Identifier
Mp00138:
Dyck paths
—to noncrossing partition⟶
Set partitions
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Images
[1,0] => {{1}} => [1] => [1]
[1,0,1,0] => {{1},{2}} => [1,1] => [1,1]
[1,1,0,0] => {{1,2}} => [2] => [2]
[1,0,1,0,1,0] => {{1},{2},{3}} => [1,1,1] => [1,1,1]
[1,0,1,1,0,0] => {{1},{2,3}} => [1,2] => [2,1]
[1,1,0,0,1,0] => {{1,2},{3}} => [2,1] => [1,2]
[1,1,0,1,0,0] => {{1,3},{2}} => [2,1] => [1,2]
[1,1,1,0,0,0] => {{1,2,3}} => [3] => [3]
[1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => [1,1,1,1] => [1,1,1,1]
[1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => [1,1,2] => [2,1,1]
[1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => [1,2,1] => [1,2,1]
[1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => [1,2,1] => [1,2,1]
[1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => [1,3] => [3,1]
[1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => [2,1,1] => [1,1,2]
[1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => [2,2] => [2,2]
[1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => [2,1,1] => [1,1,2]
[1,1,0,1,0,1,0,0] => {{1,4},{2},{3}} => [2,1,1] => [1,1,2]
[1,1,0,1,1,0,0,0] => {{1,3,4},{2}} => [3,1] => [1,3]
[1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => [3,1] => [1,3]
[1,1,1,0,0,1,0,0] => {{1,4},{2,3}} => [2,2] => [2,2]
[1,1,1,0,1,0,0,0] => {{1,2,4},{3}} => [3,1] => [1,3]
[1,1,1,1,0,0,0,0] => {{1,2,3,4}} => [4] => [4]
[1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => [1,1,1,2] => [2,1,1,1]
[1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => [1,1,2,1] => [1,2,1,1]
[1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => [1,1,2,1] => [1,2,1,1]
[1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => [1,1,3] => [3,1,1]
[1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => [1,2,1,1] => [1,1,2,1]
[1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => [1,2,2] => [2,2,1]
[1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => [1,2,1,1] => [1,1,2,1]
[1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => [1,2,1,1] => [1,1,2,1]
[1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => [1,3,1] => [1,3,1]
[1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => [1,3,1] => [1,3,1]
[1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => [1,2,2] => [2,2,1]
[1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => [1,3,1] => [1,3,1]
[1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => [1,4] => [4,1]
[1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => [2,1,1,1] => [1,1,1,2]
[1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => [2,1,2] => [2,1,2]
[1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => [2,2,1] => [1,2,2]
[1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => [2,2,1] => [1,2,2]
[1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => [2,3] => [3,2]
[1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => [2,1,1,1] => [1,1,1,2]
[1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => [2,1,2] => [2,1,2]
[1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => [2,1,1,1] => [1,1,1,2]
[1,1,0,1,0,1,0,1,0,0] => {{1,5},{2},{3},{4}} => [2,1,1,1] => [1,1,1,2]
[1,1,0,1,0,1,1,0,0,0] => {{1,4,5},{2},{3}} => [3,1,1] => [1,1,3]
[1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => [3,1,1] => [1,1,3]
[1,1,0,1,1,0,0,1,0,0] => {{1,5},{2},{3,4}} => [2,1,2] => [2,1,2]
[1,1,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4}} => [3,1,1] => [1,1,3]
[1,1,0,1,1,1,0,0,0,0] => {{1,3,4,5},{2}} => [4,1] => [1,4]
[1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => [3,1,1] => [1,1,3]
[1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => [3,2] => [2,3]
[1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => [2,2,1] => [1,2,2]
[1,1,1,0,0,1,0,1,0,0] => {{1,5},{2,3},{4}} => [2,2,1] => [1,2,2]
[1,1,1,0,0,1,1,0,0,0] => {{1,4,5},{2,3}} => [3,2] => [2,3]
[1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => [3,1,1] => [1,1,3]
[1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3}} => [2,2,1] => [1,2,2]
[1,1,1,0,1,0,1,0,0,0] => {{1,2,5},{3},{4}} => [3,1,1] => [1,1,3]
[1,1,1,0,1,1,0,0,0,0] => {{1,2,4,5},{3}} => [4,1] => [1,4]
[1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => [4,1] => [1,4]
[1,1,1,1,0,0,0,1,0,0] => {{1,5},{2,3,4}} => [2,3] => [3,2]
[1,1,1,1,0,0,1,0,0,0] => {{1,2,5},{3,4}} => [3,2] => [2,3]
[1,1,1,1,0,1,0,0,0,0] => {{1,2,3,5},{4}} => [4,1] => [1,4]
[1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5}} => [5] => [5]
[1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => [1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => [1,1,1,1,2] => [2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => [1,1,1,2,1] => [1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}} => [1,1,1,2,1] => [1,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => [1,1,1,3] => [3,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => [1,1,2,1,1] => [1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => [1,1,2,2] => [2,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,5},{4},{6}} => [1,1,2,1,1] => [1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}} => [1,1,2,1,1] => [1,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,5,6},{4}} => [1,1,3,1] => [1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => [1,1,3,1] => [1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,6},{4,5}} => [1,1,2,2] => [2,2,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => [1,1,3,1] => [1,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => [1,1,4] => [4,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => [1,2,1,1,1] => [1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => [1,2,1,2] => [2,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => [1,2,2,1] => [1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,6},{5}} => [1,2,2,1] => [1,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => [1,2,3] => [3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5},{6}} => [1,2,1,1,1] => [1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6}} => [1,2,1,2] => [2,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,5},{3},{4},{6}} => [1,2,1,1,1] => [1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}} => [1,2,1,1,1] => [1,1,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}} => [1,3,1,1] => [1,1,3,1]
[1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,4,5},{3},{6}} => [1,3,1,1] => [1,1,3,1]
[1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => [1,2,1,2] => [2,1,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => [1,3,1,1] => [1,1,3,1]
[1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}} => [1,4,1] => [1,4,1]
[1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => [1,3,1,1] => [1,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => [1,3,2] => [2,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,5},{3,4},{6}} => [1,2,2,1] => [1,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => [1,2,2,1] => [1,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}} => [1,3,2] => [2,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => [1,3,1,1] => [1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => [1,2,2,1] => [1,2,2,1]
[1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => [1,3,1,1] => [1,1,3,1]
[1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}} => [1,4,1] => [1,4,1]
>>> Load all 1951 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => [1,4,1] => [1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => [1,2,3] => [3,2,1]
[1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}} => [1,3,2] => [2,3,1]
[1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}} => [1,4,1] => [1,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => [1,5] => [5,1]
[1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => [2,1,1,1,1] => [1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => [2,1,1,2] => [2,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => [2,1,2,1] => [1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4,6},{5}} => [2,1,2,1] => [1,2,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => [2,1,3] => [3,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => [2,2,1,1] => [1,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => [2,2,2] => [2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,5},{4},{6}} => [2,2,1,1] => [1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,6},{4},{5}} => [2,2,1,1] => [1,1,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => [2,3,1] => [1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => [2,3,1] => [1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => [2,2,2] => [2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}} => [2,3,1] => [1,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => [2,4] => [4,2]
[1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}} => [2,1,1,1,1] => [1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5,6}} => [2,1,1,2] => [2,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6}} => [2,1,2,1] => [1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6},{5}} => [2,1,2,1] => [1,2,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}} => [2,1,3] => [3,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => [1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6}} => [2,1,1,2] => [2,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => [1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => [1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0] => {{1,5,6},{2},{3},{4}} => [3,1,1,1] => [1,1,1,3]
[1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => [3,1,1,1] => [1,1,1,3]
[1,1,0,1,0,1,1,0,0,1,0,0] => {{1,6},{2},{3},{4,5}} => [2,1,1,2] => [2,1,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0] => {{1,4,6},{2},{3},{5}} => [3,1,1,1] => [1,1,1,3]
[1,1,0,1,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2},{3}} => [4,1,1] => [1,1,4]
[1,1,0,1,1,0,0,0,1,0,1,0] => {{1,3,4},{2},{5},{6}} => [3,1,1,1] => [1,1,1,3]
[1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => [3,1,2] => [2,1,3]
[1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => [2,1,2,1] => [1,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,0] => {{1,6},{2},{3,4},{5}} => [2,1,2,1] => [1,2,1,2]
[1,1,0,1,1,0,0,1,1,0,0,0] => {{1,5,6},{2},{3,4}} => [3,1,2] => [2,1,3]
[1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => [3,1,1,1] => [1,1,1,3]
[1,1,0,1,1,0,1,0,0,1,0,0] => {{1,6},{2},{3,5},{4}} => [2,1,2,1] => [1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,0,0] => {{1,3,6},{2},{4},{5}} => [3,1,1,1] => [1,1,1,3]
[1,1,0,1,1,0,1,1,0,0,0,0] => {{1,3,5,6},{2},{4}} => [4,1,1] => [1,1,4]
[1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => [4,1,1] => [1,1,4]
[1,1,0,1,1,1,0,0,0,1,0,0] => {{1,6},{2},{3,4,5}} => [2,1,3] => [3,1,2]
[1,1,0,1,1,1,0,0,1,0,0,0] => {{1,3,6},{2},{4,5}} => [3,1,2] => [2,1,3]
[1,1,0,1,1,1,0,1,0,0,0,0] => {{1,3,4,6},{2},{5}} => [4,1,1] => [1,1,4]
[1,1,0,1,1,1,1,0,0,0,0,0] => {{1,3,4,5,6},{2}} => [5,1] => [1,5]
[1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => [3,1,1,1] => [1,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => [3,1,2] => [2,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => [3,2,1] => [1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => [3,2,1] => [1,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => [3,3] => [3,3]
[1,1,1,0,0,1,0,0,1,0,1,0] => {{1,4},{2,3},{5},{6}} => [2,2,1,1] => [1,1,2,2]
[1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => [2,2,2] => [2,2,2]
[1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => [2,2,1,1] => [1,1,2,2]
[1,1,1,0,0,1,0,1,0,1,0,0] => {{1,6},{2,3},{4},{5}} => [2,2,1,1] => [1,1,2,2]
[1,1,1,0,0,1,0,1,1,0,0,0] => {{1,5,6},{2,3},{4}} => [3,2,1] => [1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => [3,2,1] => [1,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5}} => [2,2,2] => [2,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0] => {{1,4,6},{2,3},{5}} => [3,2,1] => [1,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2,3}} => [4,2] => [2,4]
[1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => [3,1,1,1] => [1,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => [3,1,2] => [2,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => [2,2,1,1] => [1,1,2,2]
[1,1,1,0,1,0,0,1,0,1,0,0] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => [1,1,2,2]
[1,1,1,0,1,0,0,1,1,0,0,0] => {{1,5,6},{2,4},{3}} => [3,2,1] => [1,2,3]
[1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => [3,1,1,1] => [1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => [1,1,2,2]
[1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2,6},{3},{4},{5}} => [3,1,1,1] => [1,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2,5,6},{3},{4}} => [4,1,1] => [1,1,4]
[1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => [4,1,1] => [1,1,4]
[1,1,1,0,1,1,0,0,0,1,0,0] => {{1,6},{2,4,5},{3}} => [2,3,1] => [1,3,2]
[1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2,6},{3},{4,5}} => [3,1,2] => [2,1,3]
[1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2,4,6},{3},{5}} => [4,1,1] => [1,1,4]
[1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2,4,5,6},{3}} => [5,1] => [1,5]
[1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => [4,1,1] => [1,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => [4,2] => [2,4]
[1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => [2,3,1] => [1,3,2]
[1,1,1,1,0,0,0,1,0,1,0,0] => {{1,6},{2,3,4},{5}} => [2,3,1] => [1,3,2]
[1,1,1,1,0,0,0,1,1,0,0,0] => {{1,5,6},{2,3,4}} => [3,3] => [3,3]
[1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => [3,2,1] => [1,2,3]
[1,1,1,1,0,0,1,0,0,1,0,0] => {{1,6},{2,5},{3,4}} => [2,2,2] => [2,2,2]
[1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2,6},{3,4},{5}} => [3,2,1] => [1,2,3]
[1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2,5,6},{3,4}} => [4,2] => [2,4]
[1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => [4,1,1] => [1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0] => {{1,6},{2,3,5},{4}} => [2,3,1] => [1,3,2]
[1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2,6},{3,5},{4}} => [3,2,1] => [1,2,3]
[1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2,3,6},{4},{5}} => [4,1,1] => [1,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2,3,5,6},{4}} => [5,1] => [1,5]
[1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => [5,1] => [1,5]
[1,1,1,1,1,0,0,0,0,1,0,0] => {{1,6},{2,3,4,5}} => [2,4] => [4,2]
[1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2,6},{3,4,5}} => [3,3] => [3,3]
[1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2,3,6},{4,5}} => [4,2] => [2,4]
[1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2,3,4,6},{5}} => [5,1] => [1,5]
[1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4,5,6}} => [6] => [6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => [1,1,1,1,1,2] => [2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => [1,1,1,1,2,1] => [1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,7},{6}} => [1,1,1,1,2,1] => [1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => [1,1,1,1,3] => [3,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => [1,1,1,2,1,1] => [1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => [1,1,1,2,2] => [2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4,6},{5},{7}} => [1,1,1,2,1,1] => [1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4,7},{5},{6}} => [1,1,1,2,1,1] => [1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4,6,7},{5}} => [1,1,1,3,1] => [1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => [1,1,1,3,1] => [1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4,7},{5,6}} => [1,1,1,2,2] => [2,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4,5,7},{6}} => [1,1,1,3,1] => [1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => [1,1,1,4] => [4,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => [1,1,2,1,1,1] => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => [1,1,2,1,2] => [2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => [1,1,2,2,1] => [1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5,7},{6}} => [1,1,2,2,1] => [1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => [1,1,2,3] => [3,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7}} => [1,1,2,1,1,1] => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,5},{4},{6,7}} => [1,1,2,1,2] => [2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,6},{4},{5},{7}} => [1,1,2,1,1,1] => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,7},{4},{5},{6}} => [1,1,2,1,1,1] => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4},{5}} => [1,1,3,1,1] => [1,1,3,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,5,6},{4},{7}} => [1,1,3,1,1] => [1,1,3,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,7},{4},{5,6}} => [1,1,2,1,2] => [2,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,5,7},{4},{6}} => [1,1,3,1,1] => [1,1,3,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,5,6,7},{4}} => [1,1,4,1] => [1,4,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => [1,1,3,1,1] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => [1,1,3,2] => [2,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,6},{4,5},{7}} => [1,1,2,2,1] => [1,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,7},{4,5},{6}} => [1,1,2,2,1] => [1,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4,5}} => [1,1,3,2] => [2,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,6},{5},{7}} => [1,1,3,1,1] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,7},{4,6},{5}} => [1,1,2,2,1] => [1,2,2,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,7},{5},{6}} => [1,1,3,1,1] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,6,7},{5}} => [1,1,4,1] => [1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => [1,1,4,1] => [1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,7},{4,5,6}} => [1,1,2,3] => [3,2,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,7},{5,6}} => [1,1,3,2] => [2,3,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,7},{6}} => [1,1,4,1] => [1,4,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => [1,1,5] => [5,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => [1,2,1,1,1,1] => [1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => [1,2,1,1,2] => [2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => [1,2,1,2,1] => [1