},{3,5,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2,4},{3,5,6},{7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,4,7},{3,5},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,4},{3,5,7},{6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,4},{3,5},{6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2,4},{3,5},{6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,4,6,7},{3},{5}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,2,4,6},{3,7},{5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,4,6},{3},{5,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,2,4,7},{3,6},{5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,4},{3,6,7},{5}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,4},{3,6},{5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2,4},{3,6},{5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,4,7},{3},{5,6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,4},{3,7},{5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2,4},{3},{5,6,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,4},{3},{5,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,2,4},{3,7},{5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,4},{3},{5,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,4},{3},{5},{6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,4},{3},{5},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,2,5,6,7},{3,4}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,2,5,6},{3,4,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2,5,6},{3,4},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,5,7},{3,4,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2,5},{3,4,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2,5},{3,4,6},{7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,5,7},{3,4},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,5},{3,4,7},{6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,5},{3,4},{6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2,5},{3,4},{6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,6,7},{3,4,5}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2,6},{3,4,5,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2,6},{3,4,5},{7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,7},{3,4,5,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,2},{3,4,5,6,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,2},{3,4,5,6},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,7},{3,4,5},{6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2},{3,4,5,7},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2},{3,4,5},{6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2},{3,4,5},{6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,6,7},{3,4},{5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,6},{3,4,7},{5}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,6},{3,4},{5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2,6},{3,4},{5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,7},{3,4,6},{5}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2},{3,4,6,7},{5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2},{3,4,6},{5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2},{3,4,6},{5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,7},{3,4},{5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2},{3,4,7},{5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2},{3,4},{5,6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2},{3,4},{5,6},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2},{3,4,7},{5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2},{3,4},{5,7},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2},{3,4},{5},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2},{3,4},{5},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,2,5,6,7},{3},{4}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,2,5,6},{3,7},{4}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,5,6},{3},{4,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,2,5,7},{3,6},{4}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,5},{3,6,7},{4}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,5},{3,6},{4,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2,5},{3,6},{4},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,5,7},{3},{4,6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,5},{3,7},{4,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2,5},{3},{4,6,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,5},{3},{4,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,5},{3},{4,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,5},{3},{4},{6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,2,6,7},{3,5},{4}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,6},{3,5,7},{4}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,6},{3,5},{4,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2,6},{3,5},{4},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,7},{3,5,6},{4}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2},{3,5,6,7},{4}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2},{3,5,6},{4,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2},{3,5,6},{4},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,7},{3,5},{4,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2},{3,5,7},{4,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2},{3,5},{4,6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2},{3,5},{4,6},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2},{3,5,7},{4},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2},{3,5},{4,7},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2},{3,5},{4},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2},{3,5},{4},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,2,6,7},{3},{4,5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2,6},{3,7},{4,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2,6},{3},{4,5,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2,6},{3},{4,5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,7},{3,6},{4,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2},{3,6,7},{4,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2},{3,6},{4,5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2},{3,6},{4,5},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2,7},{3},{4,5,6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,2},{3,7},{4,5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,2},{3},{4,5,6,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,2},{3},{4,5,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,7},{3},{4,5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2},{3,7},{4,5},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2},{3},{4,5,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2},{3},{4,5},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2},{3},{4,5},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,6},{3},{4,7},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,6},{3},{4},{5,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2},{3,6,7},{4},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2},{3,6},{4,7},{5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2},{3,6},{4},{5,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2},{3,6},{4},{5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,2,7},{3},{4,6},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2},{3,7},{4,6},{5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2},{3},{4,6,7},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2},{3},{4,6},{5,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2},{3},{4,6},{5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,2,7},{3},{4},{5,6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2},{3,7},{4},{5,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2},{3},{4,7},{5,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,2},{3},{4},{5,6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,2},{3},{4},{5,6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,2},{3},{4,7},{5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,2},{3},{4},{5,7},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,2},{3},{4},{5},{6,7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,3,4,5,6,7},{2}} => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 0
{{1,3,4,5,6},{2,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,3,4,5,6},{2},{7}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,3,4,5,7},{2,6}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,3,4,5},{2,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,3,4,5},{2,6},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,4,5,7},{2},{6}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,3,4,5},{2,7},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,4,5},{2},{6,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,4,5},{2},{6},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,3,4,6,7},{2,5}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,3,4,6},{2,5,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,3,4,6},{2,5},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,4,7},{2,5,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,3,4},{2,5,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,3,4},{2,5,6},{7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3,4,7},{2,5},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,4},{2,5,7},{6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3,4},{2,5},{6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3,4},{2,5},{6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,4,6,7},{2},{5}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,3,4,6},{2,7},{5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,4,6},{2},{5,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,3,4,7},{2,6},{5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,4},{2,6,7},{5}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3,4},{2,6},{5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3,4},{2,6},{5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,4,7},{2},{5,6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,4},{2,7},{5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3,4},{2},{5,6,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3,4},{2},{5,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,3,4},{2,7},{5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,4},{2},{5,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,4},{2},{5},{6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,4},{2},{5},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,3,5,6,7},{2,4}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,3,5,6},{2,4,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,3,5,6},{2,4},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,5,7},{2,4,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,3,5},{2,4,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,3,5},{2,4,6},{7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3,5,7},{2,4},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,5},{2,4,7},{6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3,5},{2,4},{6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3,5},{2,4},{6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,6,7},{2,4,5}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,3,6},{2,4,5,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,3,6},{2,4,5},{7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3,7},{2,4,5,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,3},{2,4,5,6,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,3},{2,4,5,6},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,7},{2,4,5},{6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3},{2,4,5,7},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3},{2,4,5},{6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3},{2,4,5},{6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,6,7},{2,4},{5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,6},{2,4,7},{5}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3,6},{2,4},{5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3,6},{2,4},{5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,7},{2,4,6},{5}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3},{2,4,6,7},{5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3},{2,4,6},{5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3},{2,4,6},{5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,7},{2,4},{5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3},{2,4,7},{5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3},{2,4},{5,6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3},{2,4},{5,6},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3,7},{2,4},{5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3},{2,4,7},{5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3},{2,4},{5,7},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3},{2,4},{5},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3},{2,4},{5},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,3,5,6,7},{2},{4}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,3,5,6},{2,7},{4}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,5,6},{2},{4,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,3,5,7},{2,6},{4}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,5},{2,6,7},{4}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3,5},{2,6},{4,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3,5},{2,6},{4},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,5,7},{2},{4,6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,5},{2,7},{4,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3,5},{2},{4,6,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3,5},{2},{4,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,5},{2},{4,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,5},{2},{4},{6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,3,6,7},{2,5},{4}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,6},{2,5,7},{4}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3,6},{2,5},{4,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3,6},{2,5},{4},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,7},{2,5,6},{4}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3},{2,5,6,7},{4}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3},{2,5,6},{4,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3},{2,5,6},{4},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,7},{2,5},{4,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3},{2,5,7},{4,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3},{2,5},{4,6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3},{2,5},{4,6},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3},{2,5,7},{4},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3},{2,5},{4,7},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3},{2,5},{4},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3},{2,5},{4},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,3,6,7},{2},{4,5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3,6},{2,7},{4,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3,6},{2},{4,5,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3,6},{2},{4,5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,7},{2,6},{4,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3},{2,6,7},{4,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3},{2,6},{4,5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3},{2,6},{4,5},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3,7},{2},{4,5,6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,3},{2,7},{4,5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,3},{2},{4,5,6,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,3},{2},{4,5,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,7},{2},{4,5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3},{2,7},{4,5},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3},{2},{4,5,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3},{2},{4,5},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3},{2},{4,5},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,6},{2},{4,7},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,6},{2},{4},{5,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3},{2,6,7},{4},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3},{2,6},{4},{5,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,3,7},{2},{4,6},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3},{2},{4,6,7},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3},{2},{4,6},{5,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3},{2},{4,6},{5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,3,7},{2},{4},{5,6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3},{2,7},{4},{5,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3},{2},{4,7},{5,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,3},{2},{4},{5,6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,3},{2},{4},{5,6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,3},{2},{4,7},{5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,3},{2},{4},{5,7},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,3},{2},{4},{5},{6,7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,3},{2},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,4,5,6,7},{2,3}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,4,5,6},{2,3,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,4,5,6},{2,3},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,4,5,7},{2,3,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,4,5},{2,3,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,4,5},{2,3,6},{7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,4,5,7},{2,3},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,4,5},{2,3,7},{6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,4,5},{2,3},{6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4,5},{2,3},{6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,6,7},{2,3,5}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,4,6},{2,3,5,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,4,6},{2,3,5},{7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,4,7},{2,3,5,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,4},{2,3,5,6,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,4},{2,3,5,6},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,4,7},{2,3,5},{6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,4},{2,3,5,7},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,4},{2,3,5},{6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4},{2,3,5},{6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,6,7},{2,3},{5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,4,6},{2,3,7},{5}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,4,6},{2,3},{5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4,6},{2,3},{5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,7},{2,3,6},{5}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,4},{2,3,6,7},{5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,4},{2,3,6},{5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4},{2,3,6},{5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,7},{2,3},{5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4},{2,3,7},{5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4},{2,3},{5,6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4},{2,3},{5,6},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4},{2,3,7},{5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4},{2,3},{5,7},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4},{2,3},{5},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4},{2,3},{5},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,5,6,7},{2,3,4}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,5,6},{2,3,4,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,5,6},{2,3,4},{7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,5,7},{2,3,4,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,5},{2,3,4,6,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,5},{2,3,4,6},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,5,7},{2,3,4},{6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,5},{2,3,4,7},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,5},{2,3,4},{6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5},{2,3,4},{6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,6,7},{2,3,4,5}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 0
{{1,6},{2,3,4,5,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1,6},{2,3,4,5},{7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,7},{2,3,4,5,6}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 0
{{1},{2,3,4,5,6,7}} => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 0