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5,7},{6}} => [1,2,1,2,1] => [1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => [1,2,1,3] => [3,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => [1,2,2,1,1] => [1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => [1,2,2,2] => [2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4,6},{5},{7}} => [1,2,2,1,1] => [1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4,7},{5},{6}} => [1,2,2,1,1] => [1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4,6,7},{5}} => [1,2,3,1] => [1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => [1,2,3,1] => [1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4,7},{5,6}} => [1,2,2,2] => [2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4,5,7},{6}} => [1,2,3,1] => [1,3,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => [1,2,4] => [4,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7}} => [1,2,1,1,1,1] => [1,1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6,7}} => [1,2,1,1,2] => [2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5,6},{7}} => [1,2,1,2,1] => [1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5,7},{6}} => [1,2,1,2,1] => [1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5,6,7}} => [1,2,1,3] => [3,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7}} => [1,2,1,1,1,1] => [1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,5},{3},{4},{6,7}} => [1,2,1,1,2] => [2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,6},{3},{4},{5},{7}} => [1,2,1,1,1,1] => [1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => [1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4},{5}} => [1,3,1,1,1] => [1,1,1,3,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3},{4},{7}} => [1,3,1,1,1] => [1,1,1,3,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,7},{3},{4},{5,6}} => [1,2,1,1,2] => [2,1,1,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3},{4},{6}} => [1,3,1,1,1] => [1,1,1,3,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3},{4}} => [1,4,1,1] => [1,1,4,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7}} => [1,3,1,1,1] => [1,1,1,3,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,4,5},{3},{6,7}} => [1,3,1,2] => [2,1,3,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,6},{3},{4,5},{7}} => [1,2,1,2,1] => [1,2,1,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,7},{3},{4,5},{6}} => [1,2,1,2,1] => [1,2,1,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4,5}} => [1,3,1,2] => [2,1,3,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,4,6},{3},{5},{7}} => [1,3,1,1,1] => [1,1,1,3,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => [1,2,1,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,4,7},{3},{5},{6}} => [1,3,1,1,1] => [1,1,1,3,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,4,6,7},{3},{5}} => [1,4,1,1] => [1,1,4,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,4,5,6},{3},{7}} => [1,4,1,1] => [1,1,4,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,7},{3},{4,5,6}} => [1,2,1,3] => [3,1,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,4,7},{3},{5,6}} => [1,3,1,2] => [2,1,3,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,4,5,7},{3},{6}} => [1,4,1,1] => [1,1,4,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,4,5,6,7},{3}} => [1,5,1] => [1,5,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => [1,3,1,1,1] => [1,1,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => [1,3,1,2] => [2,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => [1,3,2,1] => [1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4},{5,7},{6}} => [1,3,2,1] => [1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => [1,3,3] => [3,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7}} => [1,2,2,1,1] => [1,1,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,5},{3,4},{6,7}} => [1,2,2,2] => [2,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,6},{3,4},{5},{7}} => [1,2,2,1,1] => [1,1,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2,7},{3,4},{5},{6}} => [1,2,2,1,1] => [1,1,2,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3,4},{5}} => [1,3,2,1] => [1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3,4},{7}} => [1,3,2,1] => [1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,7},{3,4},{5,6}} => [1,2,2,2] => [2,2,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3,4},{6}} => [1,3,2,1] => [1,2,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3,4}} => [1,4,2] => [2,4,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7}} => [1,3,1,1,1] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,5},{4},{6,7}} => [1,3,1,2] => [2,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,6},{3,5},{4},{7}} => [1,2,2,1,1] => [1,1,2,2,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => [1,1,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,5},{4}} => [1,3,2,1] => [1,2,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,6},{4},{5},{7}} => [1,3,1,1,1] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => [1,1,2,2,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,7},{4},{5},{6}} => [1,3,1,1,1] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4},{5}} => [1,4,1,1] => [1,1,4,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,5,6},{4},{7}} => [1,4,1,1] => [1,1,4,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,7},{3,5,6},{4}} => [1,2,3,1] => [1,3,2,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,7},{4},{5,6}} => [1,3,1,2] => [2,1,3,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,5,7},{4},{6}} => [1,4,1,1] => [1,1,4,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,5,6,7},{4}} => [1,5,1] => [1,5,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => [1,4,1,1] => [1,1,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => [1,4,2] => [2,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,6},{3,4,5},{7}} => [1,2,3,1] => [1,3,2,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,7},{3,4,5},{6}} => [1,2,3,1] => [1,3,2,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,4,5}} => [1,3,3] => [3,3,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,6},{4,5},{7}} => [1,3,2,1] => [1,2,3,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4,5}} => [1,2,2,2] => [2,2,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,7},{4,5},{6}} => [1,3,2,1] => [1,2,3,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4,5}} => [1,4,2] => [2,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,6},{5},{7}} => [1,4,1,1] => [1,1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,7},{3,4,6},{5}} => [1,2,3,1] => [1,3,2,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,7},{4,6},{5}} => [1,3,2,1] => [1,2,3,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,7},{5},{6}} => [1,4,1,1] => [1,1,4,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,6,7},{5}} => [1,5,1] => [1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => [1,5,1] => [1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,7},{3,4,5,6}} => [1,2,4] => [4,2,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,7},{4,5,6}} => [1,3,3] => [3,3,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,7},{5,6}} => [1,4,2] => [2,4,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,7},{6}} => [1,5,1] => [1,5,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => [1,6] => [6,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => [2,1,1,1,2] => [2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => [2,1,1,2,1] => [1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5,7},{6}} => [2,1,1,2,1] => [1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => [2,1,1,3] => [3,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => [2,1,2,1,1] => [1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => [2,1,2,2] => [2,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4,6},{5},{7}} => [2,1,2,1,1] => [1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4,7},{5},{6}} => [2,1,2,1,1] => [1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4,6,7},{5}} => [2,1,3,1] => [1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => [2,1,3,1] => [1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4,7},{5,6}} => [2,1,2,2] => [2,2,1,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4,5,7},{6}} => [2,1,3,1] => [1,3,1,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => [2,1,4] => [4,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => [2,2,1,1,1] => [1,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => [2,2,1,2] => [2,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => [2,2,2,1] => [1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,4},{5,7},{6}} => [2,2,2,1] => [1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => [2,2,3] => [3,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7}} => [2,2,1,1,1] => [1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2},{3,5},{4},{6,7}} => [2,2,1,2] => [2,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,2},{3,6},{4},{5},{7}} => [2,2,1,1,1] => [1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => [1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,2},{3,6,7},{4},{5}} => [2,3,1,1] => [1,1,3,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3,5,6},{4},{7}} => [2,3,1,1] => [1,1,3,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3,7},{4},{5,6}} => [2,2,1,2] => [2,1,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2},{3,5,7},{4},{6}} => [2,3,1,1] => [1,1,3,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3,5,6,7},{4}} => [2,4,1] => [1,4,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => [2,3,1,1] => [1,1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => [2,3,2] => [2,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3,6},{4,5},{7}} => [2,2,2,1] => [1,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3,7},{4,5},{6}} => [2,2,2,1] => [1,2,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3,6,7},{4,5}} => [2,3,2] => [2,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3,4,6},{5},{7}} => [2,3,1,1] => [1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3,7},{4,6},{5}} => [2,2,2,1] => [1,2,2,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3,4,7},{5},{6}} => [2,3,1,1] => [1,1,3,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2},{3,4,6,7},{5}} => [2,4,1] => [1,4,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => [2,4,1] => [1,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2},{3,7},{4,5,6}} => [2,2,3] => [3,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3,4,7},{5,6}} => [2,3,2] => [2,3,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3,4,5,7},{6}} => [2,4,1] => [1,4,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => [2,5] => [5,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6,7}} => [2,1,1,1,2] => [2,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5,6},{7}} => [2,1,1,2,1] => [1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5,7},{6}} => [2,1,1,2,1] => [1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5,6,7}} => [2,1,1,3] => [3,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,3},{2},{4,5},{6},{7}} => [2,1,2,1,1] => [1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4,5},{6,7}} => [2,1,2,2] => [2,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4,6},{5},{7}} => [2,1,2,1,1] => [1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4,7},{5},{6}} => [2,1,2,1,1] => [1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4,6,7},{5}} => [2,1,3,1] => [1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4,5,6},{7}} => [2,1,3,1] => [1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4,7},{5,6}} => [2,1,2,2] => [2,2,1,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,3},{2},{4,5,7},{6}} => [2,1,3,1] => [1,3,1,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4,5,6,7}} => [2,1,4] => [4,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [1,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2},{3},{5},{6,7}} => [2,1,1,1,2] => [2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5,6},{7}} => [2,1,1,2,1] => [1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5,7},{6}} => [2,1,1,2,1] => [1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5,6,7}} => [2,1,1,3] => [3,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => [2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => [2,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => [1,1,1,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2},{3},{6,7}} => [3,1,1,2] => [2,1,1,3]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2},{3},{4,5},{7}} => [2,1,1,2,1] => [1,2,1,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => [1,2,1,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => [2,1,1,3]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => [1,2,1,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => [1,1,1,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => [1,1,1,4]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => [3,1,1,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => [2,1,1,3]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => [1,1,1,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2},{3}} => [5,1,1] => [1,1,5]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6,7}} => [3,1,1,2] => [2,1,1,3]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,3,4},{2},{5,6},{7}} => [3,1,2,1] => [1,2,1,3]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,3,4},{2},{5,7},{6}} => [3,1,2,1] => [1,2,1,3]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,3,4},{2},{5,6,7}} => [3,1,3] => [3,1,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7}} => [2,1,2,1,1] => [1,1,2,1,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2},{3,4},{6,7}} => [2,1,2,2] => [2,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2},{3,4},{5},{7}} => [2,1,2,1,1] => [1,1,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => [1,1,2,1,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3,4},{5}} => [3,1,2,1] => [1,2,1,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3,4},{7}} => [3,1,2,1] => [1,2,1,3]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2},{3,4},{5,6}} => [2,1,2,2] => [2,2,1,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3,4},{6}} => [3,1,2,1] => [1,2,1,3]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3,4}} => [4,1,2] => [2,1,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,3,5},{2},{4},{6,7}} => [3,1,1,2] => [2,1,1,3]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => [1,1,2,1,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => [1,1,2,1,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => [1,2,1,3]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => [1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => [1,1,1,4]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => [1,1,1,4]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => [1,3,1,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,3,7},{2},{4},{5,6}} => [3,1,1,2] => [2,1,1,3]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => [1,1,1,4]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,3,5,6,7},{2},{4}} => [5,1,1] => [1,1,5]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7}} => [4,1,1,1] => [1,1,1,4]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,3,4,5},{2},{6,7}} => [4,1,2] => [2,1,4]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2},{3,4,5},{7}} => [2,1,3,1] => [1,3,1,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2},{3,4,5},{6}} => [2,1,3,1] => [1,3,1,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,4,5}} => [3,1,3] => [3,1,3]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,3,6},{2},{4,5},{7}} => [3,1,2,1] => [1,2,1,3]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => [2,2,1,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,3,7},{2},{4,5},{6}} => [3,1,2,1] => [1,2,1,3]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4,5}} => [4,1,2] => [2,1,4]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => [1,1,1,4]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => [1,3,1,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => [1,2,1,3]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => [1,1,1,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,3,4,6,7},{2},{5}} => [5,1,1] => [1,1,5]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,3,4,5,6},{2},{7}} => [5,1,1] => [1,1,5]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2},{3,4,5,6}} => [2,1,4] => [4,1,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,3,7},{2},{4,5,6}} => [3,1,3] => [3,1,3]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,3,4,7},{2},{5,6}} => [4,1,2] => [2,1,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,3,4,5,7},{2},{6}} => [5,1,1] => [1,1,5]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,3,4,5,6,7},{2}} => [6,1] => [1,6]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => [3,1,1,2] => [2,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => [3,1,2,1] => [1,2,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5,7},{6}} => [3,1,2,1] => [1,2,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => [3,1,3] => [3,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => [3,2,2] => [2,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4,6},{5},{7}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3},{4,7},{5},{6}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3},{4,6,7},{5}} => [3,3,1] => [1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => [3,3,1] => [1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4,7},{5,6}} => [3,2,2] => [2,2,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4,5,7},{6}} => [3,3,1] => [1,3,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => [3,4] => [4,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7}} => [2,2,1,1,1] => [1,1,1,2,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6,7}} => [2,2,1,2] => [2,1,2,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2,3},{5,6},{7}} => [2,2,2,1] => [1,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2,3},{5,7},{6}} => [2,2,2,1] => [1,2,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2,3},{5,6,7}} => [2,2,3] => [3,2,2]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7}} => [2,2,1,1,1] => [1,1,1,2,2]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2,3},{4},{6,7}} => [2,2,1,2] => [2,1,2,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => [1,1,1,2,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => [1,1,1,2,2]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3},{4},{7}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2,3},{4},{5,6}} => [2,2,1,2] => [2,1,2,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3},{4}} => [4,2,1] => [1,2,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2,3},{6},{7}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2,3},{6,7}} => [3,2,2] => [2,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2,3},{4,5},{7}} => [2,2,2,1] => [1,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => [1,2,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2,3},{4,5}} => [3,2,2] => [2,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2,3},{5},{7}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => [1,2,2,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2,3},{5}} => [4,2,1] => [1,2,4]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2,3},{7}} => [4,2,1] => [1,2,4]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2,3},{4,5,6}} => [2,2,3] => [3,2,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2,3},{5,6}} => [3,2,2] => [2,2,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2,3},{6}} => [4,2,1] => [1,2,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2,3}} => [5,2] => [2,5]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,4},{3},{5},{6,7}} => [3,1,1,2] => [2,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,4},{3},{5,6},{7}} => [3,1,2,1] => [1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,4},{3},{5,7},{6}} => [3,1,2,1] => [1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,4},{3},{5,6,7}} => [3,1,3] => [3,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => [1,1,1,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2,4},{3},{6,7}} => [2,2,1,2] => [2,1,2,2]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => [1,1,1,2,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => [1,1,1,2,2]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => [2,1,2,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,4},{3}} => [4,2,1] => [1,2,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3},{4},{6,7}} => [3,1,1,2] => [2,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => [1,1,1,2,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => [1,1,1,2,2]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => [1,1,1,2,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => [1,1,1,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => [1,1,1,4]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => [1,1,3,2]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3},{4},{5,6}} => [3,1,1,2] => [2,1,1,3]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => [1,1,1,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3},{4}} => [5,1,1] => [1,1,5]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7}} => [4,1,1,1] => [1,1,1,4]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,4,5},{3},{6,7}} => [4,1,2] => [2,1,4]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2,4,5},{3},{7}} => [2,3,1,1] => [1,1,3,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => [1,1,3,2]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,4,5},{3}} => [3,3,1] => [1,3,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3},{4,5},{7}} => [3,1,2,1] => [1,2,1,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => [2,1,2,2]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3},{4,5},{6}} => [3,1,2,1] => [1,2,1,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4,5}} => [4,1,2] => [2,1,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => [1,1,1,4]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => [1,1,3,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => [1,2,1,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => [1,1,1,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,4,6,7},{3},{5}} => [5,1,1] => [1,1,5]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,4,5,6},{3},{7}} => [5,1,1] => [1,1,5]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2,4,5,6},{3}} => [2,4,1] => [1,4,2]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3},{4,5,6}} => [3,1,3] => [3,1,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,2,4,7},{3},{5,6}} => [4,1,2] => [2,1,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,4,5,7},{3},{6}} => [5,1,1] => [1,1,5]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,4,5,6,7},{3}} => [6,1] => [1,6]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => [4,1,1,1] => [1,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => [4,1,2] => [2,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => [4,2,1] => [1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4},{5,7},{6}} => [4,2,1] => [1,2,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => [4,3] => [3,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7}} => [2,3,1,1] => [1,1,3,2]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,5},{2,3,4},{6,7}} => [2,3,2] => [2,3,2]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,6},{2,3,4},{5},{7}} => [2,3,1,1] => [1,1,3,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,7},{2,3,4},{5},{6}} => [2,3,1,1] => [1,1,3,2]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3,4},{5}} => [3,3,1] => [1,3,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3,4},{7}} => [3,3,1] => [1,3,3]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,7},{2,3,4},{5,6}} => [2,3,2] => [2,3,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3,4},{6}} => [3,3,1] => [1,3,3]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3,4}} => [4,3] => [3,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3,4},{6,7}} => [3,2,2] => [2,2,3]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => [1,2,2,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => [1,2,2,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3,4}} => [3,2,2] => [2,2,3]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3,4},{5},{7}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => [1,2,2,2]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4},{5}} => [4,2,1] => [1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => [4,2,1] => [1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3,4}} => [2,3,2] => [2,3,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3,4},{5,6}} => [3,2,2] => [2,2,3]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3,4},{6}} => [4,2,1] => [1,2,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3,4}} => [5,2] => [2,5]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7}} => [4,1,1,1] => [1,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,5},{4},{6,7}} => [4,1,2] => [2,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,6},{2,3,5},{4},{7}} => [2,3,1,1] => [1,1,3,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => [1,1,3,2]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,5},{4}} => [3,3,1] => [1,3,3]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => [1,2,2,2]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,5},{4}} => [4,2,1] => [1,2,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => [1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => [1,1,3,2]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => [1,1,2,3]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => [1,1,1,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4},{5}} => [5,1,1] => [1,1,5]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => [5,1,1] => [1,1,5]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,7},{2,3,5,6},{4}} => [2,4,1] => [1,4,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3,5,6},{4}} => [3,3,1] => [1,3,3]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4},{5,6}} => [4,1,2] => [2,1,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,5,7},{4},{6}} => [5,1,1] => [1,1,5]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,5,6,7},{4}} => [6,1] => [1,6]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => [5,1,1] => [1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => [5,2] => [2,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => [2,4,1] => [1,4,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,7},{2,3,4,5},{6}} => [2,4,1] => [1,4,2]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,4,5}} => [3,4] => [4,3]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => [3,3,1] => [1,3,3]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4,5}} => [2,2,3] => [3,2,2]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,7},{3,4,5},{6}} => [3,3,1] => [1,3,3]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4,5}} => [4,3] => [3,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => [4,2,1] => [1,2,4]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4,5}} => [2,3,2] => [2,3,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4,5}} => [3,2,2] => [2,2,3]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4,5},{6}} => [4,2,1] => [1,2,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4,5}} => [5,2] => [2,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => [5,1,1] => [1,1,5]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,7},{2,3,4,6},{5}} => [2,4,1] => [1,4,2]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,7},{3,4,6},{5}} => [3,3,1] => [1,3,3]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4,6},{5}} => [4,2,1] => [1,2,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5},{6}} => [5,1,1] => [1,1,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,6,7},{5}} => [6,1] => [1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => [6,1] => [1,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,7},{2,3,4,5,6}} => [2,5] => [5,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,7},{3,4,5,6}} => [3,4] => [4,3]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,7},{4,5,6}} => [4,3] => [3,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5,6}} => [5,2] => [2,5]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,7},{6}} => [6,1] => [1,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7}} => [7] => [7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8}} => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,8}} => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6,8},{7}} => [1,1,1,1,1,2,1] => [1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8}} => [1,1,1,1,1,3] => [3,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5,6},{7},{8}} => [1,1,1,1,2,1,1] => [1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6},{7,8}} => [1,1,1,1,2,2] => [2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5,7},{6},{8}} => [1,1,1,1,2,1,1] => [1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,8},{6},{7}} => [1,1,1,1,2,1,1] => [1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5,7,8},{6}} => [1,1,1,1,3,1] => [1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,7},{8}} => [1,1,1,1,3,1] => [1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4},{5,8},{6,7}} => [1,1,1,1,2,2] => [2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4},{5,6,8},{7}} => [1,1,1,1,3,1] => [1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8}} => [1,1,1,1,4] => [4,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5},{6},{7,8}} => [1,1,1,2,1,2] => [2,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,8},{5},{6},{7}} => [1,1,1,2,1,1,1] => [1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3},{4,6,7,8},{5}} => [1,1,1,4,1] => [1,4,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3},{4,8},{5,6},{7}} => [1,1,1,2,2,1] => [1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3},{4,7,8},{5,6}} => [1,1,1,3,2] => [2,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3},{4,8},{5,7},{6}} => [1,1,1,2,2,1] => [1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3},{4,8},{5,6,7}} => [1,1,1,2,3] => [3,2,1,1,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8}} => [1,1,1,5] => [5,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6},{7,8}} => [1,1,2,1,1,2] => [2,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5},{6,8},{7}} => [1,1,2,1,2,1] => [1,2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5,6},{7},{8}} => [1,1,2,2,1,1] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,4},{5,8},{6},{7}} => [1,1,2,2,1,1] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,4},{5,8},{6,7}} => [1,1,2,2,2] => [2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4},{5,6,7,8}} => [1,1,2,4] => [4,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,5},{4},{6,7,8}} => [1,1,2,1,3] => [3,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,8},{4},{5},{6},{7}} => [1,1,2,1,1,1,1] => [1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4},{5},{6}} => [1,1,3,1,1,1] => [1,1,1,3,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4},{5,6}} => [1,1,3,1,2] => [2,1,3,1,1]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,5,7,8},{4},{6}} => [1,1,4,1,1] => [1,1,4,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4},{5,6,7}} => [1,1,2,1,3] => [3,1,2,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,5,8},{4},{6,7}} => [1,1,3,1,2] => [2,1,3,1,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,5,6,7,8},{4}} => [1,1,5,1] => [1,5,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7},{8}} => [1,1,3,1,1,1] => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2},{3,4,5},{6,7,8}} => [1,1,3,3] => [3,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2},{3,8},{4,5},{6},{7}} => [1,1,2,2,1,1] => [1,1,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2},{3,6,7,8},{4,5}} => [1,1,4,2] => [2,4,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4,6},{5},{7}} => [1,1,2,2,1,1] => [1,1,2,2,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,6},{5}} => [1,1,3,2,1] => [1,2,3,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4,7},{5},{6}} => [1,1,2,2,1,1] => [1,1,2,2,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4,6,7},{5}} => [1,1,2,3,1] => [1,3,2,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => [1,1,4,2] => [2,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4,5,6},{7}} => [1,1,2,3,1] => [1,3,2,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,5,6}} => [1,1,3,3] => [3,3,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4,7},{5,6}} => [1,1,2,2,2] => [2,2,2,1,1]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2},{3,4,7,8},{5,6}} => [1,1,4,2] => [2,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,8},{6},{7}} => [1,1,4,1,1] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7},{8}} => [1,1,5,1] => [1,5,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2},{3,8},{4,5,6,7}} => [1,1,2,4] => [4,2,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2},{3,4,8},{5,6,7}} => [1,1,3,3] => [3,3,1,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2},{3,4,5,8},{6,7}} => [1,1,4,2] => [2,4,1,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,8},{7}} => [1,1,5,1] => [1,5,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => [1,1,6] => [6,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7,8}} => [1,2,1,1,1,2] => [2,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5},{6,7},{8}} => [1,2,1,1,2,1] => [1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5},{6,8},{7}} => [1,2,1,1,2,1] => [1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4},{5,8},{6,7}} => [1,2,1,2,2] => [2,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4},{5,6,7,8}} => [1,2,1,4] => [4,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => [1,2,2,2,1] => [1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,5},{6,8},{7}} => [1,2,2,2,1] => [1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => [1,2,2,3] => [3,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,3},{4,6,7},{5},{8}} => [1,2,3,1,1] => [1,1,3,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,3},{4,6,8},{5},{7}} => [1,2,3,1,1] => [1,1,3,2,1]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,3},{4,6,7,8},{5}} => [1,2,4,1] => [1,4,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => [1,2,3,2] => [2,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,3},{4,7},{5,6},{8}} => [1,2,2,2,1] => [1,2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,3},{4,8},{5,6},{7}} => [1,2,2,2,1] => [1,2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,3},{4,7,8},{5,6}} => [1,2,3,2] => [2,3,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,3},{4,8},{5,7},{6}} => [1,2,2,2,1] => [1,2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3},{4,5,8},{6},{7}} => [1,2,3,1,1] => [1,1,3,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,3},{4,8},{5,6,7}} => [1,2,2,3] => [3,2,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3},{4,5,8},{6,7}} => [1,2,3,2] => [2,3,2,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3},{4,5,6,8},{7}} => [1,2,4,1] => [1,4,2,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => [1,2,5] => [5,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6},{7,8}} => [1,2,1,1,1,2] => [2,1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5},{6,8},{7}} => [1,2,1,1,2,1] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5},{6,7,8}} => [1,2,1,1,3] => [3,1,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6},{7,8}} => [1,2,1,2,2] => [2,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5,7},{6},{8}} => [1,2,1,2,1,1] => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,4},{3},{5,7,8},{6}} => [1,2,1,3,1] => [1,3,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,4},{3},{5,8},{6,7}} => [1,2,1,2,2] => [2,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,4},{3},{5,6,7,8}} => [1,2,1,4] => [4,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,5},{3},{4},{6,8},{7}} => [1,2,1,1,2,1] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,8},{3},{4},{5},{6},{7}} => [1,2,1,1,1,1,1] => [1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4},{5},{6}} => [1,3,1,1,1,1] => [1,1,1,1,3,1]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,5,8},{3},{4},{6},{7}} => [1,3,1,1,1,1] => [1,1,1,1,3,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4},{5,6,7}} => [1,2,1,1,3] => [3,1,1,2,1]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,5,6,8},{3},{4},{7}} => [1,4,1,1,1] => [1,1,1,4,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,5,6,7,8},{3},{4}} => [1,5,1,1] => [1,1,5,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,4,5},{3},{6,7},{8}