{{1},{2,3,4,5,6},{7}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,7},{2,3,4,5},{6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,3,4,5,7},{6}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1},{2,3,4,5},{6,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,3,4,5},{6},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,6,7},{2,3,4},{5}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,6},{2,3,4,7},{5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,6},{2,3,4},{5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,6},{2,3,4},{5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,7},{2,3,4,6},{5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,3,4,6,7},{5}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1},{2,3,4,6},{5,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,3,4,6},{5},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,7},{2,3,4},{5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1},{2,3,4,7},{5,6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,3,4},{5,6,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1},{2,3,4},{5,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,7},{2,3,4},{5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3,4,7},{5},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1},{2,3,4},{5,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3,4},{5},{6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3,4},{5},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,5,6,7},{2,3},{4}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,5,6},{2,3,7},{4}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,5,6},{2,3},{4,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5,6},{2,3},{4},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5,7},{2,3,6},{4}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,5},{2,3,6,7},{4}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,5},{2,3,6},{4,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5},{2,3,6},{4},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5,7},{2,3},{4,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5},{2,3,7},{4,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5},{2,3},{4,6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5},{2,3},{4,6},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5},{2,3,7},{4},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5},{2,3},{4,7},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5},{2,3},{4},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5},{2,3},{4},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,6,7},{2,3,5},{4}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,6},{2,3,5,7},{4}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,6},{2,3,5},{4,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,6},{2,3,5},{4},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,7},{2,3,5,6},{4}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,3,5,6,7},{4}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1},{2,3,5,6},{4,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,3,5,6},{4},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,7},{2,3,5},{4,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1},{2,3,5,7},{4,6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,3,5},{4,6,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1},{2,3,5},{4,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,7},{2,3,5},{4},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3,5,7},{4},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1},{2,3,5},{4,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3,5},{4},{6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3,5},{4},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,6,7},{2,3},{4,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,6},{2,3,7},{4,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,6},{2,3},{4,5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,6},{2,3},{4,5},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,7},{2,3,6},{4,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1},{2,3,6,7},{4,5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,3,6},{4,5,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1},{2,3,6},{4,5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,7},{2,3},{4,5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1},{2,3,7},{4,5,6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1},{2,3},{4,5,6,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,3},{4,5,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,3,7},{4,5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3},{4,5,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3},{4,5},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,3},{4,5},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,6},{2,3,7},{4},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,6},{2,3},{4},{5,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2,3,6},{4},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3,6,7},{4},{5}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1},{2,3,6},{4,7},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3,6},{4},{5,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3,6},{4},{5},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,3,7},{4,6},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3},{4,6,7},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3},{4,6},{5,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,3},{4,6},{5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2,3},{4},{5,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,3,7},{4},{5,6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3},{4,7},{5,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,3},{4},{5,6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,3},{4},{5,6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,3,7},{4},{5},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1},{2,3},{4,7},{5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,3},{4},{5,7},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,3},{4},{5},{6,7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,4,5,6,7},{2},{3}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1,4,5,6},{2,7},{3}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,4,5,6},{2},{3,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,4,5,7},{2,6},{3}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,4,5},{2,6,7},{3}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,4,5},{2,6},{3,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4,5},{2,6},{3},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,5,7},{2},{3,6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,4,5},{2,7},{3,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4,5},{2},{3,6,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,4,5},{2},{3,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,5},{2},{3,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,5},{2},{3},{6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,4,6,7},{2,5},{3}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,4,6},{2,5,7},{3}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,4,6},{2,5},{3,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4,6},{2,5},{3},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,7},{2,5,6},{3}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,4},{2,5,6,7},{3}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,4},{2,5,6},{3,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4},{2,5,6},{3},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,7},{2,5},{3,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4},{2,5,7},{3,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4},{2,5},{3,6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4},{2,5},{3,6},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4},{2,5,7},{3},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4},{2,5},{3},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,4,6,7},{2},{3,5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,4,6},{2,7},{3,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4,6},{2},{3,5,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,4,6},{2},{3,5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,7},{2,6},{3,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4},{2,6,7},{3,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4},{2,6},{3,5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4},{2,6},{3,5},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4,7},{2},{3,5,6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,4},{2,7},{3,5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,4},{2},{3,5,6,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,4},{2},{3,5,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,7},{2},{3,5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4},{2},{3,5,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4},{2},{3,5},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4},{2},{3,5},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,6},{2},{3,7},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,6},{2},{3},{5,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4},{2,6,7},{3},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4},{2,6},{3},{5,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,4,7},{2},{3,6},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4},{2},{3,6,7},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4},{2},{3,6},{5,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4},{2},{3,6},{5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,4,7},{2},{3},{5,6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4},{2,7},{3},{5,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4},{2},{3,7},{5,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,4},{2},{3},{5,6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,4},{2},{3},{5,6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,4},{2},{3,7},{5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,4},{2},{3},{5,7},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,4},{2},{3},{5},{6,7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,5,6,7},{2,4},{3}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,5,6},{2,4,7},{3}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,5,6},{2,4},{3,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5,7},{2,4,6},{3}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,5},{2,4,6,7},{3}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,5},{2,4,6},{3,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5},{2,4,6},{3},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5,7},{2,4},{3,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5},{2,4,7},{3,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5},{2,4},{3,6,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5},{2,4},{3,6},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5},{2,4,7},{3},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5},{2,4},{3},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,6,7},{2,4,5},{3}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,6},{2,4,5,7},{3}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,6},{2,4,5},{3,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,6},{2,4,5},{3},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,7},{2,4,5,6},{3}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,4,5,6,7},{3}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1},{2,4,5,6},{3,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,4,5,6},{3},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,7},{2,4,5},{3,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1},{2,4,5,7},{3,6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,4,5},{3,6,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1},{2,4,5},{3,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,7},{2,4,5},{3},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,4,5,7},{3},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1},{2,4,5},{3,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,4,5},{3},{6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,4,5},{3},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,6,7},{2,4},{3,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,6},{2,4,7},{3,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,6},{2,4},{3,5,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,6},{2,4},{3,5},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,7},{2,4,6},{3,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1},{2,4,6,7},{3,5}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,4,6},{3,5,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1},{2,4,6},{3,5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,7},{2,4},{3,5,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1},{2,4,7},{3,5,6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1},{2,4},{3,5,6,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,4},{3,5,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,4,7},{3,5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,4},{3,5,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,4},{3,5},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,4},{3,5},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,6},{2,4,7},{3},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,6},{2,4},{3},{5,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2,4,6},{3},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,4,6,7},{3},{5}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1},{2,4,6},{3,7},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,4,6},{3},{5,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,4,6},{3},{5},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,4,7},{3,6},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,4},{3,6,7},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,4},{3,6},{5,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,4},{3,6},{5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2,4},{3},{5,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,4,7},{3},{5,6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,4},{3,7},{5,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,4},{3},{5,6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,4},{3},{5,6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,4,7},{3},{5},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1},{2,4},{3,7},{5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,4},{3},{5,7},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,4},{3},{5},{6,7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,4},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,5,6,7},{2},{3,4}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,5,6},{2,7},{3,4}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5,6},{2},{3,4,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,5,6},{2},{3,4},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5,7},{2,6},{3,4}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5},{2,6,7},{3,4}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5},{2,6},{3,4,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5},{2,6},{3,4},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5,7},{2},{3,4,6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,5},{2,7},{3,4,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,5},{2},{3,4,6,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,5},{2},{3,4,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5,7},{2},{3,4},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5},{2},{3,4,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5},{2},{3,4},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5},{2},{3,4},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,6,7},{2,5},{3,4}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,6},{2,5,7},{3,4}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,6},{2,5},{3,4,7}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,7},{2,5,6},{3,4}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1},{2,5,6,7},{3,4}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,5,6},{3,4,7}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1},{2,5,6},{3,4},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,7},{2,5},{3,4,6}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1},{2,5,7},{3,4,6}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1},{2,5},{3,4,6,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,5},{3,4,6},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,5,7},{3,4},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,5},{3,4,7},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,5},{3,4},{6,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,5},{3,4},{6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,6,7},{2},{3,4,5}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1,6},{2,7},{3,4,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1,6},{2},{3,4,5,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1,6},{2},{3,4,5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,7},{2,6},{3,4,5}} => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
{{1},{2,6,7},{3,4,5}} => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0
{{1},{2,6},{3,4,5,7}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,6},{3,4,5},{7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,7},{2},{3,4,5,6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2,7},{3,4,5,6}} => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 0
{{1},{2},{3,4,5,6,7}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 0
{{1},{2},{3,4,5,6},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,7},{2},{3,4,5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,7},{3,4,5},{6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2},{3,4,5,7},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1},{2},{3,4,5},{6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2},{3,4,5},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,6,7},{2},{3,4},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,6},{2},{3,4,7},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,6},{2},{3,4},{5,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,6},{2},{3,4},{5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,6,7},{3,4},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,6},{3,4,7},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,6},{3,4},{5,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,6},{3,4},{5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2},{3,4,6},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,7},{3,4,6},{5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2},{3,4,6,7},{5}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1},{2},{3,4,6},{5,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2},{3,4,6},{5},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,7},{2},{3,4},{5,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,7},{3,4},{5,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2},{3,4,7},{5,6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2},{3,4},{5,6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2},{3,4},{5,6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2},{3,4},{5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,7},{3,4},{5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3,4,7},{5},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1},{2},{3,4},{5,7},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3,4},{5},{6,7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3,4},{5},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5,6},{2},{3,7},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5,6},{2},{3},{4,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5},{2,6,7},{3},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5},{2,6},{3},{4,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,5,7},{2},{3,6},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5},{2},{3,6,7},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5},{2},{3,6},{4,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5},{2},{3,6},{4},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,5,7},{2},{3},{4,6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5},{2,7},{3},{4,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5},{2},{3,7},{4,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,5},{2},{3},{4,6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,5},{2},{3},{4,6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,5},{2},{3,7},{4},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,5},{2},{3},{4,7},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,5},{2},{3},{4},{6,7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,6},{2,5,7},{3},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,6},{2,5},{3},{4,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2,5,6},{3},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,5,6,7},{3},{4}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1},{2,5,6},{3,7},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,5,6},{3},{4,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,5,6},{3},{4},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,5,7},{3,6},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,5},{3,6,7},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,5},{3,6},{4,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,5},{3,6},{4},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2,5},{3},{4,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,5,7},{3},{4,6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,5},{3,7},{4,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,5},{3},{4,6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,5},{3},{4,6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,5,7},{3},{4},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1},{2,5},{3,7},{4},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,5},{3},{4,7},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,5},{3},{4},{6,7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,5},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,6,7},{2},{3,5},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,6},{2},{3,5,7},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,6},{2},{3,5},{4,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,6},{2},{3,5},{4},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,6,7},{3,5},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,6},{3,5,7},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,6},{3,5},{4,7}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,6},{3,5},{4},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2},{3,5,6},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,7},{3,5,6},{4}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2},{3,5,6,7},{4}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1},{2},{3,5,6},{4,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2},{3,5,6},{4},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,7},{2},{3,5},{4,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,7},{3,5},{4,6}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2},{3,5,7},{4,6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2},{3,5},{4,6,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2},{3,5},{4,6},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2},{3,5},{4},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,7},{3,5},{4},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3,5,7},{4},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1},{2},{3,5},{4,7},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3,5},{4},{6,7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3,5},{4},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,6,7},{2},{3},{4,5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,6},{2,7},{3},{4,5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,6},{2},{3,7},{4,5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1,6},{2},{3},{4,5,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1,6},{2},{3},{4,5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2,6},{3},{4,5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,6,7},{3},{4,5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,6},{3,7},{4,5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,6},{3},{4,5,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,6},{3},{4,5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2},{3,6},{4,5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2,7},{3,6},{4,5}} => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 1
{{1},{2},{3,6,7},{4,5}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2},{3,6},{4,5,7}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2},{3,6},{4,5},{7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,7},{2},{3},{4,5,6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2,7},{3},{4,5,6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2},{3,7},{4,5,6}} => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 0
{{1},{2},{3},{4,5,6,7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 0