} => [1,3,1,2,1] => [1,2,1,3,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,4,5},{3},{6,8},{7}} => [1,3,1,2,1] => [1,2,1,3,1]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,4,5},{3},{6,7,8}} => [1,3,1,3] => [3,1,3,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3},{4,5},{7,8}} => [1,2,1,2,2] => [2,2,1,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3},{4,5},{7}} => [1,3,1,2,1] => [1,2,1,3,1]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3},{4,5}} => [1,4,1,2] => [2,1,4,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,4,6},{3},{5},{7,8}} => [1,3,1,1,2] => [2,1,1,3,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,4,6,7},{3},{5},{8}} => [1,4,1,1,1] => [1,1,1,4,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4,6,7},{5}} => [1,2,1,3,1] => [1,3,1,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5},{6,7}} => [1,3,1,1,2] => [2,1,1,3,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,4,6,8},{3},{5},{7}} => [1,4,1,1,1] => [1,1,1,4,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,4,6,7,8},{3},{5}} => [1,5,1,1] => [1,1,5,1]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4,5,6}} => [1,3,1,3] => [3,1,3,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,4,7},{3},{5,6},{8}} => [1,3,1,2,1] => [1,2,1,3,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3},{4,7},{5,6}} => [1,2,1,2,2] => [2,2,1,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,4,8},{3},{5,6},{7}} => [1,3,1,2,1] => [1,2,1,3,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,4,7,8},{3},{5,6}} => [1,4,1,2] => [2,1,4,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5,7},{6}} => [1,3,1,2,1] => [1,2,1,3,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,4,5,7,8},{3},{6}} => [1,5,1,1] => [1,1,5,1]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5,6,7}} => [1,3,1,3] => [3,1,3,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,4,5,8},{3},{6,7}} => [1,4,1,2] => [2,1,4,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,4,5,6,8},{3},{7}} => [1,5,1,1] => [1,1,5,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8},{3}} => [1,6,1] => [1,6,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8}} => [1,3,1,1,1,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3,4},{5},{6,8},{7}} => [1,3,1,2,1] => [1,2,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}} => [1,3,1,3] => [3,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => [1,3,2,2] => [2,2,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5,6,7},{8}} => [1,3,3,1] => [1,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3,4},{5,8},{6,7}} => [1,3,2,2] => [2,2,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3,4},{5,6,8},{7}} => [1,3,3,1] => [1,3,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1},{2,5},{3,4},{6,7},{8}} => [1,2,2,2,1] => [1,2,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1},{2,5},{3,4},{6,8},{7}} => [1,2,2,2,1] => [1,2,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1},{2,5},{3,4},{6,7,8}} => [1,2,2,3] => [3,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,4},{5},{6},{7}} => [1,2,2,1,1,1] => [1,1,1,2,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,4},{5},{8}} => [1,3,2,1,1] => [1,1,2,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,4},{5},{7}} => [1,3,2,1,1] => [1,1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,4},{5,6},{8}} => [1,2,2,2,1] => [1,2,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,4},{5,6},{7}} => [1,2,2,2,1] => [1,2,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4},{5,6}} => [1,3,2,2] => [2,2,3,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,4},{5,7},{6}} => [1,2,2,2,1] => [1,2,2,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,4},{5,6,7}} => [1,2,2,3] => [3,2,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1},{2,5,8},{3,4},{6,7}} => [1,3,2,2] => [2,2,3,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1},{2,5,6,7,8},{3,4}} => [1,5,2] => [2,5,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7},{8}} => [1,3,1,1,1,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,5},{4},{6,7,8}} => [1,3,1,3] => [3,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3,5},{4},{7,8}} => [1,2,2,1,2] => [2,1,2,2,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1},{2,7},{3,5},{4},{6},{8}} => [1,2,2,1,1,1] => [1,1,1,2,2,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,5},{4},{6},{7}} => [1,2,2,1,1,1] => [1,1,1,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,5},{4},{8}} => [1,3,2,1,1] => [1,1,2,3,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,5},{4},{6,7}} => [1,2,2,1,2] => [2,1,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,5},{4},{7}} => [1,3,2,1,1] => [1,1,2,3,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,5},{4}} => [1,4,2,1] => [1,2,4,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,6},{4},{5},{7},{8}} => [1,3,1,1,1,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,7},{4},{5},{6},{8}} => [1,3,1,1,1,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4},{5},{6}} => [1,2,2,1,1,1] => [1,1,1,2,2,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,8},{4},{5},{6},{7}} => [1,3,1,1,1,1] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4},{5},{6}} => [1,4,1,1,1] => [1,1,1,4,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,6,7},{4},{5},{8}} => [1,4,1,1,1] => [1,1,1,4,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,6,8},{4},{5},{7}} => [1,4,1,1,1] => [1,1,1,4,1]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,6,7,8},{4},{5}} => [1,5,1,1] => [1,1,5,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1},{2,7},{3,5,6},{4},{8}} => [1,2,3,1,1] => [1,1,3,2,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,5,6},{4},{7}} => [1,2,3,1,1] => [1,1,3,2,1]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,5,6},{4}} => [1,3,3,1] => [1,3,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,7},{4},{5,6},{8}} => [1,3,1,2,1] => [1,2,1,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4},{5,6}} => [1,2,2,1,2] => [2,1,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,5,7},{4},{6},{8}} => [1,4,1,1,1] => [1,1,1,4,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,5,7},{4},{6}} => [1,2,3,1,1] => [1,1,3,2,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,5,8},{4},{6},{7}} => [1,4,1,1,1] => [1,1,1,4,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,5,7,8},{4},{6}} => [1,5,1,1] => [1,1,5,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,5,6,7},{4},{8}} => [1,5,1,1] => [1,1,5,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,5,6,7},{4}} => [1,2,4,1] => [1,4,2,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4},{5,6,7}} => [1,3,1,3] => [3,1,3,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,5,8},{4},{6,7}} => [1,4,1,2] => [2,1,4,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,5,6,8},{4},{7}} => [1,5,1,1] => [1,1,5,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,5,6,7,8},{4}} => [1,6,1] => [1,6,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,4,5},{6},{7}} => [1,2,3,1,1] => [1,1,3,2,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,4,5},{6,7}} => [1,2,3,2] => [2,3,2,1]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,4,5},{7}} => [1,3,3,1] => [1,3,3,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,4,5}} => [1,4,3] => [3,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1},{2,3,6},{4,5},{7,8}} => [1,3,2,2] => [2,2,3,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,6},{4,5},{8}} => [1,2,2,2,1] => [1,2,2,2,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,6},{4,5},{7}} => [1,2,2,2,1] => [1,2,2,2,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,6},{4,5}} => [1,3,2,2] => [2,2,3,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,5},{6}} => [1,2,2,2,1] => [1,2,2,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,5},{6},{7}} => [1,3,2,1,1] => [1,1,2,3,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1},{2,3,6,7},{4,5},{8}} => [1,4,2,1] => [1,2,4,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,6,7},{4,5}} => [1,2,3,2] => [2,3,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,5},{6,7}} => [1,3,2,2] => [2,2,3,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,3,6,8},{4,5},{7}} => [1,4,2,1] => [1,2,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,6},{5},{7,8}} => [1,4,1,2] => [2,1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,4,6},{5},{7}} => [1,2,3,1,1] => [1,1,3,2,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4,6},{5}} => [1,3,3,1] => [1,3,3,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,6},{5}} => [1,2,2,2,1] => [1,2,2,2,1]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,6},{5},{7}} => [1,3,2,1,1] => [1,1,2,3,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4,6},{5}} => [1,4,2,1] => [1,2,4,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,4,7},{5},{6}} => [1,2,3,1,1] => [1,1,3,2,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,8},{5},{6},{7}} => [1,4,1,1,1] => [1,1,1,4,1]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,7,8},{5},{6}} => [1,5,1,1] => [1,1,5,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,6,7},{5}} => [1,2,4,1] => [1,4,2,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,6,7},{5}} => [1,3,3,1] => [1,3,3,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,6,8},{5},{7}} => [1,5,1,1] => [1,1,5,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,6,7,8},{5}} => [1,6,1] => [1,6,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6},{7},{8}} => [1,5,1,1] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => [1,5,2] => [2,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,4,5,6},{7}} => [1,2,4,1] => [1,4,2,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,5,6}} => [1,2,2,3] => [3,2,2,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,5,6},{7}} => [1,3,3,1] => [1,3,3,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,4,7},{5,6}} => [1,2,3,2] => [2,3,2,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,7},{5,6}} => [1,3,2,2] => [2,2,3,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6},{7}} => [1,4,2,1] => [1,2,4,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,7},{6},{8}} => [1,5,1,1] => [1,1,5,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,5,7},{6}} => [1,2,4,1] => [1,4,2,1]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,5,7},{6}} => [1,3,3,1] => [1,3,3,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,7},{6}} => [1,4,2,1] => [1,2,4,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6},{7}} => [1,5,1,1] => [1,1,5,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,7,8},{6}} => [1,6,1] => [1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => [1,6,1] => [1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,5,6,7}} => [1,2,5] => [5,2,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6,7}} => [1,4,3] => [3,4,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6,7}} => [1,5,2] => [2,5,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8},{7}} => [1,6,1] => [1,6,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => [1,7] => [7,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7,8}} => [2,1,1,1,1,2] => [2,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5},{6,7},{8}} => [2,1,1,1,2,1] => [1,2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5},{6,8},{7}} => [2,1,1,1,2,1] => [1,2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5},{6,7,8}} => [2,1,1,1,3] => [3,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4},{5,6},{7},{8}} => [2,1,1,2,1,1] => [1,1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4},{5,8},{6},{7}} => [2,1,1,2,1,1] => [1,1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4},{5,8},{6,7}} => [2,1,1,2,2] => [2,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4},{5,6,7,8}} => [2,1,1,4] => [4,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7},{8}} => [2,1,2,1,1,1] => [1,1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => [2,1,2,3] => [3,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3},{4,8},{5},{6},{7}} => [2,1,2,1,1,1] => [1,1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3},{4,6,7,8},{5}} => [2,1,4,1] => [1,4,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => [2,1,3,2] => [2,3,1,2]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3},{4,5,8},{6},{7}} => [2,1,3,1,1] => [1,1,3,1,2]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3},{4,5,8},{6,7}} => [2,1,3,2] => [2,3,1,2]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3},{4,5,6,8},{7}} => [2,1,4,1] => [1,4,1,2]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8}} => [2,1,5] => [5,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}} => [2,2,1,3] => [3,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => [2,2,2,2] => [2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,4},{5,7,8},{6}} => [2,2,3,1] => [1,3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,8},{6,7}} => [2,2,2,2] => [2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4},{5,6,8},{7}} => [2,2,3,1] => [1,3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => [2,2,4] => [4,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7},{8}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1,2},{3,5},{4},{6,7,8}} => [2,2,1,3] => [3,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1,2},{3,6},{4},{5},{7},{8}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1,2},{3,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1,2},{3,6,7,8},{4},{5}} => [2,4,1,1] => [1,1,4,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1,2},{3,5,6},{4},{7,8}} => [2,3,1,2] => [2,1,3,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4},{5,6}} => [2,3,1,2] => [2,1,3,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,2},{3,5,7,8},{4},{6}} => [2,4,1,1] => [1,1,4,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1,2},{3,8},{4},{5,6,7}} => [2,2,1,3] => [3,1,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1,2},{3,5,8},{4},{6,7}} => [2,3,1,2] => [2,1,3,2]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1,2},{3,5,6,8},{4},{7}} => [2,4,1,1] => [1,1,4,2]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1,2},{3,5,6,7,8},{4}} => [2,5,1] => [1,5,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7},{8}} => [2,3,1,1,1] => [1,1,1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,6},{4,5},{7,8}} => [2,2,2,2] => [2,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1,2},{3,8},{4,5},{6},{7}} => [2,2,2,1,1] => [1,1,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,5},{6}} => [2,3,2,1] => [1,2,3,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,8},{4,5},{6,7}} => [2,2,2,2] => [2,2,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1,2},{3,6,8},{4,5},{7}} => [2,3,2,1] => [1,2,3,2]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1,2},{3,6,7,8},{4,5}} => [2,4,2] => [2,4,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2},{3,4,6},{5},{7,8}} => [2,3,1,2] => [2,1,3,2]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,6},{5}} => [2,3,2,1] => [1,2,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2},{3,4,8},{5},{6},{7}} => [2,3,1,1,1] => [1,1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2},{3,4,7,8},{5},{6}} => [2,4,1,1] => [1,1,4,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1,2},{3,8},{4,6,7},{5}} => [2,2,3,1] => [1,3,2,2]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2},{3,4,8},{5},{6,7}} => [2,3,1,2] => [2,1,3,2]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2},{3,4,6,8},{5},{7}} => [2,4,1,1] => [1,1,4,2]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2},{3,4,6,7,8},{5}} => [2,5,1] => [1,5,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => [2,4,2] => [2,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1,2},{3,8},{4,5,6},{7}} => [2,2,3,1] => [1,3,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,8},{4,7},{5,6}} => [2,2,2,2] => [2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2},{3,4,8},{5,6},{7}} => [2,3,2,1] => [1,2,3,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2},{3,4,5,7},{6},{8}} => [2,4,1,1] => [1,1,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1,2},{3,8},{4,5,7},{6}} => [2,2,3,1] => [1,3,2,2]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2},{3,4,8},{5,7},{6}} => [2,3,2,1] => [1,2,3,2]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2},{3,4,5,8},{6},{7}} => [2,4,1,1] => [1,1,4,2]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2},{3,4,5,7,8},{6}} => [2,5,1] => [1,5,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => [2,5,1] => [1,5,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1,2},{3,8},{4,5,6,7}} => [2,2,4] => [4,2,2]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2},{3,4,8},{5,6,7}} => [2,3,3] => [3,3,2]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2},{3,4,5,8},{6,7}} => [2,4,2] => [2,4,2]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2},{3,4,5,6,8},{7}} => [2,5,1] => [1,5,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => [2,6] => [6,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6},{7,8}} => [2,1,1,1,1,2] => [2,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5},{6,8},{7}} => [2,1,1,1,2,1] => [1,2,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5},{6,7,8}} => [2,1,1,1,3] => [3,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4},{5,7,8},{6}} => [2,1,1,3,1] => [1,3,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4},{5,8},{6,7}} => [2,1,1,2,2] => [2,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4},{5,6,7,8}} => [2,1,1,4] => [4,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6,7},{8}} => [2,1,2,2,1] => [1,2,2,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,5},{6,8},{7}} => [2,1,2,2,1] => [1,2,2,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5},{6,7,8}} => [2,1,2,3] => [3,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,6},{5},{7,8}} => [2,1,2,1,2] => [2,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,3},{2},{4,6,7},{5},{8}} => [2,1,3,1,1] => [1,1,3,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,3},{2},{4,8},{5},{6,7}} => [2,1,2,1,2] => [2,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,6,8},{5},{7}} => [2,1,3,1,1] => [1,1,3,1,2]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,3},{2},{4,6,7,8},{5}} => [2,1,4,1] => [1,4,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,3},{2},{4,5,6},{7,8}} => [2,1,3,2] => [2,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,3},{2},{4,7},{5,6},{8}} => [2,1,2,2,1] => [1,2,2,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,3},{2},{4,8},{5,6},{7}} => [2,1,2,2,1] => [1,2,2,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,3},{2},{4,7,8},{5,6}} => [2,1,3,2] => [2,3,1,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3},{2},{4,8},{5,7},{6}} => [2,1,2,2,1] => [1,2,2,1,2]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,3},{2},{4,5,7,8},{6}} => [2,1,4,1] => [1,4,1,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,3},{2},{4,8},{5,6,7}} => [2,1,2,3] => [3,2,1,2]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,3},{2},{4,5,8},{6,7}} => [2,1,3,2] => [2,3,1,2]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,5,6,8},{7}} => [2,1,4,1] => [1,4,1,2]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,3},{2},{4,5,6,7,8}} => [2,1,5] => [5,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5},{6,8},{7}} => [2,1,1,1,2,1] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5},{6,7,8}} => [2,1,1,1,3] => [3,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6},{7,8}} => [2,1,1,2,2] => [2,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2},{3},{5,8},{6,7}} => [2,1,1,2,2] => [2,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,4},{2},{3},{5,6,7,8}} => [2,1,1,4] => [4,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2},{3},{4},{6},{7,8}} => [2,1,1,1,1,2] => [2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2},{3},{4},{6,7,8}} => [2,1,1,1,3] => [3,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2},{3},{4},{5},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2},{3},{4},{5},{7,8}} => [2,1,1,1,1,2] => [2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2},{3},{4},{5},{6},{8}} => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3},{4},{5},{6}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3},{4},{5},{8}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,2] => [2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3},{4},{5},{7}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3},{4},{5}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2},{3},{4},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4},{5,6},{8}} => [2,1,1,1,2,1] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2},{3},{4},{5,6},{7}} => [2,1,1,1,2,1] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2},{3},{4},{6},{8}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2},{3},{4},{5,7},{6}} => [2,1,1,1,2,1] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,5,8},{2},{3},{4},{6},{7}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2},{3},{4},{6}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2},{3},{4},{8}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2},{3},{4},{5,6,7}} => [2,1,1,1,3] => [3,1,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2},{3},{4},{7}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2},{3},{4}} => [5,1,1,1] => [1,1,1,5]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,4,5},{2},{3},{6,8},{7}} => [3,1,1,2,1] => [1,2,1,1,3]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,4,5},{2},{3},{6,7,8}} => [3,1,1,3] => [3,1,1,3]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3},{4,5},{7},{8}} => [2,1,1,2,1,1] => [1,1,2,1,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2},{3},{4,5},{6},{7}} => [2,1,1,2,1,1] => [1,1,2,1,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3},{4,5},{8}} => [3,1,1,2,1] => [1,2,1,1,3]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3},{4,5}} => [4,1,1,2] => [2,1,1,4]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,4,6},{2},{3},{5},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4,6},{5},{8}} => [2,1,1,2,1,1] => [1,1,2,1,1,2]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,4,6,8},{2},{3},{5},{7}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,4,5,6},{2},{3},{7},{8}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,4,5,6},{2},{3},{7,8}} => [4,1,1,2] => [2,1,1,4]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4,5,6},{8}} => [2,1,1,3,1] => [1,3,1,1,2]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,4,8},{2},{3},{5,6},{7}} => [3,1,1,2,1] => [1,2,1,1,3]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,4,7,8},{2},{3},{5,6}} => [4,1,1,2] => [2,1,1,4]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,4,5,8},{2},{3},{6},{7}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,4,5,6,7},{2},{3},{8}} => [5,1,1,1] => [1,1,1,5]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,4,8},{2},{3},{5,6,7}} => [3,1,1,3] => [3,1,1,3]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,4,5,8},{2},{3},{6,7}} => [4,1,1,2] => [2,1,1,4]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,4,5,6,8},{2},{3},{7}} => [5,1,1,1] => [1,1,1,5]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,4,5,6,7,8},{2},{3}} => [6,1,1] => [1,1,6]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6},{7,8}} => [3,1,1,1,2] => [2,1,1,1,3]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,3,4},{2},{5},{6,8},{7}} => [3,1,1,2,1] => [1,2,1,1,3]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,3,4},{2},{5},{6,7,8}} => [3,1,1,3] => [3,1,1,3]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,3,4},{2},{5,6},{7,8}} => [3,1,2,2] => [2,2,1,3]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,3,4},{2},{5,7,8},{6}} => [3,1,3,1] => [1,3,1,3]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,3,4},{2},{5,8},{6,7}} => [3,1,2,2] => [2,2,1,3]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,3,4},{2},{5,6,8},{7}} => [3,1,3,1] => [1,3,1,3]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,3,4},{2},{5,6,7,8}} => [3,1,4] => [4,1,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7},{8}} => [2,1,2,1,1,1] => [1,1,1,2,1,2]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2},{3,4},{6},{7,8}} => [2,1,2,1,2] => [2,1,2,1,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2},{3,4},{6,8},{7}} => [2,1,2,2,1] => [1,2,2,1,2]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2},{3,4},{6,7,8}} => [2,1,2,3] => [3,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2},{3,4},{5},{6},{7}} => [2,1,2,1,1,1] => [1,1,1,2,1,2]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3,4},{5}} => [4,1,2,1] => [1,2,1,4]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2},{3,4},{7,8}} => [3,1,2,2] => [2,2,1,3]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,4},{5,6}} => [3,1,2,2] => [2,2,1,3]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2},{3,4},{6},{8}} => [3,1,2,1,1] => [1,1,2,1,3]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2},{3,4},{6}} => [4,1,2,1] => [1,2,1,4]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2},{3,4},{8}} => [4,1,2,1] => [1,2,1,4]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2},{3,4},{5,6,7}} => [2,1,2,3] => [3,2,1,2]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2},{3,4},{6,7}} => [3,1,2,2] => [2,2,1,3]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2},{3,4},{7}} => [4,1,2,1] => [1,2,1,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,3,5},{2},{4},{6},{7,8}} => [3,1,1,1,2] => [2,1,1,1,3]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,3,5},{2},{4},{6,7},{8}} => [3,1,1,2,1] => [1,2,1,1,3]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,5},{2},{4},{6,8},{7}} => [3,1,1,2,1] => [1,2,1,1,3]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,3,5},{2},{4},{6,7,8}} => [3,1,1,3] => [3,1,1,3]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3,5},{4},{7},{8}} => [2,1,2,1,1,1] => [1,1,1,2,1,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2},{3,5},{4},{7,8}} => [2,1,2,1,2] => [2,1,2,1,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2},{3,5},{4},{6},{7}} => [2,1,2,1,1,1] => [1,1,1,2,1,2]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3,5},{4},{7}} => [3,1,2,1,1] => [1,1,2,1,3]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3,5},{4}} => [4,1,2,1] => [1,2,1,4]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,3,6},{2},{4},{5},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,3,7},{2},{4},{5},{6},{8}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,3,8},{2},{4},{5},{6},{7}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4},{5},{6}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,3,5,6},{2},{4},{7,8}} => [4,1,1,2] => [2,1,1,4]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2},{3,5,6},{4},{8}} => [2,1,3,1,1] => [1,1,3,1,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,5,6},{4}} => [3,1,3,1] => [1,3,1,3]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,3,7},{2},{4},{5,6},{8}} => [3,1,1,2,1] => [1,2,1,1,3]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4},{5,6}} => [4,1,1,2] => [2,1,1,4]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,3,5,7},{2},{4},{6},{8}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,3,5,7,8},{2},{4},{6}} => [5,1,1,1] => [1,1,1,5]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4},{5,6,7}} => [3,1,1,3] => [3,1,1,3]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,3,5,8},{2},{4},{6,7}} => [4,1,1,2] => [2,1,1,4]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,3,5,6,8},{2},{4},{7}} => [5,1,1,1] => [1,1,1,5]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,3,5,6,7,8},{2},{4}} => [6,1,1] => [1,1,6]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7},{8}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,3,4,5},{2},{6},{7,8}} => [4,1,1,2] => [2,1,1,4]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,3,4,5},{2},{6,7},{8}} => [4,1,2,1] => [1,2,1,4]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,3,4,5},{2},{6,8},{7}} => [4,1,2,1] => [1,2,1,4]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,3,4,5},{2},{6,7,8}} => [4,1,3] => [3,1,4]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3,4,5},{7},{8}} => [2,1,3,1,1] => [1,1,3,1,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2},{3,4,5},{7,8}} => [2,1,3,2] => [2,3,1,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,8},{2},{3,4,5},{6},{7}} => [2,1,3,1,1] => [1,1,3,1,2]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3,4,5},{6}} => [3,1,3,1] => [1,3,1,3]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2},{3,4,5},{6,7}} => [2,1,3,2] => [2,3,1,2]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3,4,5},{7}} => [3,1,3,1] => [1,3,1,3]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,3,6},{2},{4,5},{7,8}} => [3,1,2,2] => [2,2,1,3]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2},{3,6},{4,5},{8}} => [2,1,2,2,1] => [1,2,2,1,2]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,6},{4,5}} => [3,1,2,2] => [2,2,1,3]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,5},{6},{8}} => [3,1,2,1,1] => [1,1,2,1,3]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4,5},{6}} => [4,1,2,1] => [1,2,1,4]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2},{3,6,7},{4,5}} => [2,1,3,2] => [2,3,1,2]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,3,8},{2},{4,5},{6,7}} => [3,1,2,2] => [2,2,1,3]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,3,6,8},{2},{4,5},{7}} => [4,1,2,1] => [1,2,1,4]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,3,4,6},{2},{5},{7,8}} => [4,1,1,2] => [2,1,1,4]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,4,6},{5}} => [3,1,3,1] => [1,3,1,3]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,6},{5},{8}} => [3,1,2,1,1] => [1,1,2,1,3]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4,6},{5}} => [4,1,2,1] => [1,2,1,4]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,3,4,8},{2},{5},{6},{7}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,3,4,7,8},{2},{5},{6}} => [5,1,1,1] => [1,1,1,5]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2},{3,4,6,7},{5}} => [2,1,4,1] => [1,4,1,2]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4,6,7},{5}} => [3,1,3,1] => [1,3,1,3]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,3,4,6,8},{2},{5},{7}} => [5,1,1,1] => [1,1,1,5]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,3,4,6,7,8},{2},{5}} => [6,1,1] => [1,1,6]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,3,4,5,6},{2},{7},{8}} => [5,1,1,1] => [1,1,1,5]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,3,4,5,6},{2},{7,8}} => [5,1,2] => [2,1,5]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2},{3,4,5,6},{7}} => [2,1,4,1] => [1,4,1,2]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,4,5,6}} => [3,1,4] => [4,1,3]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,5,6},{8}} => [3,1,3,1] => [1,3,1,3]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,3,8},{2},{4,5,6},{7}} => [3,1,3,1] => [1,3,1,3]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2},{3,4,7},{5,6}} => [2,1,3,2] => [2,3,1,2]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,3,8},{2},{4,7},{5,6}} => [3,1,2,2] => [2,2,1,3]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,3,4,8},{2},{5,6},{7}} => [4,1,2,1] => [1,2,1,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2},{3,4,5,7},{6}} => [2,1,4,1] => [1,4,1,2]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4,5,7},{6}} => [3,1,3,1] => [1,3,1,3]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,3,4,8},{2},{5,7},{6}} => [4,1,2,1] => [1,2,1,4]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,3,4,5,8},{2},{6},{7}} => [5,1,1,1] => [1,1,1,5]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,3,4,5,7,8},{2},{6}} => [6,1,1] => [1,1,6]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,3,4,5,6,7},{2},{8}} => [6,1,1] => [1,1,6]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2},{3,4,5,6,7}} => [2,1,5] => [5,1,2]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,3,4,5,8},{2},{6,7}} => [5,1,2] => [2,1,5]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,3,4,5,6,8},{2},{7}} => [6,1,1] => [1,1,6]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8},{2}} => [7,1] => [1,7]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6},{7,8}} => [3,1,1,1,2] => [2,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5},{6,8},{7}} => [3,1,1,2,1] => [1,2,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5},{6,7,8}} => [3,1,1,3] => [3,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4},{5,6},{7,8}} => [3,1,2,2] => [2,2,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4},{5,8},{6,7}} => [3,1,2,2] => [2,2,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4},{5,6,8},{7}} => [3,1,3,1] => [1,3,1,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2,3},{4,6},{5},{7,8}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2,3},{4,6,7},{5},{8}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2,3},{4,8},{5},{6,7}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2,3},{4,6,8},{5},{7}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2,3},{4,8},{5,7},{6}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2,3},{4,5,8},{6},{7}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2,3},{4,5,7,8},{6}} => [3,4,1] => [1,4,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => [3,4,1] => [1,4,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2,3},{4,8},{5,6,7}} => [3,2,3] => [3,2,3]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2,3},{4,5,8},{6,7}} => [3,3,2] => [2,3,3]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2,3},{4,5,6,8},{7}} => [3,4,1] => [1,4,3]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => [3,5] => [5,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7},{8}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6},{7,8}} => [2,2,1,1,2] => [2,1,1,2,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,4},{2,3},{5},{6,7},{8}} => [2,2,1,2,1] => [1,2,1,2,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,4},{2,3},{5},{6,8},{7}} => [2,2,1,2,1] => [1,2,1,2,2]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,4},{2,3},{5},{6,7,8}} => [2,2,1,3] => [3,1,2,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,4},{2,3},{5,6},{7},{8}} => [2,2,2,1,1] => [1,1,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6},{7,8}} => [2,2,2,2] => [2,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,4},{2,3},{5,7},{6},{8}} => [2,2,2,1,1] => [1,1,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,4},{2,3},{5,8},{6},{7}} => [2,2,2,1,1] => [1,1,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,4},{2,3},{5,7,8},{6}} => [2,2,3,1] => [1,3,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,4},{2,3},{5,6,7},{8}} => [2,2,3,1] => [1,3,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,8},{6,7}} => [2,2,2,2] => [2,2,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,4},{2,3},{5,6,8},{7}} => [2,2,3,1] => [1,3,2,2]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,4},{2,3},{5,6,7,8}} => [2,2,4] => [4,2,2]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7},{8}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2,3},{4},{6,7},{8}} => [2,2,1,2,1] => [1,2,1,2,2]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,3},{4},{6,8},{7}} => [2,2,1,2,1] => [1,2,1,2,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2,3},{4},{5},{7},{8}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2,3},{4},{5},{7,8}} => [2,2,1,1,2] => [2,1,1,2,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2,3},{4},{5},{6},{8}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,3},{4},{5},{6},{7}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3},{4},{5},{7}} => [3,2,1,1,1] => [1,1,1,2,3]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2,3},{4},{7,8}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,3},{4},{5,6},{8}} => [2,2,1,2,1] => [1,2,1,2,2]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2,3},{4},{5,6}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2,3},{4},{6},{8}} => [3,2,1,1,1] => [1,1,1,2,3]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2,3},{4},{6}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2,3},{4},{8}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2,3},{4},{5,6,7}} => [2,2,1,3] => [3,1,2,2]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2,3},{4},{6,7}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2,3},{4},{7}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2,3},{4}} => [5,2,1] => [1,2,5]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,4,5},{2,3},{6},{7,8}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,4,5},{2,3},{6,7},{8}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,4,5},{2,3},{6,8},