{{1},{2},{3},{4,5,6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,7},{2},{3},{4,5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,7},{3},{4,5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3,7},{4,5},{6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3},{4,5,7},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1},{2},{3},{4,5},{6,7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3},{4,5},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,6},{2},{3,7},{4},{5}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,6},{2},{3},{4,7},{5}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,6},{2},{3},{4},{5,7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,6,7},{3},{4},{5}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1},{2,6},{3,7},{4},{5}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,6},{3},{4,7},{5}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,6},{3},{4},{5,7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,6},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,7},{2},{3,6},{4},{5}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,7},{3,6},{4},{5}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3,6,7},{4},{5}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1},{2},{3,6},{4,7},{5}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3,6},{4},{5,7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3,6},{4},{5},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,7},{2},{3},{4,6},{5}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,7},{3},{4,6},{5}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3,7},{4,6},{5}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3},{4,6,7},{5}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1},{2},{3},{4,6},{5,7}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3},{4,6},{5},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,7},{2},{3},{4},{5,6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2,7},{3},{4},{5,6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3,7},{4},{5,6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3},{4,7},{5,6}} => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 0
{{1},{2},{3},{4},{5,6,7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 0
{{1},{2},{3},{4},{5,6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1},{2,7},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1},{2},{3,7},{4},{5},{6}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1},{2},{3},{4,7},{5},{6}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1},{2},{3},{4},{5,7},{6}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 0
{{1,2},{3,4},{5,6},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,4},{5,6},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,3},{5,6},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,3},{4,6},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,3},{4,5},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,3},{4,5},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,4},{3,5},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,4},{3,5},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,4},{3,5},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,4},{3,6},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,5},{3,6},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,5},{4,6},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,2},{3,5},{4,6},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,2},{3,6},{4,5},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,6},{4,5},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,6},{3,5},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,6},{3,4},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,5},{3,4},{7,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,5},{3,4},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,6},{3,4},{5,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,6},{3,4},{5,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,7},{3,4},{5,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,7},{3,4},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,7},{3,5},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,7},{4,5},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,2},{3,7},{4,5},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,2},{3,8},{4,5},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,8},{4,5},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,8},{3,5},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,8},{3,4},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,8},{3,4},{5,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,8},{3,4},{5,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,7},{3,5},{4,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,8},{3,5},{4,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,8},{3,6},{4,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,8},{3,6},{5,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,8},{4,6},{5,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,2},{3,8},{4,6},{5,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,2},{3,7},{4,6},{5,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,7},{4,6},{5,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,7},{3,6},{5,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,7},{3,6},{4,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,7},{3,5},{4,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,6},{3,5},{4,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,6},{3,5},{4,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,5},{3,6},{4,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,5},{3,6},{4,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,5},{3,7},{4,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,2},{3,6},{4,7},{5,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,2},{3,5},{4,7},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,5},{4,7},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,4},{3,7},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,4},{3,7},{5,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,4},{3,6},{5,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,4},{3,6},{5,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,3},{4,6},{5,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,3},{4,6},{5,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,3},{4,7},{5,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,3},{4,7},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,3},{5,7},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,4},{5,7},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,2},{3,4},{5,7},{6,8}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,2},{3,4},{5,8},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,4},{5,8},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,3},{5,8},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,3},{4,8},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,3},{4,8},{5,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,3},{4,8},{5,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,4},{3,8},{5,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,4},{3,8},{5,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,4},{3,8},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,5},{3,8},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,5},{4,8},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,2},{3,5},{4,8},{6,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,2},{3,6},{4,8},{5,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,6},{4,8},{5,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,6},{3,8},{5,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,6},{3,8},{4,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,5},{3,8},{4,7}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,5},{3,8},{4,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,5},{3,7},{4,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,6},{3,7},{4,5}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,6},{3,8},{4,5}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,7},{3,8},{4,5}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,7},{3,8},{4,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,7},{3,8},{5,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,7},{4,8},{5,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,2},{3,7},{4,8},{5,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,2},{3,8},{4,7},{5,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,3},{2,8},{4,7},{5,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,8},{3,7},{4,5}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,7},{2,8},{3,6},{4,5}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 2
{{1,6},{2,7},{3,8},{4,9},{5,10}} => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => 3
{{1},{2},{3},{4,7,8},{5,6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2},{3},{4,8},{5,6,7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2},{3,4},{5,6,7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2},{3,5},{4},{6,7,8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2},{3,7,8},{4},{5,6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2},{3,8},{4},{5,6,7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2},{3,5,8},{4},{6,7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2},{3,4,5},{6,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2},{3,6,7,8},{4,5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2},{3,7,8},{4,6},{5}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2},{3,8},{4,6,7},{5}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2},{3,4,5,6},{7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2},{3,8},{4,5,6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2},{3,7,8},{4,5,6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2},{3,8},{4,7},{5,6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2},{3,8},{4,5,6,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2},{3,4,8},{5,6,7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2},{3,4,5,8},{6,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3},{4},{5,6,7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3},{4,5},{6,7},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,3},{4,5},{6,8},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,3},{4,5},{6,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3},{4,6,7},{5},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,3},{4,6,8},{5},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,3},{4,6,7,8},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3},{4,5,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3},{4,7},{5,6},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,3},{4,8},{5,6},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,3},{4,7,8},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3},{4,8},{5,7},{6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,3},{4,5,8},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,3},{4,8},{5,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3},{4,5,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3},{4,5,6,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3},{4,5,6,7,8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1},{2,4},{3},{5},{6,7,8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4},{3},{5,6},{7,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,4},{3},{5,7,8},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4},{3},{5,8},{6,7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,4},{3},{5,6,7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,8},{3},{4},{5,6,7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4,5},{3},{6,7},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4,5},{3},{6,8},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4,5},{3},{6,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,6},{3},{4,5},{7,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,6,8},{3},{4,5},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,6,7,8},{3},{4,5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4,6},{3},{5},{7,8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,8},{3},{4,6,7},{5}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4,8},{3},{5},{6,7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,7,8},{3},{4,5,6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,4,7},{3},{5,6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,8},{3},{4,7},{5,6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,4,8},{3},{5,6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4,7,8},{3},{5,6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4,8},{3},{5,7},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4,8},{3},{5,6,7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,4,5,8},{3},{6,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,4},{5},{6,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,3,4},{5,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,4},{5,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,4},{5,6,8},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,5},{3,4},{6,7},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,5},{3,4},{6,8},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,5},{3,4},{6,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6,7},{3,4},{5},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,6,8},{3,4},{5},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,7},{3,4},{5,6},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,8},{3,4},{5,6},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,7,8},{3,4},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,8},{3,4},{5,7},{6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,8},{3,4},{5,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5,8},{3,4},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5,6,7,8},{3,4}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1},{2,3,5},{4},{6,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,6},{3,5},{4},{7,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,6,7},{3,5},{4},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,8},{3,5},{4},{6,7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,6,8},{3,5},{4},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,6,7,8},{3,5},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,7},{3,5,6},{4},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,8},{3,5,6},{4},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,3,7},{4},{5,6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,8},{3,7},{4},{5,6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,8},{3,5,7},{4},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,8},{3,5,6,7},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,8},{4},{5,6,7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,3,5,8},{4},{6,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,8},{3,4,5},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,8},{3,4,5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6,8},{3,4,5},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,6,7,8},{3,4,5}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1},{2,3,6},{4,5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,7},{3,6},{4,5},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,8},{3,6},{4,5},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,7,8},{3,6},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,8},{3,7},{4,5},{6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,3,8},{4,5},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,3,6,7},{4,5},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,8},{3,6,7},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,8},{4,5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,6,8},{4,5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,4,6},{5},{7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,8},{3,4,6},{5},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,7,8},{3,4,6},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,8},{3,7},{4,6},{5}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,3,8},{4,6},{5},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,3,7,8},{4,6},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,8},{3,4,6,7},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,8},{4,6,7},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,3,4,5,6},{7,8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1},{2,8},{3,4,5,6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,8},{3,7},{4,5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,8},{4,5,6},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,8},{3,4,7},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,8},{4,7},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,4,8},{5,6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,8},{3,4,5,7},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,8},{4,5,7},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,3,4,8},{5,7},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,4,8},{5,6,7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1},{2,3,4,5,8},{6,7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2},{3},{4},{5,6,7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2},{3},{4,5},{6,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3},{4,6,7,8},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2},{3},{4,5,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3},{4,5,8},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,2},{3},{4,5,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3},{4,5,6,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2},{3},{4,5,6,7,8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2},{3,4},{5},{6,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,4},{5,7,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,4},{5,6,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,4},{5,6,7,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2},{3,5},{4},{6,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,6,7,8},{4},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2},{3,5,6},{4},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,7,8},{4},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,5,7,8},{4},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2},{3,8},{4},{5,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,5,8},{4},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,5,6,8},{4},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2},{3,5,6,7,8},{4}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2},{3,4,5},{6},{7},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,2},{3,8},{4,5},{6},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,2},{3,7,8},{4,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,6,8},{4,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,6,7,8},{4,5}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2},{3,4,6},{5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,7,8},{4,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,4,8},{5},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,2},{3,4,7,8},{5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2},{3,8},{4,6,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,4,8},{5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,4,6,8},{5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2},{3,4,6,7,8},{5}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2},{3,4,5,6},{7,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2},{3,8},{4,5,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,4,8},{5,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,8},{4,5,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,4,8},{5,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,4,5,8},{6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2},{3,4,5,7,8},{6}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2},{3,4,5,6,7},{8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2},{3,8},{4,5,6,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2},{3,4,8},{5,6,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2},{3,4,5,8},{6,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2},{3,4,5,6,8},{7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2},{3,4,5,6,7,8}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,3},{2},{4},{5},{6,7,8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3},{2},{4},{5,7,8},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3},{2},{4},{5,8},{6,7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3},{2},{4},{5,6,7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3},{2},{4,5},{6,7},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3},{2},{4,5},{6,8},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3},{2},{4,5},{6,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2},{4,6},{5},{7,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3},{2},{4,6,7},{5},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3},{2},{4,8},{5},{6,7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3},{2},{4,6,8},{5},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3},{2},{4,6,7,8},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3},{2},{4,5,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2},{4,7},{5,6},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3},{2},{4,8},{5,6},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3},{2},{4,7,8},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2},{4,8},{5,7},{6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3},{2},{4,5,7,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3},{2},{4,8},{5,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2},{4,5,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2},{4,5,6,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3},{2},{4,5,6,7,8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,4},{2},{3},{5},{6,7,8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4},{2},{3},{5,6},{7,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,4},{2},{3},{5,6,7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5},{2},{3},{4},{6,7,8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,8},{2},{3},{4},{5,6,7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4,5},{2},{3},{6,8},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4,5},{2},{3},{6,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6,7},{2},{3},{4,5},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,6,7,8},{2},{3},{4,5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,5,6},{2},{3},{7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,7},{2},{3},{4,5,6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4,8},{2},{3},{5,6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4,7,8},{2},{3},{5,6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,8},{2},{3},{5,6,7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,5,8},{2},{3},{6,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4},{2},{5},{6},{7,8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3,4},{2},{5},{6,8},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3,4},{2},{5},{6,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,4},{2},{5,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,4},{2},{5,7,8},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,4},{2},{5,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,4},{2},{5,6,8},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,4},{2},{5,6,7,8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,5},{2},{3,4},{6},{7,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5},{2},{3,4},{6,8},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,6,7,8},{2},{3,4},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,6},{2},{3,4},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7,8},{2},{3,4},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2},{3,4},{6