{7}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3},{4,5},{7,8}} => [2,2,2,2] => [2,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2,3},{4,5},{6},{8}} => [2,2,2,1,1] => [1,1,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2,3},{4,5},{6},{7}} => [2,2,2,1,1] => [1,1,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3},{4,5},{6}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3},{4,5},{8}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => [2,2,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3},{4,5},{7}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3},{4,5}} => [4,2,2] => [2,2,4]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,4,6},{2,3},{5},{7,8}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2,3},{4,6},{5},{8}} => [2,2,2,1,1] => [1,1,2,2,2]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,3},{4,6},{5}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,4,8},{2,3},{5},{6},{7}} => [3,2,1,1,1] => [1,1,1,2,3]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,4,7,8},{2,3},{5},{6}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,4,6,7},{2,3},{5},{8}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2,3},{4,6,7},{5}} => [2,2,3,1] => [1,3,2,2]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,4,8},{2,3},{5},{6,7}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,4,6,8},{2,3},{5},{7}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,4,6,7,8},{2,3},{5}} => [5,2,1] => [1,2,5]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,4,5,6},{2,3},{7,8}} => [4,2,2] => [2,2,4]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2,3},{4,5,6},{8}} => [2,2,3,1] => [1,3,2,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,4,7},{2,3},{5,6},{8}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => [2,2,2,2]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,4,8},{2,3},{5,6},{7}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,4,5,7},{2,3},{6},{8}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2,3},{4,5,7},{6}} => [2,2,3,1] => [1,3,2,2]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,4,8},{2,3},{5,7},{6}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,4,5,8},{2,3},{6},{7}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,4,5,7,8},{2,3},{6}} => [5,2,1] => [1,2,5]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,4,5,6,7},{2,3},{8}} => [5,2,1] => [1,2,5]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,4,8},{2,3},{5,6,7}} => [3,2,3] => [3,2,3]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,4,5,8},{2,3},{6,7}} => [4,2,2] => [2,2,4]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,4,5,6,8},{2,3},{7}} => [5,2,1] => [1,2,5]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,4,5,6,7,8},{2,3}} => [6,2] => [2,6]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,4},{3},{5,6},{7,8}} => [3,1,2,2] => [2,2,1,3]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,4},{3},{5,7,8},{6}} => [3,1,3,1] => [1,3,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,4},{3},{5,6,7},{8}} => [3,1,3,1] => [1,3,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,4},{3},{5,8},{6,7}} => [3,1,2,2] => [2,2,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,4},{3},{5,6,8},{7}} => [3,1,3,1] => [1,3,1,3]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,4},{3},{5,6,7,8}} => [3,1,4] => [4,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7},{8}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2,4},{3},{6},{7,8}} => [2,2,1,1,2] => [2,1,1,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2,4},{3},{6,7},{8}} => [2,2,1,2,1] => [1,2,1,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,4},{3},{6,8},{7}} => [2,2,1,2,1] => [1,2,1,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2,4},{3},{6,7,8}} => [2,2,1,3] => [3,1,2,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2,4},{3},{5},{6},{8}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2,4},{3},{5},{6,7}} => [2,2,1,1,2] => [2,1,1,2,2]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,4},{3},{5}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2,4},{3},{7,8}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,4},{3},{5,6},{8}} => [2,2,1,2,1] => [1,2,1,2,2]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2,4},{3},{5,6}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2,4},{3},{6},{8}} => [3,2,1,1,1] => [1,1,1,2,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2,4},{3},{5,7},{6}} => [2,2,1,2,1] => [1,2,1,2,2]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2,4},{3},{6}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2,4},{3},{8}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2,4},{3},{5,6,7}} => [2,2,1,3] => [3,1,2,2]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2,4},{3},{6,7}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2,4},{3},{7}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2,4},{3}} => [5,2,1] => [1,2,5]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,5},{3},{4},{6},{7,8}} => [3,1,1,1,2] => [2,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2,5},{3},{4},{7},{8}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,5},{3},{4},{7,8}} => [2,2,1,1,2] => [2,1,1,2,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2,5},{3},{4},{6},{8}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2,5},{3},{4},{6},{7}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,5},{3},{4},{6}} => [3,2,1,1,1] => [1,1,1,2,3]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,5},{3},{4}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3},{4},{5},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3},{4},{5},{7,8}} => [3,1,1,1,2] => [2,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3},{4},{5}} => [3,2,1,1,1] => [1,1,1,2,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,7},{3},{4},{5},{6},{8}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => [1,1,1,1,2,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4},{5},{6}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3},{4},{5}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,5,6},{3},{4},{7,8}} => [4,1,1,2] => [2,1,1,4]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,5,6},{3},{4}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4},{5,6}} => [4,1,1,2] => [2,1,1,4]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => [1,1,1,3,2]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,5,7,8},{3},{4},{6}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,5,6,7},{3},{4},{8}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2,5,6,7},{3},{4}} => [2,4,1,1] => [1,1,4,2]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,2,5,8},{3},{4},{6,7}} => [4,1,1,2] => [2,1,1,4]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,5,6,8},{3},{4},{7}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,5,6,7,8},{3},{4}} => [6,1,1] => [1,1,6]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2,4,5},{3},{7,8}} => [2,3,1,2] => [2,1,3,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,7},{2,4,5},{3},{6},{8}} => [2,3,1,1,1] => [1,1,1,3,2]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,4,5},{3},{6}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,4,5},{3},{8}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2,4,5},{3},{6,7}} => [2,3,1,2] => [2,1,3,2]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,4,5},{3},{7}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3},{4,5},{7,8}} => [3,1,2,2] => [2,2,1,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3},{4,5},{8}} => [2,2,1,2,1] => [1,2,1,2,2]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3},{4,5}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4,5},{6}} => [4,1,2,1] => [1,2,1,4]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3},{4,5}} => [2,3,1,2] => [2,1,3,2]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3},{4,5},{6,7}} => [3,1,2,2] => [2,2,1,3]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3},{4,5},{7}} => [4,1,2,1] => [1,2,1,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,4,6},{3},{5},{7,8}} => [4,1,1,2] => [2,1,1,4]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,7},{2,4,6},{3},{5},{8}} => [2,3,1,1,1] => [1,1,1,3,2]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,4,6},{3},{5}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4,6},{5}} => [4,1,2,1] => [1,2,1,4]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2,4,7},{3},{5},{6}} => [2,3,1,1,1] => [1,1,1,3,2]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,4,8},{3},{5},{6},{7}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,4,7,8},{3},{5},{6}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,4,6,7},{3},{5}} => [2,4,1,1] => [1,1,4,2]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3},{4,6,7},{5}} => [3,1,3,1] => [1,3,1,3]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,4,8},{3},{5},{6,7}} => [4,1,1,2] => [2,1,1,4]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,4,6,8},{3},{5},{7}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,4,6,7,8},{3},{5}} => [6,1,1] => [1,1,6]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,4,5,6},{3},{7,8}} => [5,1,2] => [2,1,5]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2,4,5,6},{3},{8}} => [2,4,1,1] => [1,1,4,2]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,4,5,6},{3},{7}} => [2,4,1,1] => [1,1,4,2]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2,4,5,6},{3}} => [3,4,1] => [1,4,3]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4,5,6}} => [2,2,1,3] => [3,1,2,2]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3},{4,5,6},{7}} => [3,1,3,1] => [1,3,1,3]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4,5,6}} => [4,1,3] => [3,1,4]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,4,7},{3},{5,6},{8}} => [4,1,2,1] => [1,2,1,4]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,4,7},{3},{5,6}} => [2,3,1,2] => [2,1,3,2]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3},{4,7},{5,6}} => [3,1,2,2] => [2,2,1,3]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,4,8},{3},{5,6},{7}} => [4,1,2,1] => [1,2,1,4]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,4,7,8},{3},{5,6}} => [5,1,2] => [2,1,5]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,4,5,7},{3},{6}} => [2,4,1,1] => [1,1,4,2]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3},{4,5,7},{6}} => [3,1,3,1] => [1,3,1,3]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,4,8},{3},{5,7},{6}} => [4,1,2,1] => [1,2,1,4]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,4,5,7,8},{3},{6}} => [6,1,1] => [1,1,6]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,4,5,6,7},{3},{8}} => [6,1,1] => [1,1,6]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2,4,5,6,7},{3}} => [2,5,1] => [1,5,2]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3},{4,5,6,7}} => [3,1,4] => [4,1,3]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,4,5,8},{3},{6,7}} => [5,1,2] => [2,1,5]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,4,5,6,8},{3},{7}} => [6,1,1] => [1,1,6]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8},{3}} => [7,1] => [1,7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3,4},{5},{6,7},{8}} => [4,1,2,1] => [1,2,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3,4},{5},{6,8},{7}} => [4,1,2,1] => [1,2,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => [4,2,2] => [2,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3,4},{5,7,8},{6}} => [4,3,1] => [1,3,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => [4,3,1] => [1,3,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3,4},{5,8},{6,7}} => [4,2,2] => [2,2,4]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3,4},{5,6,8},{7}} => [4,3,1] => [1,3,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => [4,4] => [4,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7},{8}} => [2,3,1,1,1] => [1,1,1,3,2]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,3,4},{6,8},{7}} => [2,3,2,1] => [1,2,3,2]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2,3,4},{6,7,8}} => [2,3,3] => [3,3,2]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2,3,4},{5},{7},{8}} => [2,3,1,1,1] => [1,1,1,3,2]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2,3,4},{5},{7,8}} => [2,3,1,2] => [2,1,3,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2,3,4},{5},{6},{8}} => [2,3,1,1,1] => [1,1,1,3,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,3,4},{5},{6},{7}} => [2,3,1,1,1] => [1,1,1,3,2]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2,3,4},{5},{6,7}} => [2,3,1,2] => [2,1,3,2]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3,4},{5},{7}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2,3,4},{7},{8}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,3,4},{5,6},{8}} => [2,3,2,1] => [1,2,3,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2,3,4},{5,6},{7}} => [2,3,2,1] => [1,2,3,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2,3,4},{6},{8}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2,3,4},{5,7},{6}} => [2,3,2,1] => [1,2,3,2]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => {{1,5,8},{2,3,4},{6},{7}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2,3,4},{8}} => [4,3,1] => [1,3,4]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2,3,4},{6,7}} => [3,3,2] => [2,3,3]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2,3,4},{7}} => [4,3,1] => [1,3,4]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2,3,4}} => [5,3] => [3,5]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7},{8}} => [3,2,1,1,1] => [1,1,1,2,3]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,5},{3,4},{6},{7,8}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,5},{3,4},{6,7},{8}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,5},{3,4},{6,8},{7}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,5},{3,4},{6,7,8}} => [3,2,3] => [3,2,3]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,5},{3,4},{7,8}} => [2,2,2,2] => [2,2,2,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2,5},{3,4},{6},{8}} => [2,2,2,1,1] => [1,1,2,2,2]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,5},{3,4},{6}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,5},{3,4},{8}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => [2,2,2,2]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,5},{3,4},{7}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,5},{3,4}} => [4,2,2] => [2,2,4]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,4},{5},{7,8}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,4},{5},{8}} => [2,2,2,1,1] => [1,1,2,2,2]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3,4},{5},{7}} => [2,2,2,1,1] => [1,1,2,2,2]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,4},{5}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4},{5},{6}} => [2,2,2,1,1] => [1,1,2,2,2]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3,4},{5},{6},{7}} => [3,2,1,1,1] => [1,1,1,2,3]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4},{5},{6}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3,4},{5}} => [2,3,2,1] => [1,2,3,2]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,4},{5},{6,7}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3,4},{5},{7}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,5,6},{3,4},{7},{8}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => {{1,8},{2,5,6},{3,4},{7}} => [2,3,2,1] => [1,2,3,2]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,5,6},{3,4}} => [3,3,2] => [2,3,3]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3,4},{5,6},{8}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => [2,2,2,2]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3,4},{5,6},{7}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,5,7},{3,4},{6},{8}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2,5,7},{3,4},{6}} => [2,3,2,1] => [1,2,3,2]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3,4},{5,7},{6}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,5,8},{3,4},{6},{7}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,5,6,8},{3,4},{7}} => [5,2,1] => [1,2,5]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,5,6,7,8},{3,4}} => [6,2] => [2,6]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,5},{4},{6},{7,8}} => [4,1,1,2] => [2,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,5},{4},{6,8},{7}} => [4,1,2,1] => [1,2,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,5},{4},{6,7,8}} => [4,1,3] => [3,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3,5},{4},{7,8}} => [2,3,1,2] => [2,1,3,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => {{1,8},{2,3,5},{4},{6},{7}} => [2,3,1,1,1] => [1,1,1,3,2]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3,5},{4},{6}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3,5},{4},{8}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2,3,5},{4},{6,7}} => [2,3,1,2] => [2,1,3,2]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3,5},{4},{7}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3,5},{4}} => [4,3,1] => [1,3,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,5},{4},{7,8}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,5},{4},{8}} => [2,2,2,1,1] => [1,1,2,2,2]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,5},{4}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3,5},{4},{6}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3,5},{4}} => [2,3,2,1] => [1,2,3,2]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,5},{4},{6,7}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3,5},{4},{7}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3,5},{4}} => [5,2,1] => [1,2,5]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,6},{4},{5},{7,8}} => [4,1,1,2] => [2,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => {{1,8},{2,3,6},{4},{5},{7}} => [2,3,1,1,1] => [1,1,1,3,2]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,6},{4},{5}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,6},{4},{5}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4},{5},{6}} => [2,3,1,1,1] => [1,1,1,3,2]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4},{5},{6},{7}} => [4,1,1,1,1] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4},{5},{6}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,3,6,7},{4},{5}} => [2,4,1,1] => [1,1,4,2]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3,6,7},{4},{5}