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,5,7,8},{2},{3,4},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,6,7},{2},{3,4},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2},{3,4},{5,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2},{3,4},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6,8},{2},{3,4},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,5},{2},{4},{6},{7,8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3,5},{2},{4},{6,7},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3,5},{2},{4},{6,8},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3,5},{2},{4},{6,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6},{2},{3,5},{4},{7,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,6,8},{2},{3,5},{4},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,6,7,8},{2},{3,5},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,5,6},{2},{4},{7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,7},{2},{3,5,6},{4},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,7,8},{2},{3,5,6},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,7},{2},{4},{5,6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3,8},{2},{4},{5,6,7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,5,8},{2},{4},{6,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,5},{2},{6},{7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,5},{2},{6,7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,5},{2},{6,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,5},{2},{6,7,8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,6},{2},{3,4,5},{7},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,6},{2},{3,4,5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2},{3,4,5},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,7,8},{2},{3,4,5},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,8},{2},{3,4,5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2},{3,4,5},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,6},{2},{4,5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2},{3,6},{4,5},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,7,8},{2},{3,6},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,7},{2},{4,5},{6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3,7,8},{2},{4,5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2},{3,6,7},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2},{4,5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6,8},{2},{4,5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,6},{2},{5},{7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,7},{2},{4,6},{5},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3,7,8},{2},{4,6},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2},{3,4,6,7},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,8},{2},{4,6,7},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,4,5,6},{2},{7,8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,8},{2},{3,4,5,6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,7},{2},{4,5,6},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,8},{2},{4,5,6},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,8},{2},{3,4,7},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2},{4,7},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,4,8},{2},{5,6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2},{3,4,5,7},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,8},{2},{4,5,7},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,4,8},{2},{5,7},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,5,8},{2},{6,7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,3},{4},{5},{6},{7,8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,2,3},{4},{5},{6,8},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,2,3},{4,6,7},{5},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,3},{4,5,8},{6},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,3},{4,5,7,8},{6}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,3},{4,5,6,7},{8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,3},{4,5,8},{6,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,3},{4,5,6,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,4},{2,3},{5,7,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,3},{5,6,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,3},{5,6,7,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,5},{2,3},{4},{6,7},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5},{2,3},{4},{6,8},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,6},{2,3},{4},{5},{7,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,6,8},{2,3},{4},{5},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,5,6},{2,3},{4},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3},{4},{5,6},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,7,8},{2,3},{4},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2,3},{4},{6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,5,7,8},{2,3},{4},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,6,7},{2,3},{4},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,3},{4},{5,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2,3},{4},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6,8},{2,3},{4},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,5},{2,3},{6,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3},{4,5},{6},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,8},{2,3},{4,5},{6},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,7,8},{2,3},{4,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2,3},{4,5},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2,3},{4,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7,8},{2,3},{4,5}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,4,6},{2,3},{5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3},{4,6},{5},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,7,8},{2,3},{4,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2,3},{5},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4,7,8},{2,3},{5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,6,7},{2,3},{5},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,3},{4,6,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2,3},{5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6,8},{2,3},{5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,6,7,8},{2,3},{5}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,4,5,6},{2,3},{7,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,7},{2,3},{4,5,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,7},{2,3},{5,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2,3},{5,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,5,7},{2,3},{6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,3},{4,5,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2,3},{5,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,5,8},{2,3},{6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,5,6,7},{2,3},{8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,4,8},{2,3},{5,6,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4,5,8},{2,3},{6,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,4,5,6,8},{2,3},{7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,4,5,6,7,8},{2,3}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,2,4},{3},{5,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,4},{3},{5,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,4},{3},{5,6,8},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,4},{3},{5,6,7,8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,5},{2,4},{3},{6},{7,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5},{2,4},{3},{6,7},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5},{2,4},{3},{6,8},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5},{2,4},{3},{6,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,4},{3},{5},{6,7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,6,7,8},{2,4},{3},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,6},{2,4},{3},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4},{3},{5,6},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,7,8},{2,4},{3},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2,4},{3},{6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,8},{2,4},{3},{5,7},{6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5,7,8},{2,4},{3},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,4},{3},{5,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2,4},{3},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6,8},{2,4},{3},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,5},{3},{4},{6},{7,8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,6},{2,5},{3},{4},{7,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,7,8},{2,5},{3},{4},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,6,7,8},{2,5},{3},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,6},{3},{4},{5},{7,8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,7,8},{2,6},{3},{4},{5}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,2,5,6},{3},{4},{7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,7,8},{2,5,6},{3},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,8},{2,5,7},{3},{4},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,8},{2,5,6,7},{3},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6},{2,4,5},{3},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4,5},{3},{6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,7,8},{2,4,5},{3},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6,7},{2,4,5},{3},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,8},{2,4,5},{3},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2,4,5},{3},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,6},{3},{4,5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,6},{3},{4,5},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,7,8},{2,6},{3},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,7,8},{3},{4,5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,6,7},{3},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3},{4,5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6,8},{3},{4,5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,6},{3},{5},{7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,7},{2,4,6},{3},{5},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,7,8},{2,4,6},{3},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,7,8},{3},{4,6},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,4,7},{3},{5},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,8},{2,4,6,7},{3},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,8},{3},{4,6,7},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,4,8},{3},{5},{6,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,5,6},{3},{7,8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,7},{2,4,5,6},{3},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,4,5,6},{3},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,7},{3},{4,5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3},{4,5,6},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,4,7},{3},{5,6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,4,7},{3},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3},{4,7},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,4,8},{3},{5,6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,4,5,7},{3},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,8},{3},{4,5,7},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,4,8},{3},{5,7},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,5,8},{3},{6,7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,3,4},{5},{6,7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,3,4},{5,6},{7,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2,3,4},{5,7,8},{6}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,3,4},{5,6,7},{8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,3,4},{5,8},{6,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2,3,4},{5,6,8},{7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,3,4},{5,6,7,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,5},{2,3,4},{6},{7},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,5},{2,3,4},{6,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,3,4},{5},{7},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,6},{2,3,4},{5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3,4},{5},{6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,8},{2,3,4},{5},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,8},{2,3,4},{5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2,3,4},{5},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5,6},{2,3,4},{7},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,7},{2,3,4},{5,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,3,4},{5,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2,3,4},{6},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,8},{2,3,4},{5,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2,3,4},{6},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5,6,7},{2,3,4},{8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,5,8},{2,3,4},{6,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,5,6,8},{2,3,4},{7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,5,6,7,8},{2,3,4}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,5},{3,4},{6},{7},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,2,5},{3,4},{6,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5},{3,4},{6,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5},{3,4},{6,7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,7},{2,5},{3,4},{6},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,7,8},{2,5},{3,4},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2,5},{3,4},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2,5},{3,4},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7,8},{2,5},{3,4}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2,6},{3,4},{5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,6},{3,4},{5},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,8},{2,6},{3,4},{5},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,7,8},{2,6},{3,4},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,7},{3,4},{5},{6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,2,8},{3,4},{5},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,2,7,8},{3,4},{5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,6,7},{3,4},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3,4},{5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6,8},{3,4},{5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,5,6},{3,4},{7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,5,6},{3,4},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7,8},{2,5,6},{3,4}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,7},{3,4},{5,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3,4},{5,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5,7},{3,4},{6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,5,7},{3,4},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3,4},{5,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5,8},{3,4},{6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,5,6,8},{3,4},{7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,3,5},{4},{6},{7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,3,5},{4},{6,7,8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,6},{2,3,5},{4},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,3,5},{4},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,7,8},{2,3,5},{4},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6,7},{2,3,5},{4},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,8},{2,3,5},{4},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2,3,5},{4},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,6},{3,5},{4},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,6},{3,5},{4},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,7,8},{2,6},{3,5},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,7,8},{3,5},{4},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,6,7},{3,5},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3,5},{4},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6,8},{3,5},{4},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,3,6},{4},{5},{7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,3,6},{4},{5},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,7,8},{2,3,6},{4},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,7,8},{3,6},{4},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,3,7},{4},{5},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,8},{2,3,6,7},{4},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,8},{3,6,7},{4},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,3,8},{4},{5},{6,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,3,5,6},{4},{7,8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,7},{2,3,5,6},{4},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,3,5,6},{4},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,7},{3,5,6},{4},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,8},{2,7},{3,5,6},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3,5,6},{4},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,3,7},{4},{5,6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,3,7},{4},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3,7},{4},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,3,8},{4},{5,6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,3,5,7},{4},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,8},{3,5,7},{4},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,3,8},{4},{5,7},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,3,5,6,7},{4}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,3,4,5},{6,7},{8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,3,4,5},{6,8},{7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,3,4,5},{6,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,6},{2,3,4,5},{7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,7},{2,3,4,5},{6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6,7,8},{2,3,4,5}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,2,6},{3,4,5},{7},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,6},{3,4,5},{7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,7},{2,6},{3,4,5},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,6},{3,4,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7,8},{2,6},{3,4,5}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,8},{2,7},{3,4,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3,4,5},{6,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,6,7,8},{3,4,5}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,3,6},{4,5},{7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,3,6},{4,5},{7,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,8},{2,3,6},{4,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3,6},{4,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,3,7},{4,5},{6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,3,7},{4,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3,7},{4,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,3,8},{4,5},{6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,3,6,7},{4,5},{8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,8},{2,3,6,7},{4,5}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2,3,8},{4,5},{6,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2,3,6,8},{4,5},{7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,3,6,7,8},{4,5}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,2,3,4,6},{5},{7,8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,8},{2,3,4,6},{5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,7},{3,4,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3,4,6},{5},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,7,8},{3,4,6},{5}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,3,7},{4,6},{5},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,3,7},{4,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3,7},{4,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,3,8},{4,6},{5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,3,7,8},{4,6},{5}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,8},{2,3,4,7},{5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,8},{3,4,7},{5},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,3,8},{4,7},{5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,3,4,6,7},{5}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,3,4,5,6},{7,8}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,7},{2,3,4,5,6},{8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,8},{2,3,4,5,6},{7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,7},{3,4,5,6},{8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,7,8},{3,4,5,6}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,2,3,7},{4,5,6},{8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,8},{2,3,7},{4,5,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,8},{3,7},{4,5,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,3,8},{4,5,6},{7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,3,7,8},{4,5,6}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,3,4,7},{5,6},{8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,8},{2,3,4,7},{5,6}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2,8},{3,4,7},{5,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,3,8},{4,7},{5,6}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2,3,4,8},{5,6},{7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,8},{2,3,4,5,7},{6}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,8},{3,4,5,7},{6}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,3,8},{4,5,7},{6}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,3,4,8},{5,7},{6}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,8},{2,3,4,5,6,7}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,2,8},{3,4,5,6,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,3,8},{4,5,6,7}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,2,3,4,8},{5,6,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,3,4,5,8},{6,7}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,3,5,6,7,8},{2,4}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,3,4,6,7,8},{2,5}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,2,4,6,7,8},{3,5}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,2,4,5,7,8},{3,6}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,2,3,5,7,8},{4,6}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,2,4,5,6,8},{3,7}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,2,3,5,6,8},{4,7}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,2,3,4,6,8},{5,7}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,2,4,5,6,7},{3,8}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,3,5,7,8},{2,4,6}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,5,7,8},{3,4,6}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,3,4,7,8},{2,5,6}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,4,7,8},{3,5,6}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,5,6,8},{3,4,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,3,4,6,8},{2,5,