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4},{5},{6,7}} => [4,1,1,2] => [2,1,1,4]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,6,8},{4},{5},{7}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,6,7,8},{4},{5}} => [6,1,1] => [1,1,6]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,5,6},{4},{7},{8}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,5,6},{4},{7,8}} => [5,1,2] => [2,1,5]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2,3,5,6},{4},{8}} => [2,4,1,1] => [1,1,4,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,5,6},{4},{7}} => [2,4,1,1] => [1,1,4,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3,5,6},{4},{8}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,5,6},{4}} => [2,2,3,1] => [1,3,2,2]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3,5,6},{4},{7}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4},{5,6},{8}} => [4,1,2,1] => [1,2,1,4]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4},{5,6}} => [2,3,1,2] => [2,1,3,2]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4},{5,6}} => [3,2,1,2] => [2,1,2,3]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4},{5,6},{7}} => [4,1,2,1] => [1,2,1,4]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4},{5,6}} => [5,1,2] => [2,1,5]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,5,7},{4},{6},{8}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,5,7},{4},{6}} => [2,4,1,1] => [1,1,4,2]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,5,7},{4},{6}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4},{5,7},{6}} => [4,1,2,1] => [1,2,1,4]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,5,8},{4},{6},{7}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,5,7,8},{4},{6}} => [6,1,1] => [1,1,6]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => [6,1,1] => [1,1,6]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2,3,5,6,7},{4}} => [2,5,1] => [1,5,2]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4},{5,6,7}} => [4,1,3] => [3,1,4]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,5,6,8},{4},{7}} => [6,1,1] => [1,1,6]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,5,6,7,8},{4}} => [7,1] => [1,7]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8}} => [5,2,1] => [1,2,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4,5},{6,8},{7}} => [5,2,1] => [1,2,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => [5,3] => [3,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => {{1,6},{2,3,4,5},{7},{8}} => [2,4,1,1] => [1,1,4,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => {{1,7},{2,3,4,5},{6},{8}} => [2,4,1,1] => [1,1,4,2]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3,4,5},{7}} => [3,4,1] => [1,4,3]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3,4,5}} => [4,4] => [4,4]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3,4,5},{7},{8}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,4,5},{7,8}} => [3,3,2] => [2,3,3]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,4,5},{8}} => [2,2,3,1] => [1,3,2,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3,4,5},{7}} => [2,2,3,1] => [1,3,2,2]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,4,5}} => [3,2,3] => [3,2,3]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4,5},{6}} => [2,2,3,1] => [1,3,2,2]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,4,5},{6,7}} => [3,3,2] => [2,3,3]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3,4,5}} => [5,3] => [3,5]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,6},{4,5},{7},{8}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,6},{4,5},{7,8}} => [4,2,2] => [2,2,4]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => {{1,8},{2,3,6},{4,5},{7}} => [2,3,2,1] => [1,2,3,2]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,6},{4,5}} => [3,3,2] => [2,3,3]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3,6},{4,5},{8}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => [2,2,2,2]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3,6},{4,5},{7}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5},{6},{8}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4,5},{6}} => [2,3,2,1] => [1,2,3,2]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,5},{6}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,5},{6},{7}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,6,7},{4,5},{8}} => [5,2,1] => [1,2,5]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,3,6,7},{4,5}} => [2,4,2] => [2,4,2]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5},{6,7}} => [4,2,2] => [2,2,4]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,6,8},{4,5},{7}} => [5,2,1] => [1,2,5]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,6,7,8},{4,5}} => [6,2] => [2,6]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,6},{5},{7},{8}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,6},{5},{7,8}} => [5,1,2] => [2,1,5]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,4,6},{5},{7}} => [2,4,1,1] => [1,1,4,2]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,4,6},{5}} => [3,4,1] => [1,4,3]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3,4,6},{5},{8}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4,6},{5}} => [2,2,3,1] => [1,3,2,2]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3,4,6},{5},{7}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4,6},{5}} => [4,3,1] => [1,3,4]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,6},{5},{8}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4,6},{5}} => [2,3,2,1] => [1,2,3,2]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,6},{5}} => [3,2,2,1] => [1,2,2,3]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,6},{5},{7}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4,6},{5}} => [5,2,1] => [1,2,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,4,7},{5},{6}} => [2,4,1,1] => [1,1,4,2]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,4,7},{5},{6}} => [3,3,1,1] => [1,1,3,3]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,7},{5},{6}} => [4,2,1,1] => [1,1,2,4]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5},{6},{7}} => [5,1,1,1] => [1,1,1,5]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,7,8},{5},{6}} => [6,1,1] => [1,1,6]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => [6,1,1] => [1,1,6]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,6,7},{5}} => [2,5,1] => [1,5,2]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,6,7},{5}} => [3,4,1] => [1,4,3]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5},{6,7}} => [5,1,2] => [2,1,5]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,6,8},{5},{7}} => [6,1,1] => [1,1,6]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,6,7,8},{5}} => [7,1] => [1,7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8}} => [6,1,1] => [1,1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => [6,2] => [2,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => {{1,7},{2,3,4,5,6},{8}} => [2,5,1] => [1,5,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,4,5,6},{7}} => [2,5,1] => [1,5,2]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,4,5,6}} => [3,5] => [5,3]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3,4,5,6},{8}} => [3,4,1] => [1,4,3]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4,5,6}} => [4,4] => [4,4]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => [4,3,1] => [1,3,4]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4,5,6}} => [2,3,3] => [3,3,2]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,5,6}} => [3,2,3] => [3,2,3]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,5,6},{7}} => [4,3,1] => [1,3,4]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4,5,6}} => [5,3] => [3,5]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => [5,2,1] => [1,2,5]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,4,7},{5,6}} => [2,4,2] => [2,4,2]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,4,7},{5,6}} => [3,3,2] => [2,3,3]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,7},{5,6}} => [4,2,2] => [2,2,4]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,6},{7}} => [5,2,1] => [1,2,5]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,7,8},{5,6}} => [6,2] => [2,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => [6,1,1] => [1,1,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,5,7},{6}} => [2,5,1] => [1,5,2]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,5,7},{6}} => [3,4,1] => [1,4,3]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5,7},{6}} => [4,3,1] => [1,3,4]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,7},{6}} => [5,2,1] => [1,2,5]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,8},{6},{7}} => [6,1,1] => [1,1,6]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,8},{6}} => [7,1] => [1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => [7,1] => [1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,5,6,7}} => [2,6] => [6,2]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,5,6,7}} => [3,5] => [5,3]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5,6,7}} => [4,4] => [4,4]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,6,7}} => [5,3] => [3,5]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,8},{6,7}} => [6,2] => [2,6]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,8},{7}} => [7,1] => [1,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8}} => [8] => [8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => [8,1] => [1,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9}} => [1,8] => [8,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => [9,1] => [1,9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => [7,1,1] => [1,1,7]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,9},{8}} => [1,7,1] => [1,7,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => [1,9] => [9,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => [10,1] => [1,10]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => [8,1,1] => [1,1,8]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => [6,2,1] => [1,2,6]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => [7,1,1] => [1,1,7]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,9},{7,8}} => [1,6,2] => [2,6,1]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8,9},{7}} => [1,7,1] => [1,7,1]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,10},{9}} => [1,8,1] => [1,8,1]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => [1,10] => [10,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,9},{7},{8}} => [1,6,1,1] => [1,1,6,1]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,10},{8,9}} => [1,7,2] => [2,7,1]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,10},{8},{9}} => [1,7,1,1] => [1,1,7,1]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,9},{6,7},{8}} => [1,5,2,1] => [1,2,5,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => {{1,8},{2,3,4,5,6,7},{9}} => [2,6,1] => [1,6,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,3,4,5,6,7,8},{2},{9}} => [7,1,1] => [1,1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7},{8,9}} => [7,2] => [2,7]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,9},{6},{7},{8}} => [1,5,1,1,1] => [1,1,1,5,1]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => [2,7] => [7,2]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8,9},{3}} => [1,7,1] => [1,7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6,7},{8},{9}} => [7,1,1] => [1,1,7]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8},{9}} => [1,7,1] => [1,7,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,7},{6},{8,9}} => [6,1,2] => [2,1,6]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,10},{7},{8},{9}} => [1,6,1,1,1] => [1,1,1,6,1]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,9},{8}} => [2,6,1] => [1,6,2]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,9}} => [1,1,7] => [7,1,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,3,4,5,6,7,8,9},{2},{10}} => [8,1,1] => [1,1,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8},{9,10}} => [8,2] => [2,8]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => [2,8] => [8,2]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8,9,10},{3}} => [1,8,1] => [1,8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6,7,8},{9},{10}} => [8,1,1] => [1,1,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7,8,9},{10}} => [1,8,1] => [1,8,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,9},{5,6},{7},{8}} => [1,4,2,1,1] => [1,1,2,4,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,8,9},{2},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,9},{2},{3},{4},{5},{6},{7,8}} => [2,1,1,1,1,1,2] => [2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,7,9},{2},{3},{4},{5},{6},{8}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2},{3},{4},{5},{6}} => [4,1,1,1,1,1] => [1,1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,9},{2},{3},{4},{5},{6,7},{8}} => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,9},{2},{3},{4},{5},{6,8},{7}} => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,6,9},{2},{3},{4},{5},{7},{8}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,6,8,9},{2},{3},{4},{5},{7}} => [4,1,1,1,1,1] => [1,1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,9},{2},{3},{4},{5},{6,7,8}} => [2,1,1,1,1,3] => [3,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,6,7,9},{2},{3},{4},{5},{8}} => [4,1,1,1,1,1] => [1,1,1,1,1,4]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,5,9},{2},{3},{4},{6},{7},{8}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,5,6,9},{2},{3},{4},{7},{8}} => [4,1,1,1,1,1] => [1,1,1,1,1,4]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,4,5,9},{2},{3},{6},{7},{8}} => [4,1,1,1,1,1] => [1,1,1,1,1,4]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,4,5,6,7,8,9},{2},{3}} => [7,1,1] => [1,1,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2},{3,4},{5},{6},{7},{8}} => [2,1,2,1,1,1,1] => [1,1,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,3,9},{2},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,3,4,9},{2},{5},{6},{7},{8}} => [4,1,1,1,1,1] => [1,1,1,1,1,4]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,9},{2},{3,4,5,6,7,8}} => [2,1,6] => [6,1,2]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,3,4,5,6,9},{2},{7,8}} => [6,1,2] => [2,1,6]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,9},{2},{8}} => [7,1,1] => [1,1,7]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8,9},{2}} => [8,1] => [1,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2,3},{4},{5},{6},{7},{8}} => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,4,5,6,7,8,9},{2,3}} => [7,2] => [2,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,9},{2,4},{3},{5},{6},{7},{8}} => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,5,6,7,8,9},{2,4},{3}} => [6,2,1] => [1,2,6]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,9},{2,8},{3},{4},{5},{6},{7}} => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,9},{3},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,4,8,9},{3},{5},{6},{7}} => [5,1,1,1,1] => [1,1,1,1,5]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => {{1,2,9},{3},{4,5,6,7,8}} => [3,1,5] => [5,1,3]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8,9},{3}} => [8,1] => [1,8]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,5,6,7,8,9},{2,3,4}} => [6,3] => [3,6]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,5,9},{3,4},{6},{7},{8}} => [4,2,1,1,1] => [1,1,1,2,4]
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,6,7,8,9},{2,3,5},{4}} => [5,3,1] => [1,3,5]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,9},{3,6},{4},{5},{7},{8}} => [3,2,1,1,1,1] => [1,1,1,1,2,3]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,8,9},{3,7},{4},{5},{6}} => [4,2,1,1,1] => [1,1,1,2,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,9},{4},{5},{6},{7},{8}} => [4,1,1,1,1,1] => [1,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,8,9},{4},{5},{6},{7}} => [5,1,1,1,1] => [1,1,1,1,5]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => {{1,2,3,9},{4},{5,6,7,8}} => [4,1,4] => [4,1,4]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,5,6,7,8,9},{4}} => [8,1] => [1,8]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,6,7,8,9},{2,3,4,5}} => [5,4] => [4,5]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,9},{3,8},{4,5},{6},{7}} => [3,2,2,1,1] => [1,1,2,2,3]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,9},{4,5},{6},{7},{8}} => [4,2,1,1,1] => [1,1,1,2,4]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2,3,4,6},{5}} => [4,4,1] => [1,4,4]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,8,9},{5},{6},{7}} => [6,1,1,1] => [1,1,1,6]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,6,8,9},{5},{7}} => [7,1,1] => [1,1,7]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5},{6,7,8}} => [5,1,3] => [3,1,5]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,6,7,8,9},{5}} => [8,1] => [1,8]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => {{1,7,8,9},{2,3,4,5,6}} => [4,5] => [5,4]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5,6},{7},{8}} => [5,2,1,1] => [1,1,2,5]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,7,9},{5,6},{8}} => [6,2,1] => [1,2,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => {{1,8,9},{2,3,4,5,7},{6}} => [3,5,1] => [1,5,3]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,8,9},{5,7},{6}} => [6,2,1] => [1,2,6]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,8,9},{6},{7}} => [7,1,1] => [1,1,7]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => {{1,9},{2,3,4,5,7,8},{6}} => [2,6,1] => [1,6,2]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,9},{6},{7,8}} => [6,1,2] => [2,1,6]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,8,9},{6}} => [8,1] => [1,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => {{1,8,9},{2,3,4,5,6,7}} => [3,6] => [6,3]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => {{1,9},{2,3,4,5,8},{6,7}} => [2,5,2] => [2,5,2]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5,8},{6,7}} => [5,2,2] => [2,2,5]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,9},{6,7},{8}} => [6,2,1] => [1,2,6]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => {{1,9},{2,3,4,5,6,8},{7}} => [2,6,1] => [1,6,2]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,9},{7},{8}} => [7,1,1] => [1,1,7]