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,4,6,8},{3,5,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,3,6,8},{4,5,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,3,5,8},{4,6,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,3,6,7},{4,5,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,3,4,5,7},{2,6,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,3,4,7},{5,6,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,4,5,6},{3,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,3,5,6},{4,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,3,4,6},{5,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,3,6,7,8},{2,4},{5}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,3,4,7,8},{2,6},{5}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,4,7,8},{3,6},{5}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,3,4,5,8},{2,7},{6}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,3,4,6,7},{2,8},{5}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,4,6,7},{3,8},{5}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,3,4,5,7},{2,8},{6}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,3,5,7},{4,8},{6}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,3,4,5,6},{2,8},{7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,3,5,6},{4,8},{7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,3,4,6},{5,8},{7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,3,5,6,7},{2,4},{8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,3,5,7},{4,6},{8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,3,5,6},{4,7},{8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,3,4,6},{5,7},{8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,3,5,7},{2,4,6,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,2,5,7},{3,4,6,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,3,4,7},{2,5,6,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,2,3,7},{4,5,6,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,3,5,6},{2,4,7,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,2,5,6},{3,4,7,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,2,4,6},{3,5,7,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,2,3,6},{4,5,7,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,3,6,8},{2,5,7},{4}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,6,8},{3,5,7},{4}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,5,8},{3,6,7},{4}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,5,8},{3,4,6},{7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,4,8},{3,5,6},{7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,4,7},{3,6,8},{5}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,3,5,7},{2,4,8},{6}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,4,7},{3,5,8},{6}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,3,4,5},{2,7,8},{6}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,4,5},{3,7,8},{6}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,3,5,6},{2,4,8},{7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,3,6},{4,5,8},{7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,3,5},{4,6,7},{8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,7,8},{3,5},{4,6}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2,6,8},{3,5},{4,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,3,6,8},{2,4},{5,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,3,5,8},{2,6},{4,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,3,5,8},{2,4},{6,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2,4,8},{3,5},{6,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,4,5,7},{2,6},{3,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,3,5,7},{2,6},{4,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,3,5,6},{2,4},{7,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2,4,6},{3,5},{7,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,5,7,8},{2,6},{3},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,7,8},{2,6},{3},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,7,8},{2,6},{4},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,7,8},{2,5},{4},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,7,8},{2,4},{5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,6,8},{2,7},{3},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,6,8},{2,7},{3},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,6,8},{2,7},{4},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,6,8},{3,7},{4},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,5,8},{2,7},{3},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,5,8},{2,7},{4},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,5,8},{3,7},{4},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,8},{2,7},{5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,8},{3,7},{5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,6,8},{2,5},{3},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,6,8},{2,5},{4},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,6,8},{2,4},{5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,5,8},{2,6},{3},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,5,8},{2,6},{4},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,5,8},{3,6},{4},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,8},{2,6},{5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,8},{3,6},{5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,8},{2,5},{6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,8},{3,5},{6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,6,7},{2,8},{3},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,6,7},{2,8},{3},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,6,7},{2,8},{4},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,6,7},{3,8},{4},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,5,7},{2,8},{3},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,5,7},{2,8},{4},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,5,7},{3,8},{4},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,7},{2,8},{5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,7},{3,8},{5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,5,6},{2,8},{3},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,5,6},{2,8},{4},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,5,6},{3,8},{4},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,6},{2,8},{5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,6},{3,8},{5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,3,6},{4,8},{5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,5},{2,8},{6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,5},{3,8},{6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,3,5},{4,8},{6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,6,7},{2,5},{3},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,6,7},{2,5},{4},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,5,7},{2,6},{3},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,5,7},{2,6},{4},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,5,7},{3,6},{4},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,7},{2,6},{5},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,7},{3,6},{5},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,5,7},{2,4},{6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,7},{3,5},{6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,5,6},{2,7},{3},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,6},{2,7},{5},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,6},{3,7},{5},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,3,6},{4,7},{5},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,5},{2,7},{6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,5},{3,7},{6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,3,5},{4,7},{6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,6},{3,5},{7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,5},{2,6},{7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4,5},{3,6},{7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,3,5},{4,6},{7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,7},{2,4,8},{5,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4,5},{2,6,8},{3,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3,4},{2,6,8},{5,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3,5},{2,4,8},{6,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,5},{3,4,8},{6,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3,4},{2,5,8},{6,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,4},{3,5,8},{6,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4,6},{2,5,7},{3,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,5},{3,4,6},{7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3,4},{2,5,6},{7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,4},{3,5,6},{7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,5,7},{2,6,8},{3},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,7},{2,6,8},{3},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,7},{2,6,8},{4},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,7},{3,6,8},{4},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,7},{2,5,8},{3},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,7},{2,5,8},{4},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,7},{3,5,8},{4},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,7},{2,4,8},{5},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,7},{3,4,8},{5},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5,6},{2,7,8},{3},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,6},{2,7,8},{3},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,6},{2,7,8},{4},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,6},{3,7,8},{4},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,5},{2,7,8},{3},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,5},{2,7,8},{4},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,5},{3,7,8},{4},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,4},{2,7,8},{5},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,4},{3,7,8},{5},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,6},{2,5,8},{3},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,6},{2,5,8},{4},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,6},{3,5,8},{4},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,6},{2,4,8},{5},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,6},{3,4,8},{5},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,5},{2,6,8},{3},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,5},{2,6,8},{4},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,5},{3,6,8},{4},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,4},{2,6,8},{5},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,4},{3,6,8},{5},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,5},{3,4,8},{6},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,4},{3,5,8},{6},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,6},{2,5,7},{3},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,6},{2,5,7},{4},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,6},{3,5,7},{4},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,6},{2,4,7},{5},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,5},{2,6,7},{4},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,5},{3,6,7},{4},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,4},{2,6,7},{5},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,5},{2,4,7},{6},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,5},{3,4,7},{6},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,4},{3,5,7},{6},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,5},{3,4,6},{7},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5,8},{2,6},{3,7},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2,6},{3,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,6},{4,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3,6},{4,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2,5},{3,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,5},{4,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3,5},{4,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,4},{5,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2,5},{3,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,5},{4,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3,5},{4,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,4},{5,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2,6},{3,8},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,7},{2,6},{3,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,7},{2,6},{4,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,7},{3,6},{4,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,7},{2,5},{3,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,7},{2,5},{4,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,7},{3,5},{4,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,7},{2,4},{5,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,7},{3,4},{5,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6},{2,7},{3,8},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2,7},{3,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6},{2,7},{4,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6},{3,7},{4,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,5},{2,7},{3,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,5},{2,7},{4,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5},{3,7},{4,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,4},{2,7},{5,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,4},{3,7},{5,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2,5},{3,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6},{2,5},{4,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6},{3,5},{4,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6},{2,4},{5,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6},{3,4},{5,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,5},{2,6},{3,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,5},{2,6},{4,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5},{3,6},{4,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,4},{2,6},{5,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,4},{3,6},{5,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,3},{4,6},{5,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,5},{2,4},{6,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,4},{2,5},{6,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,7},{2,5},{3,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,7},{2,5},{4,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,7},{2,4},{5,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6},{3,4},{5,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,5},{2,6},{3,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,4},{2,6},{5,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,4},{3,6},{5,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,3},{4,6},{5,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,4},{2,5},{6,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,4},{5},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,6,7},{2,8},{3},{4},{5}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3,4},{2,8},{5},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4,7},{2,6},{3},{5},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4,7},{2,5},{3},{6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3,7},{2,4},{5},{6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4,6},{2,7},{3},{5},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3,5},{2,4},{6},{7},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,5},{2,6},{3,7},{4},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3},{2,6},{4,7},{5},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3},{2,5},{4,7},{6},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,4},{2,5},{3,6},{7},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3},{2,5},{4,6},{7},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3,5,8},{2},{4,6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,5,7},{2},{4},{6,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,7},{2,4},{3},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,4,8},{3},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2,4},{3,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2,4},{3,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,5,8},{4,6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,8},{2,6},{3,4},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2,6},{3,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,5,8},{3},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,7},{2,5},{3},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2},{3,6,7},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2},{3,6},{5,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2},{3,7},{5,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2},{3,5,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2},{3,4,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5},{3},{4,7,8},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,5,7},{3},{4,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,5,7},{4},{6,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,7},{2},{3,4},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,7},{2},{3,5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2},{3,8},{5,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2},{3,8},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2},{3,7},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6},{3,4,7},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,3,7},{4},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,6,7},{4,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,6},{4,7,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,3},{4},{5,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6},{3,4},{5,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,7},{3,4},{5,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3},{4},{5,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,7},{4,6,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,5,8},{4,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3,8},{4,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5},{3,4,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4},{3,5,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4},{3,7},{5,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4},{3,6},{5,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4},{3,6,7},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,6,7},{4},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,6},{4},{5,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,7},{4},{5,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,7,8},{4,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,4,7},{5},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,8},{2,3,7},{5},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,7},{2,3,8},{5},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,7},{2,8},{4,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,8},{4},{5,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6},{2,8},{4},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6},{2,7},{4},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,6},{3,7},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,6},{3,8},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4},{3,8},{5,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,7},{3,5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5,7},{3,4},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,8},{3,4,6},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,3,6},{4},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6},{3,8},{4,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3,6},{4},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,7},{3,4,6},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,6,8},{4,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,5,7},{4,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,7},{4,5,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2,7},{3},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,7},{2,8},{4},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,7},{2,8},{4,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,7},{2},{4,5,8},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,7},{2,3},{4,5,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3,8},{4,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3,8},{4},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7,8},{2,5},{3,6},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4,6,8},{3},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,7},{2,4,5},{3,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2,5},{3},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7,8},{2},{3,6},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,8},{2,7},{3,6},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,5,7},{3,6},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2,6,7},{3},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,5,7},{2},{3,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,5},{2,6},{4},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6},{2,8},{4,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6,8},{2},{3,7},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,8},{2,4,6},{3,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2,5},{3},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,5},{2,8},{4},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,3,8},{4},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,6},{3,4,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2},{3,4,7},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6,8},{2,4},{3,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,3,8},{4,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,3,7,8},{4},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5},{2,3,7},{4,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,3,6},{4},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2,4},{3,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2,4,8},{3},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6,8},{2,5,7},{3},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6,8},{2,7},{3,5},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2,7},{3},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2,8},{3,4},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2},{3,4,8},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,7},{2,5},{3,4,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,6,8},{3,4},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2,3,6},{5},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5},{2,4,8},{3,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,4,7},{3,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,4,8},{3,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,4,8},{3,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,5},{3,4,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,3,5},{4,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,3,6},{4,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,6},{3,4,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2,7},{3,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,7},{2,8},{3,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2,8},{3,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,7},{2,8},{3,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,8},{3,4,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,3,8},{4,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5},{3,8},{4,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,7},{3,4,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2,7},{3,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,6},{3,4,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3,6},{4,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,3,6},{4,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,3,5},{4,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,5},{3,4,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,4,7},{3,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,4,7},{3,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4,8},{3,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,5},{2,8},{4,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,7},{4,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,4,8},{3,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,4,7},{3,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4,6},{3,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4,8},{3,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3,5},{4,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,7},{3,8},{4,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,8},{3,4,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,8},{3,4,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,3,7},{4,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,7},{3,4,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,5},{2},{4,6,8},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3},{2,4,6,8},{5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4,6,8},{3},{5,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3},{2},{4,6,8},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6},{2},{4,8},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6},{2},{4,7},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,5},{2},{4,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,5,7},{2},{4,6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,7},{2},{4,6,8},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,7},{2},{4,6},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,5,7},{2},{4,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3},{2,4,8},{5,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,8},{3,5,7},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4},{2,8},{3,5,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,5,7},{3,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,5,7},{4,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,7},{4,6,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,7},{2,4,6},{5},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,7},{2,4,6},{3},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2,4,8},{3},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,8},{3,5,7},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4,6},{3,5},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,7},{2,6},{3,5},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5,8},{3,7},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5,8},{3,6},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,8},{3,6},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,6,8},{3,5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4},{2,6,8},{3,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,5},{3,6,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,5},{4,6,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,4,6,8},{3},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5},{2,4},{3,6,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6,8},{3,5,7},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6},{2,8},{3,5,7},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,4,8},{3},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,4,7},{3},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,4,7},{3},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2,4,6},{3},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5,7},{2,4},{3,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6,8},{3,5},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,6,8},{3,7},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6},{2,7},{3,5,8},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,5},{2,7},{4},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,6,8},{3,5},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,6},{3,5,8},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,4,6},{5,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,6},{4,5,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,5,6},{4,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5,6},{3},{4,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,6},{3},{4,5,8},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6},{2,3},{4,5,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6},{2,3},{4,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6},{2,3,8},{4},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5,6},{2,8},{3,4},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,8},{3,4,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,3,8},{4,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,3,5,8},{4},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,5},{3,8},{4,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,4},{3,6},{5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,4,6},{3},{5,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4},{3,8},{5,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,4},{3,8},{5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,3,8},{5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,4},{2,8},{5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,4},{2,8},{5,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,3,8},{5,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2,3},{5,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,3,6},{5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,3,6,8},{5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4},{2,3,6},{5,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,4,5},{3,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,6},{4,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,4},{2,6},{5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,5,8},{3,4},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,4,5},{3,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,5},{2,8},{3,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,5,6},{4},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,8},{2,5},{4},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,4},{3,7,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6},{2,4},{3,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,8},{3,5,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,7,8},{3,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,7},{2,8},{3},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2,8},{3,4},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2,3,8},{4},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,5},{3,7},{4},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,3,7},{4},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,5},{2,7},{3},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,7},{3},{5,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,6,7},{3},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,6},{3},{5,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,5,7,8},{3},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6,7},{2,5,8},{3},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,7},{2,5,6,8},{3},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,7},{2,6,8},{3},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3,6,8},{4},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,8},{3,6},{4},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,6},{3},{4,5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,5,6},{3},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,5},{3},{4,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7,8},{2,5},{3},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,4},{3,6,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7,8},{2,4},{3,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,3,7},{5,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,7},{4,5,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,6,7},{4,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,6},{4,7,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,4,7,8},{3},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,7},{2,4,8},{3},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4,5,8},{3},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,7},{2,5,8},{3,4},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3,5,8},{4},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,7},{3},{4,6},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2},{3,4,6},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2},{3,6},{4,5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2},{3,5,6},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2},{3,5},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2},{3,5},{4,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2},{3,7,8},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2},{3,8},{4,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6},{2},{3,8},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2},{3,8},{4,5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2},{3,4,8},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6},{3},{4,8},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6,8},{3},{4,7},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6,8},{2,3},{4,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2},{3,7},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6,8},{2},{3,7},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,8},{2},{3,6,7},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,6,8},{2},{3,5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,7},{2,3},{4,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2},{3,6},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2},{4,6},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,7,8},{2},{3,6},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,6,7},{2},{3,5},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,8},{2},{3,7},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2},{3,7},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2},{3,6},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,7},{2,3},{5,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,5,8},{4,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,4,7,8},{3},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3},{2,4,8},{5,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,5,8},{4,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,4},{3,5,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,6},{3,5,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,5,6},{3,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,6,7},{3,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5},{3,6},{4},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,4},{3,7},{5,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,4},{2,7},{5,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2,8},{3},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6},{2,3},{4,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2,3},{5,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,3,6},{5,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,3,7},{5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,4},{3,7},{5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,4},{2,7},{5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6},{3},{4},{5,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,7},{2,3,4},{5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4},{3,6,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,7},{3,6,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,6},{3,5,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,4},{3,5,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,7,8},{3},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4},{3,5,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,5},{3,7,8},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,6},{3,7,8},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,8},{3,6,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,4,5,6,7,8}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,4},{2,3,5,6,7,8}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,5},{2,3,4,6,7,8}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,4},{2,6},{3,5,7,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,5},{2,6},{3,4,7,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,5},{2,4,6,8},{3,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,4,5,8},{2,3,6,7}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,4},{2},{3,5,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,5},{2},{3,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2},{3,4,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2},{3,4,7,8},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5},{2},{3,4,7,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,5},{2},{3,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2},{3,4,8},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,7},{2},{3,4,8},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6,7},{2},{3,8},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,6},{2},{3,7,8},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,6},{2},{4},{5,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2},{3,6},{4},{5,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2},{3,5,7,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6},{2,4},{3},{5,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2,3},{4},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4},{3},{5,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2,4},{3},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,6,7},{4},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6,7},{2},{4},{5,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,7},{2},{4},{5,6,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2},{3,7},{4},{5,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,7},{2},{3,8},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4,5},{3},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,4,5},{3,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,4},{3,5,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2,3},{4,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,5},{3,4,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2},{3,5,6},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4},{2},{3,6,8},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2,3},{4},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2},{3},{5,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,5,6},{3,7},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5,6},{3},{4,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,5},{3,7},{4,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2},{3,6,7},{4,5,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,3,6,7},{4},{5,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,6},{4,8},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2},{3,4,6,8},{5,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2},{3,6},{4,5,7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,5},{3},{4,6,7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,5},{3,6},{4,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5},{3,6,7},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2},{3,5,6,7},{4,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2},{3,5,6},{4,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2},{3,5},{4,6,7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4,8},{3,5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4},{3,6,8},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,7},{3,6},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,8},{4,5,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,4,7,8},{5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,7},{2,3,4,8},{5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4,7},{3},{5,6,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,7},{2},{3,4,5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,7},{4,8},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2},{3,7},{4,5,6,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2},{3,5,7},{4,6,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,6},{3,5},{4,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6},{3,5,7},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2},{3,6,7},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2},{3,6},{4,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2},{3},{4,6,7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,6},{3},{4,5,7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6},{2},{3,4},{5,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6},{3},{4,7,8},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6},{2},{3,4,7},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6},{3,7},{4,5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2},{3,7},{4,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,6},{3},{4,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6},{2,5},{4},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,4,6},{3},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,5},{2,6},{3},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2,7},{3,4},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,5},{2,8},{3},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2,8},{3,5},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,8},{3},{4,5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,5,8},{3},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,4,5,8},{3},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5},{2,7},{3},{4,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,5},{3,6,8},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,6},{3,5,7},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2,3},{4,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3},{4,6,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2,3},{4,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,5,6},{3,7},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,6},{4},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2,5},{3,8},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,6,7},{3},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,7},{4,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6},{2,4,8},{3},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5,6},{2,8},{3},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2},{3,6,8},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5},{2},{3,6,8},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2,5},{3},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,6,8},{3},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2,6},{3},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,5,7},{3},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2},{3,6},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2},{3,8},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6},{2},{3,7},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2,6},{3},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,5,8},{3,6},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,5,8},{3},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,5,6},{3},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2,5},{3},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,5},{3},{4,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6},{2,7},{3},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2,7},{3},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,5,8},{3,7},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6},{2,8},{3,7},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,8},{3,6,7},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,7,8},{3,6},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,5},{3,6,7},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,5,7},{3},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2,8},{3,6},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,7},{3,6,8},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,5},{3},{4,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2,5},{3,7},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,6,8},{3,7},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,5,7},{3,8},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7},{2,8},{3},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,8},{3},{4,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,7,8},{3,5},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,8},{3,5,6},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,5,6},{3,8},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,6,7},{3,8},{4}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,4,6},{5},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,8},{2,3,5},{4,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,4,6},{3,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,8},{3,4,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,7},{3,8},{4,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,5},{2},{4,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6},{2},{4,7,8},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6},{2},{3,7,8},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2},{3,8},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6,7},{2},{4,8},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,8},{2},{3,6,7},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5,6},{2},{3,4,8},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6},{2},{3,5,7,8},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6,7},{2},{3,5,8},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4},{2,6,8},{3},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,4,6},{3},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2},{3,6,8},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2},{3,5,7},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4},{2},{3,5,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,5,7},{4},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2},{3,4,7},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2},{3,4,7},{5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5},{3},{4,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5,8},{3},{4,7},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2},{3,4,7},{5,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,5},{4,6,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6},{3},{4,7},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,7},{2,6},{4},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6},{3,7},{4},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5},{3},{4,6,8},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,5},{3},{4,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,5,6},{4,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,8},{4,5,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,5},{2,8},{4,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6},{3,8},{4,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,4,7},{3},{5,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,7},{2,5},{4},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,7},{3,4},{5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,4,7},{3},{5},{6,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4},{3},{5,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,4},{5,6,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,4,7},{5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,5,8},{3,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3,4},{5,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,4,7},{5,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,4,6},{5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,4},{2,8},{5,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,3,4,8},{5},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4},{2,5,6},{3,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2,8},{3,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,8},{3,4,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5,7},{3},{4},{6,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,5,8},{3},{4,6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,6},{2,8},{4,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2},{3,5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3,5,8},{4,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,5,7},{4},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,7},{3,5},{4},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,7},{2,4},{5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,4,7},{5},{6,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4},{2,5,7},{3},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,4,6},{5,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,4},{5,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,5},{3,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,5},{4,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,5},{4,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,5,8},{3,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,5},{3,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,3,4,5},{6,7,8,9,10}} => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => 0
{{1,6},{2,4},{3,7,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6},{2,3,4,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,5,7},{2,4,6,8},{3}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,5,6},{2,3,4,8},{7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,5},{2,3},{4,7,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,4},{3,5,7,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,6},{2,5},{3,4,7,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,3,7},{2},{4,8},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6},{2},{4,7},{5},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3},{2},{4,7},{5,8},{6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,4,7},{3},{5,8},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,7},{3,4,5,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6},{2,3,4,7},{5},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,8},{2,6,7},{3},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,6},{2,8},{3},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4},{3,5,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2,3,7},{4},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,5,8},{3,7},{4},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,7},{3,5,8},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,4,7},{3,5},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,5},{3,4,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,8},{3,6},{4,5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,3,7},{4,5},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,7},{3,4,8},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,6,8},{3,4},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,5,7},{3},{6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4},{2,5},{3},{6,8},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5},{2,3,6,8},{4},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,5},{3,6,8},{4},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,5,6,7},{3,8},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,8},{3,5},{4,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6,7},{3,4,8},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5,6},{2,3,7},{4},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,6},{3,7},{4,8},{5}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,6,7},{2,3,8},{4},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,4,6},{3,5,7},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,6},{2},{3,5,8},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,7},{2},{3,4},{5,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2},{3,4},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,7},{3},{4,5,8},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6,7},{2},{3,4},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2},{3,4,6},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,8},{3,7},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,7},{4},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,7,8},{4},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4},{3,7,8},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,6,8},{4},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6,8},{3,4},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2,3},{4},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6,7},{3,4},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,6,8},{4,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6,8},{2},{4,7},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,7},{2,6},{3},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2,4,7},{3},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,5,7},{2},{3},{6,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4},{2},{5,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,4},{5,7,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,5,6},{3},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,6,7,8},{3},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5},{2},{3,6,7,8},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,5,8},{2},{3,7},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5},{2,4,6},{3,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,5},{2},{3,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,7},{3,8},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,3,8},{4},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6},{3,4,8},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3},{4,5,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3},{4,6,8},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,5,6},{4,7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,5,7},{4,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,7},{4,6},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,6},{4,7},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,5,8},{4,6,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,5},{2},{3,4,6,7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5},{2,6,7},{3,4},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,5,7,8},{4,6}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,4,5,7},{2},{3,6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4},{2},{3,5,6,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,8},{2},{3,5,7},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,8},{2,5,7},{4},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3},{2,5,6,8},{4},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,7},{2,6},{4,5},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2,4,7},{3},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6,8},{2,4},{3},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,8},{2,6},{3},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2},{3,4,6,8},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,7},{3,4,5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6},{3,4,5,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6},{2},{3,4,5,7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6},{2,7},{3,4,5},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4},{3,5,6,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,4},{2,7},{3,5,6,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,4,8},{2,6},{3,5,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,6,8},{2,4},{3,5,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3,8},{2,5,7},{4,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,5},{2,7},{3,4,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,8},{3,5,6},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6},{2,4,5},{3,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5,7},{3,8},{4},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,7},{3,5,6},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5,8},{3,6,7},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,7},{2,5,6},{3},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,6,8},{3,4,7},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5,7},{2,3,6},{4},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3},{2,6},{4,5,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2,3,8},{5},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4},{2,3,8},{5,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,5},{4,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,5},{2},{4,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6,7},{2},{3,4,8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,5},{3},{4,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5},{3},{4,8},{6,7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5,8},{2,4},{3,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,7},{3,5,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,4,6},{3,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,3,5},{4,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2,7},{3},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5},{3,8},{4,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,7},{4,8},{5},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4,7},{2,3},{5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4},{3,7,8},{5},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,5,7},{3,4,8},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5,6},{2,4},{3,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4},{3,5},{6,7},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,4,8},{3,5},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4,6},{3,5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5},{3,6},{4},{7,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,5,7},{3,6,8},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,5,7},{3,8},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2,4},{3,5,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2,4},{3,5},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5},{3,6},{4,7},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,5},{3,6,8},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,6,7},{4,8},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,5,8},{2},{4,7},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,6},{2},{3,7,8},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,7},{2},{3,5,8},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4},{2,6,8},{3,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,3,7,8},{4},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,6,8},{4},{5,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2},{3},{4,6},{5,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5,6,8},{3},{4,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2},{3,5,6,8},{4,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4,5,7},{3,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2},{3,4,6,7},{5,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,6},{3,7,8},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6,7},{3,5},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2},{3,6,8},{4,5,7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,3},{4,7},{5,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7,8},{2,4},{3,5},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6,8},{2},{3},{5,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4,6},{3,7,8},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3},{2},{4,6},{5,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,6,7},{3},{5,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,5},{3,7,8},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,7},{2},{3,6,8},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3},{2,4,5},{6,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,8},{4,6,7},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,4,5},{6,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,7,8},{3},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,3,7,8},{5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,8},{2,4},{5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2},{3},{4,5,7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5},{2,3,7},{4,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,3,6,7},{5},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,6},{2,3,7},{5},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6},{2,4,5,7},{3},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,7},{2,4,5},{3,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6,7},{2},{3},{4,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,7},{2,6},{3,4},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6,7},{3,5,8},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3},{2},{4,6,7},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,5,8},{3,4,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3,6,7},{2,4,5,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1},{2,8},{3,5,6},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5,6,7},{3},{4,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6},{2,7,8},{3,4},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,7},{3,4,6,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,7},{2},{3,8},{4,5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4,5},{3,6,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1},{2,6,8},{3,7},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,5,8},{3,7},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4,5},{3,7,8},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,6},{3,8},{4,5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,5,6},{2},{3,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,5,6},{2},{4,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4,6,7},{3,8},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5},{2,7,8},{3,4},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,5},{2},{4,7,8},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3},{2,5},{4,7,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,6},{3},{4,5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,7,8},{4,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,5},{2,8},{3,7},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6},{2,4},{5},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6},{2},{4,5,8},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2},{3,5},{4,7,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,4,7},{5,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,8},{2,5,7},{3},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,3,4,6},{5,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4,5,8},{3,6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6},{2},{3,4,5,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4},{3,6},{5,8},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3},{2},{4,6},{5,8},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3},{2,5},{4},{6,8},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,4,5,6},{3,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,6},{3,5},{4,8},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5},{2,4},{3,7},{6},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5},{2,4,6,7},{3},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,6},{3,5,7,8},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,8},{3,5},{4,7},{6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,7},{2,4},{3,6},{5},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,5,7,8},{3,6},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,6},{2,4,7},{3},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3},{2,5,6,7},{4},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3},{2,6,7,8},{4},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4},{3,6,7,8},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4},{3,8},{5,7},{6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3},{2,7},{4,6},{5},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,4,7},{3,6,8},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,7},{2,3,5},{6},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,7},{2,3,6},{5},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5},{2,3,6,7},{4},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4},{2,3,7},{5,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5,8},{3,4,6},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,5,7},{3,4,6},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,3,6},{4,5,7},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6},{2,3},{4,5,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,6},{2},{4,5,7},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4},{2,3,5},{6,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,5,7},{3,4},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,3,5},{6,8},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,6},{4,5,8},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,5,8},{3,4,7},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,3,7},{4,6,8},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,3,7},{4,5,8},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,8},{2},{3,5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,8},{2},{3,5},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,3,5,8},{6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,6,8},{3},{4},{5,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2},{3,6,8},{4},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2},{3,6},{4,5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2},{3,5,6},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,8},{2},{3,4,6},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3},{2,4,8},{5},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,6},{3,4,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,4},{3,6,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,3,6},{4,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,3,4,6},{7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,7},{2,3},{4,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,4},{3,8},{5,6},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,3,4,5,6},{7,8,9}} => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => 0
{{1,2,3,4,5},{6,7,8,9}} => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => 0
{{1,2,3,4,5},{6,7,8},{9}} => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => 0
{{1,2,3,4,5,6},{7,8,9,10}} => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => 0
{{1,2,3},{4,7},{5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5},{3},{4,6,7},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,7},{3},{4,8},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,5},{3,8},{4},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,5,7,8},{3},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,6},{3},{4,5,7},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,5,6},{3},{4,7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,6},{3,4,7,8},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3},{2},{4,7},{5,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2},{3,6,7,8},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,7},{4},{5,6,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,3,6},{4},{5,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,3},{4,6,7},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3},{4,6},{5,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,6},{3,7,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,5,6},{4,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,5},{4,7,8},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,5},{3,4,7,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,7},{2},{3,6},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,8},{3,6,7},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,3,6},{4,7,8},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,5,7},{2,3,6,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,5},{2,3,7},{4,6,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,5},{2,3,6,8},{4,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1},{2,5},{3,4,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,6,8},{3,4,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,5,7},{2,6},{3,4,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,6},{2,5,7},{3,4,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,5,7},{2,3,6},{4,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,5,7},{2,3,8},{4,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1},{2,7},{3,6},{4,5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,4,5,8},{3,6}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,7},{2,5,8},{3,4,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,6},{2,5},{3,4,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,4,5,8},{3,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,4,5},{2,7},{3,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,5,7},{3,6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,5,7},{2,8},{3,6}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,4,5},{2,7},{3,6,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,7},{2,5},{3,4,6,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1},{2,6},{3,4,5,7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,7},{3,6,8},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,4,5,7},{3,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,5,7},{2,8},{3,4,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3,6},{2,7},{4,5},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6,8},{3},{4,7},{5}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3},{2},{4,7},{5},{6,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,3,4,7},{2},{5},{6,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4},{2},{3,5},{6,8},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5,7},{2},{3,6},{4},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,7},{3,5},{4},{6,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,6},{2,4},{3},{5,7},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,7},{3,5,6,8},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,8},{3,6},{4},{5,7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,7},{2,5},{3},{4,6},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,7},{3,4,6,8},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6},{2,3,5,7},{4},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,5,8},{2},{3,6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,6},{2},{5,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,6},{3},{4,8},{5,7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5},{2},{3,7},{4,6},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,6},{3,5,8},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,4,7},{3,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5},{3,4,6,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4},{2,3,5,7},{6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,5,6,8},{3,7},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,7},{3,5},{4,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5},{2,3,7},{4},{6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,5},{2,3,8},{4},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,5,8},{2,3,6},{4},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6},{2,3,8},{4},{5},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,6},{2,4,8},{3},{5},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,6,8},{2,3,7},{4},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6},{2,3},{4,7},{5},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,6},{2,3},{4,7,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,3},{4,8},{5},{6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,7},{2,4},{3,8},{5},{6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5},{2},{3,4,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4},{3,5,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,5},{3},{4,8},{6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5,8},{2,4,6},{3},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,8},{2,3,5},{6},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,4},{3,5,7},{6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4},{3,5,8},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4,7},{3,5,6},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,7},{2,3,5},{4},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,5},{3,8},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,8},{4,6},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,5,7},{3},{6,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,7},{2},{4,5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,7},{3,5,8},{6}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2},{3,5,7,8},{4,6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2},{3,5,8},{4,6,7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,5,7},{3,6},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,7,8},{2},{3},{4,6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,5,7,8},{3},{4,6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,6,7},{2},{3,8},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,7,8},{2},{3,5},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6,8},{2},{3},{4,7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,5},{4,6,7,8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1},{2,3,5},{4,6,8},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,3,4},{5,6,7,8,9,10}} => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => 0
{{1,3},{2,5,6},{4},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,5},{3,7,8},{6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2},{3,7},{4,5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2},{3,5},{4,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,5,7,8},{4},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,7},{2},{3,5,6,8},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6},{2},{3,5,7},{4,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2},{3,5,7},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2,3,5},{7},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5,8},{2},{3},{4,6,7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5,6},{2},{3,4,7},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,6},{2,4,5},{7},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,3,7},{4,5},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2},{4,5,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3},{4,5,7},{6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2},{3,4,6},{5,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2},{3,4,7},{5,6,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2},{3},{4,6,8},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3},{4,6,7},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,4},{5},{6,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,5},{3},{6,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,5},{4},{6,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,7},{2,8},{3},{4,5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,8},{3},{5,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6,7},{3},{4,5,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,8},{2,5,6},{3},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6,8},{2,7},{3,4},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6,7},{2,4},{3,8},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2},{3,5},{6,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,7},{3},{4,5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,4,6},{5,7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,7,8},{3,5},{4,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,5,6},{2,7},{3,4},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2,7,8},{3},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,8},{2},{3,5},{4,6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,6},{2},{3,5,8},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,6,8},{3},{4,5,7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,6,7},{3,8},{4,5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5,6},{3,8},{4,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3,8},{2,6,7},{4},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,2,7},{3,6},{4},{5,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,8},{3},{4,6},{5,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,9},{2,3,4,5,8},{6,7}} => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => 1
{{1,3},{2,5,6},{4,7},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,3},{2,7},{4,5,6},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,5,8},{3},{4,6,7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4},{2,6,7},{3,5},{8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,7,8},{3,6},{5}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,5},{3,6,7},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,4,5},{3,6,8},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,5,6},{3,7,8},{4}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,4},{3,5,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6},{2,3,8},{5,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4},{2},{3,5,6,7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,6},{2,7},{4,5,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4,6},{2,3,5,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,4,6},{3},{5,7,8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1},{2,4,6,7,8},{3,5}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,6},{3,4,5,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1},{2,3,5,8},{4,7},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5,7,8},{2,3,4,6}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,3,6,8},{2,4,5,7}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,2,6,8},{3,4,5,7}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,6},{2,3,4,5,7,8}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 0
{{1,2,6},{3,4,5,8},{7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,4,8},{2,3,5,6},{7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,5},{2,3,4,8},{6,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,4,8},{2,3,5},{6,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,4},{3,5,6,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,5,8},{2,3,4,6,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,3,4},{2,5,6,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,4,6,7},{2,3,8},{5}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,3,8},{2,4,6,7},{5}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,3,5},{2,8},{4,6,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4,7,8},{2,3,6},{5}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,6},{2,3,5},{4,7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,6},{3,5},{4,7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,5},{3,6},{4,7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,5},{2,3,6},{4,7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4,7,8},{2,6},{3,5}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,7,8},{2,3,5},{4,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,7,8},{2,5},{3,4,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,7,8},{2,4,6},{3,5}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4,8},{2,3,5,7},{6}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,5},{3,4,6,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2,3},{4,5,6,7,8,9}} => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => 0
{{1,2,3,4},{5,6,7,8,9}} => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => 0
{{1,2,3},{4,5,7,8,9},{6}} => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => 0
{{1,2,3,5,6},{4},{7,8,9}} => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => 0
{{1,2,3,4},{5,6,7,9},{8}} => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => 0
{{1},{2},{3},{4,6,7},{5,8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2},{3,5,6},{4,8},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4,5},{3,8},{6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4,6,7,8},{2,3,5}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,3,6,7,8},{2,4,5}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,3,5},{2,6},{4,7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4,5,7,8},{2,3,6}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,3,7},{2,4,5,8},{6}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,5,8},{2,4,6},{3,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,5,8},{3,4,6,7}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1},{2,3,5,7},{4,6},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,4,5,7},{6,8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1},{2,3,5,8},{4,6,7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,3},{2,6,8},{4,5},{7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4,6,7},{2},{3},{5,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,7,8},{2},{3,5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4,7,8},{3,5},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4,7,8},{3,6},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4},{2},{3,7,8},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,3,4,6,8},{5,7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,5,6},{2,3},{4,7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3},{2,4,5,6,8},{7}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,6,7},{2,3,4,5,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,7},{2,3,4},{5,6,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4,5},{2,3,7,8},{6}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,4,6,8},{2,3,5,7}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,4,8},{2,3,6,7},{5}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,3,7},{2,6},{4,5,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,6},{3,7},{4,5,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2},{3,4,6},{5,7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,3},{4,7},{5,6,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,5},{2,6,7,8},{3,4}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,7},{2,6,8},{3,4,5}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,6},{3,5,7,8},{4}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1},{2,3,6},{4,5,7,8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,7,8},{2,4},{3,5,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3},{2,5,8},{4},{6,7}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4},{3,5,6,7,8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,5,6},{2},{3},{4,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,3,5},{2},{4,6},{7},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3,7},{2},{4},{5},{6,8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,3,6},{2},{4},{5,8},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4},{2,6},{3},{5,8},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5},{2,6},{3},{4,8},{7}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5,7},{2},{3},{4},{6,8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4,6},{2},{3,5,7},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,6},{2},{3},{4,7},{5,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5},{2},{3},{4,7},{6,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5,7},{2},{3},{4,6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4,7},{2},{3,6},{5},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4},{2},{3,7},{5},{6,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5},{2},{3,7},{4,8},{6}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,7},{2,5},{3,6},{4},{8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,5},{2,3,4,8},{6},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,5},{2,3,8},{6},{7}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,8},{2,3,4,6},{5,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,7},{2,3},{4,5,6,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,7},{2,3,5,6},{4,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,4,7,8},{2,3,5,6}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0
{{1,5,7,8},{2,3},{4,6}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,5,6,8},{2,3},{4,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,5},{2},{3,4,6,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,6},{2},{3},{4,5,7,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4},{2,6,7,8},{3},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,5},{3,6,7,8},{4}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4,7},{2},{5,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,6},{2,3,5},{7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2},{3,6,8},{4,5,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3},{2,4,5,6,7},{8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1},{2,5},{3,4,6,7,8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,4},{2,3,5,6,7},{8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,4},{3,5,6,7},{8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1},{2,3,5},{4,6,7,8,9}} => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => 0
{{1},{2,6},{3,4,5,7,8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1},{2,3,4,6},{5,7,8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,5},{2,3,4,6,7},{8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,2,4},{3,5,6,7,8},{9}} => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => 0
{{1,2,7},{3},{4,6,8},{5}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,4,6},{3},{5,7,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,5,7},{3},{4,6,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,5,6},{2},{3,8},{4},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2},{3},{4,6,8},{5,7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2},{3,5,8},{4,6},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,2,9},{3,4,5,6,7,8}} => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => 0
{{1,2,7},{3,8},{4},{5,6}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2,6,7},{3},{4,8},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4},{3,6},{5,7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1},{2,5},{3},{4,7},{6,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1,4,8},{2,3,7},{5,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2},{3,4,7},{5,6,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4,7},{2,3},{5,6,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3,7},{2,4},{5,6,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3,7},{2,6,8},{4,5}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,7},{2,3,5,8},{4,6}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2,6},{3,8},{4,5,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,8},{3,4,6},{5,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2},{3,5,7,8},{4,6}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,5,7,8},{2,6},{3,4}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,5,8},{2,7},{3,4,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,6,8},{2,3},{4,5,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,6,8},{2,5,7},{3,4}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,6,8},{2,4,7},{3,5}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1},{2,4},{3,5},{6,7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,5,6,8},{3},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,5},{2,3,4,6},{7,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,3,4},{2,8},{5,6,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3,6,7},{2,8},{4,5}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,8},{2,3,6},{4,5,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,7},{3,4,5,6,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,2},{3,5,6},{4,7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,5,6},{2,7,8},{3,4}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4,5},{2,7,8},{3,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,7},{2,6},{3,4,5,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2},{3,7},{4,5,6,8}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,7},{2,5,6,8},{3,4}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2,3,7},{4},{5,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,4},{2,6},{5,7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3,4,5,6},{2,8,9},{7}} => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => 0
{{1,3,4,5,6},{2},{7,8,9}} => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => 0
{{1,7},{2},{3,4,5,8},{6}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4},{2,3,5,6},{7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,5},{2,4},{6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,4},{2,5,6,7},{3},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2},{3,4,5,7},{6,8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,4,7},{2},{3},{5,6,8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1,4,5},{2},{3,6,7},{8}} => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 0
{{1},{2,5},{3,4,6,7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4,5,6},{3,7},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,3,6},{4},{5,8},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,3,7},{4},{5,8},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4},{3,7},{5},{6,8}} => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
{{1},{2,5},{3},{4,6,8},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,5},{3},{4,6,7},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,2},{3,4,6,8},{5,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2,3,4,9},{5,8},{6,7}} => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => 1
{{1,4,6,7,8},{2},{3,5}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1,4,5},{2,3,6,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 0
{{1,4,5},{2,3,6},{7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4,5},{2,3,8},{6,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4,7},{2,3,8},{5,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3,4},{2,7},{5,6,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3,6,8},{2,7},{4,5}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,2},{3,6,7},{4,5,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,6,7},{2,3},{4,5,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,6,7},{2,5,8},{3,4}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,5,6},{2,8},{3,4,7}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,6,7},{2,4,5},{3,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,4},{3,6,7,8},{5}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,4},{3,5,6,8},{7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,3,6},{4},{5,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,4},{3,5,6,8},{7}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1},{2,5},{3,4,6},{7,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1,2},{3},{4,7},{5,6,8}} => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
{{1},{2,4,6},{3},{5,7},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1,4,6},{2,3,5,8},{7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,6},{2,3,5,8},{4,7}} => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
{{1,3,5},{2,7,8},{4,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,3,4},{2,5,7,8},{6}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,4,5,6},{2},{3,7,8}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,2,5,7,8},{3},{4,6}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1},{2,3,6,8},{4,7},{5}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,3,6},{2,4},{5,7,8}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,4,8},{2,5,7},{3,6}} => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 1
{{1,2,6,8},{3},{4,5,7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1,4,6,8},{2,3,5},{7}} => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 0
{{1},{2,3,4,6,7},{5,8}} => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 0
{{1},{2,3,6},{4,7},{5},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4,7},{3,8},{5},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,5,7},{3},{4,8},{6}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4,7},{3,5},{6},{8}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,5,8},{3,6},{4},{7}} => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 0
{{1},{2,4,6,7},{3,5},{8}} => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 0
{{1,2,4},{3},{5,6,7,8,9}} => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => 0
{{1,2,3,5},{4},{6,7,8,9}} => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => 0
{{1,2,3,4,6},{5},{7,8,9}} => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => 0
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Generating function
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 5$
$F_{4} = 15$
$F_{5} = 52$
$F_{6} = 188 + 15\ q$
Description
The number of nested exceedences of a permutation.
For a permutation $\pi$, this is the number of pairs $i,j$ such that $i < j < \pi(j) < \pi(i)$. For exceedences, see St000155The number of exceedances (also excedences) of a permutation..
For a permutation $\pi$, this is the number of pairs $i,j$ such that $i < j < \pi(j) < \pi(i)$. For exceedences, see St000155The number of exceedances (also excedences) of a permutation..
Map
shape
Description
Sends a set partition to the integer partition obtained by the sizes of the blocks.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
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