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,8,9},{7}} => [8,1] => [1,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => {{1,9},{2,3,4,5,6,7,8}} => [2,7] => [7,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => {{1,2,9},{3,4,5,6,7,8}} => [3,6] => [6,3]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => {{1,2,3,9},{4,5,6,7,8}} => [4,5] => [5,4]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,9},{5,6,7,8}} => [5,4] => [4,5]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,9},{6,7,8}} => [6,3] => [3,6]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,9},{7,8}} => [7,2] => [2,7]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,9},{8}} => [8,1] => [1,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9}} => [9] => [9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}} => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9}} => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,9},{8}} => [1,1,1,1,1,1,2,1] => [1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6,9},{7},{8}} => [1,1,1,1,1,2,1,1] => [1,1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,9},{6},{7},{8}} => [1,1,1,1,2,1,1,1] => [1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,9},{5},{6},{7},{8}} => [1,1,1,2,1,1,1,1] => [1,1,1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,9},{4},{5},{6},{7},{8}} => [1,1,2,1,1,1,1,1] => [1,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,9},{3},{4},{5},{6},{7},{8}} => [1,2,1,1,1,1,1,1] => [1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,8,9}} => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,10},{9}} => [1,1,1,1,1,1,1,2,1] => [1,2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4},{5},{6,9},{7,8}} => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,10},{8},{9}} => [1,1,1,1,1,1,2,1,1] => [1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,9},{6,7},{8}} => [1,1,1,1,2,2,1] => [1,2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6,10},{7},{8},{9}} => [1,1,1,1,1,2,1,1,1] => [1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,9},{5,6},{7},{8}} => [1,1,1,2,2,1,1] => [1,1,2,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,10},{6},{7},{8},{9}} => [1,1,1,1,2,1,1,1,1] => [1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,9},{4,5},{6},{7},{8}} => [1,1,2,2,1,1,1] => [1,1,1,2,2,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,10},{5},{6},{7},{8},{9}} => [1,1,1,2,1,1,1,1,1] => [1,1,1,1,1,2,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,9},{3,4},{5},{6},{7},{8}} => [1,2,2,1,1,1,1] => [1,1,1,1,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,10},{4},{5},{6},{7},{8},{9}} => [1,1,2,1,1,1,1,1,1] => [1,1,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}} => [1,2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}} => [1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,11},{10}} => [1,1,1,1,1,1,1,1,2,1] => [1,2,1,1,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,3},{4},{5},{6},{7},{8},{9}} => [2,2,1,1,1,1,1,1] => [1,1,1,1,1,1,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1},{2},{3,9},{4,7},{5},{6},{8}} => [1,1,2,2,1,1,1] => [1,1,1,2,2,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1},{2,9},{3,8},{4},{5},{6},{7}} => [1,2,2,1,1,1,1] => [1,1,1,1,2,2,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2,6},{3},{4},{5},{7},{8},{9}} => [2,2,1,1,1,1,1,1] => [1,1,1,1,1,1,2,2]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,9},{4},{5},{6},{7},{8}} => [1,3,1,1,1,1,1] => [1,1,1,1,1,3,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,9},{5},{6},{7},{8}} => [1,4,1,1,1,1] => [1,1,1,1,4,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,10},{4},{5},{6},{7},{8},{9}} => [1,3,1,1,1,1,1,1] => [1,1,1,1,1,1,3,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,10},{2,9},{3},{4},{5},{6},{7},{8}} => [2,2,1,1,1,1,1,1] => [1,1,1,1,1,1,2,2]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,10},{5},{6},{7},{8},{9}} => [1,4,1,1,1,1,1] => [1,1,1,1,1,4,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7},{8,9}} => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7},{8},{9}} => [1,1,1,2,1,1,1,1] => [1,1,1,1,2,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7},{8},{9}} => [1,1,2,1,1,1,1,1] => [1,1,1,1,1,2,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7},{8,9}} => [1,2,1,1,1,1,2] => [2,1,1,1,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7},{8},{9}} => [1,2,2,1,1,1,1] => [1,1,1,1,2,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8},{9}} => [1,3,1,1,1,1,1] => [1,1,1,1,1,3,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => [1,6,2] => [2,6,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7},{8,9}} => [2,1,1,1,1,1,2] => [2,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5},{6},{7,8},{9}} => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7},{8},{9}} => [2,1,2,1,1,1,1] => [1,1,1,1,2,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8},{9}} => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}} => [2,6,1] => [1,6,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => [3,6] => [6,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8},{9}} => [4,1,1,1,1,1] => [1,1,1,1,1,4]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => [4,5] => [5,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8},{9}} => [5,1,1,1,1] => [1,1,1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4,5},{6,7,8},{9}} => [5,3,1] => [1,3,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => [5,4] => [4,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8},{9}} => [6,1,1,1] => [1,1,1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,6},{7,8},{9}} => [6,2,1] => [1,2,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => [6,3] => [3,6]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}} => [1,1,1,1,1,2,1,1,1] => [1,1,1,2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9,10}} => [2,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7},{8},{9},{10}} => [2,2,1,1,1,1,1,1] => [1,1,1,1,1,1,2,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,3]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => [3,7] => [7,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => [4,1,1,1,1,1,1] => [1,1,1,1,1,1,4]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => [4,6] => [6,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8},{9},{10}} => [5,1,1,1,1,1] => [1,1,1,1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => [5,5] => [5,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8},{9},{10}} => [6,1,1,1,1] => [1,1,1,1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}} => [6,4] => [4,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5,6,7},{8},{9},{10}} => [7,1,1,1] => [1,1,1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,6,7},{8,9},{10}} => [7,2,1] => [1,2,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}} => [7,3] => [3,7]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9,10}} => [10] => [10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,6},{2},{3},{4},{5},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,7},{2},{3},{4},{5},{6},{8},{9}} => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,8},{2},{3},{4},{5},{6},{7},{9}} => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,5,6},{2},{3},{4},{7},{8},{9}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,6},{2},{3},{4},{5},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,6,7},{2},{3},{4},{5},{8},{9}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,7},{2},{3},{4},{5},{6},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,7,8},{2},{3},{4},{5},{6},{9}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,8},{2},{3},{4},{5},{6},{7},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,9,10},{5},{6},{7},{8}} => [6,1,1,1,1] => [1,1,1,1,6]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,10},{5,6},{7},{8},{9}} => [5,2,1,1,1] => [1,1,1,2,5]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,10,11},{5},{6},{7},{8},{9}} => [6,1,1,1,1,1] => [1,1,1,1,1,6]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,9,10},{4},{5},{6},{7},{8}} => [5,1,1,1,1,1] => [1,1,1,1,1,5]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,10},{4,5},{6},{7},{8},{9}} => [4,2,1,1,1,1] => [1,1,1,1,2,4]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}} => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5},{6},{7,9},{8}} => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,9,10},{2},{3},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,3]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,9,10},{8}} => [9,1] => [1,9]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,10},{8,9}} => [8,2] => [2,8]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,10,11},{9}} => [10,1] => [1,10]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,9,10},{7},{8}} => [8,1,1] => [1,1,8]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,10},{7,8},{9}} => [7,2,1] => [1,2,7]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,11},{9,10}} => [9,2] => [2,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5},{6},{7},{8,10},{9}} => [2,1,1,1,1,1,2,1] => [1,2,1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5},{6},{7,9},{8}} => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5},{6},{7,9},{8}} => [1,2,1,1,1,2,1] => [1,2,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6},{7},{8,9}} => [2,1,1,1,1,1,2] => [2,1,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,8},{3},{4},{5},{6},{7},{9}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,7},{3},{4},{5},{6},{8},{9}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,6},{3},{4},{5},{7},{8},{9}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8,9,10},{2}} => [9,1] => [1,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => {{1,10},{2,3,4,5,6,7,8,9}} => [2,8] => [8,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => {{1,11},{2,3,4,5,6,7,8,9,10}} => [2,9] => [9,2]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => {{1,10},{2,3,4,5,6,7,9},{8}} => [2,7,1] => [1,7,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => {{1,7},{2,3,4,5,6},{8},{9}} => [2,5,1,1] => [1,1,5,2]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => {{1,6},{2,3,4,5},{7},{8},{9}} => [2,4,1,1,1] => [1,1,1,4,2]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7},{8},{9}} => [2,3,1,1,1,1] => [1,1,1,1,3,2]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7},{8},{9}} => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,10},{9}} => [9,1] => [1,9]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,8,9,10},{7}} => [9,1] => [1,9]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,8,9,10},{6}} => [9,1] => [1,9]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,6,7,8,9,10},{5}} => [9,1] => [1,9]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,5,6,7,8,9,10},{4}} => [9,1] => [1,9]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8,9,10},{3}} => [9,1] => [1,9]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,7},{3},{4},{5},{6},{8,9}} => [3,1,1,1,1,2] => [2,1,1,1,1,3]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2},{3,4,9},{5},{6},{7},{8}} => [2,3,1,1,1,1] => [1,1,1,1,3,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,3,8},{2},{4},{5},{6},{7},{9}} => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,3,10},{2},{4},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,3]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9,11},{10}} => [10,1] => [1,10]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,3},{2},{4,5,6,7,8,9}} => [2,1,6] => [6,1,2]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,4},{3},{5,6,7,8,9}} => [3,1,5] => [5,1,3]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,5},{4},{6,7,8,9}} => [4,1,4] => [4,1,4]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,6},{5},{7,8,9}} => [5,1,3] => [3,1,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7},{8},{9}} => [1,2,1,1,1,1,1,1] => [1,1,1,1,1,1,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7},{8},{9}} => [1,1,2,1,1,1,1,1] => [1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6,8},{7},{9},{10}} => [1,1,1,1,1,2,1,1,1] => [1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5},{6,9},{7},{8},{10}} => [1,1,1,1,1,2,1,1,1] => [1,1,1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,5},{2},{3},{4},{6},{7},{8,9}} => [2,1,1,1,1,1,2] => [2,1,1,1,1,1,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7},{8},{9}} => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2},{3,6},{4},{5},{7},{8},{9}} => [2,1,2,1,1,1,1,1] => [1,1,1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2},{3},{4,6},{5},{7},{8},{9}} => [2,1,1,2,1,1,1,1] => [1,1,1,1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,10},{2},{3},{4},{5,6},{7},{8},{9}} => [2,1,1,1,2,1,1,1] => [1,1,1,2,1,1,1,2]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,10},{6},{7},{8},{9}} => [1,5,1,1,1,1] => [1,1,1,1,5,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,9},{4,5},{6},{7},{8}} => [1,3,2,1,1,1] => [1,1,1,2,3,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,8},{2,3},{4},{5},{6},{7},{9}} => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,8,9},{3},{4},{5},{6},{7}} => [1,3,1,1,1,1,1] => [1,1,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,7},{2},{3},{4},{5},{6},{8,9}} => [2,1,1,1,1,1,2] => [2,1,1,1,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,2},{3,9},{4},{5},{6},{7},{8}} => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,6},{2},{3},{4},{5},{7,8,9}} => [2,1,1,1,1,3] => [3,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,8,9,10},{2},{3},{4},{5},{6},{7}} => [4,1,1,1,1,1,1] => [1,1,1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,5},{2},{3},{4},{6,7,8,9}} => [2,1,1,1,4] => [4,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,7,8,10},{2},{3},{4},{5},{6},{9}} => [4,1,1,1,1,1,1] => [1,1,1,1,1,1,4]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,4},{2},{3},{5,6,7,9},{8}} => [2,1,1,4,1] => [1,4,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,6,7,10},{2},{3},{4},{5},{8},{9}} => [4,1,1,1,1,1,1] => [1,1,1,1,1,1,4]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1,3},{2},{4,5,6,9},{7},{8}} => [2,1,4,1,1] => [1,1,4,1,2]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,5,6,10},{2},{3},{4},{7},{8},{9}} => [4,1,1,1,1,1,1] => [1,1,1,1,1,1,4]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2},{3,4,5,9},{6},{7},{8}} => [2,4,1,1,1] => [1,1,1,4,2]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,4,5,10},{2},{3},{6},{7},{8},{9}} => [4,1,1,1,1,1,1] => [1,1,1,1,1,1,4]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,3,4,10},{2},{5},{6},{7},{8},{9}} => [4,1,1,1,1,1,1] => [1,1,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,10},{4},{5},{6},{7},{8},{9}} => [4,1,1,1,1,1,1] => [1,1,1,1,1,1,4]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,5,6,7,8,9},{4}} => [2,6,1] => [1,6,2]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,4,5,6,7},{3},{8,9}} => [6,1,2] => [2,1,6]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,7,8,9},{6}} => [3,5,1] => [1,5,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,5,6},{4},{7,8,9}} => [5,1,3] => [3,1,5]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2,3,4},{5,6,7,9},{8}} => [4,4,1] => [1,4,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4,5,6},{7,9},{8}} => [6,2,1] => [1,2,6]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => {{1,2,10},{3,4,5,6,7,8,9}} => [3,7] => [7,3]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3,4,5},{6,7,9},{8}} => [5,3,1] => [1,3,5]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => {{1,2,3,10},{4,5,6,7,8,9}} => [4,6] => [6,4]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,10},{5,6,7,8,9}} => [5,5] => [5,5]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,9},{8}} => [3,5,1] => [1,5,3]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,10},{6,7,8,9}} => [6,4] => [4,6]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,10},{7,8,9}} => [7,3] => [3,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,4},{5},{6,9},{7},{8}} => [1,1,2,1,2,1,1] => [1,1,2,1,2,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,4},{2},{3},{5},{6,9},{7},{8}} => [2,1,1,1,2,1,1] => [1,1,2,1,1,1,2]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,7,8,9,10},{2,3,4,5,6}} => [5,5] => [5,5]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,4,6,8,10},{3},{5},{7},{9}} => [1,5,1,1,1,1] => [1,1,1,1,5,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,4,6,10},{3},{5},{7,9},{8}} => [1,4,1,1,2,1] => [1,2,1,1,4,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,4,8,10},{3},{5,7},{6},{9}} => [1,4,1,2,1,1] => [1,1,2,1,4,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,4,10},{3},{5,7,9},{6},{8}} => [1,3,1,3,1,1] => [1,1,3,1,3,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1},{2,4,10},{3},{5,9},{6,8},{7}} => [1,3,1,2,2,1] => [1,2,2,1,3,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,6,8,10},{3,5},{4},{7},{9}} => [1,4,2,1,1,1] => [1,1,1,2,4,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,6,10},{3,5},{4},{7,9},{8}} => [1,3,2,1,2,1] => [1,2,1,2,3,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,8,10},{3,5,7},{4},{6},{9}} => [1,3,3,1,1,1] => [1,1,1,3,3,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,8,10},{3,7},{4,6},{5},{9}} => [1,3,2,2,1,1] => [1,1,2,2,3,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,10},{3,5,7,9},{4},{6},{8}} => [1,2,4,1,1,1] => [1,1,1,4,2,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1},{2,10},{3,5,9},{4},{6,8},{7}} => [1,2,3,1,2,1] => [1,2,1,3,2,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,10},{3,7,9},{4,6},{5},{8}} => [1,2,3,2,1,1] => [1,1,2,3,2,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1},{2,10},{3,9},{4,6,8},{5},{7}} => [1,2,2,3,1,1] => [1,1,3,2,2,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,10},{3,9},{4,8},{5,7},{6}} => [1,2,2,2,2,1] => [1,2,2,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,6,8,10},{5},{7},{9}} => [2,1,4,1,1,1] => [1,1,1,4,1,2]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3},{2},{4,6,10},{5},{7,9},{8}} => [2,1,3,1,2,1] => [1,2,1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,8,10},{5,7},{6},{9}} => [2,1,3,2,1,1] => [1,1,2,3,1,2]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,3},{2},{4,10},{5,7,9},{6},{8}} => [2,1,2,3,1,1] => [1,1,3,2,1,2]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,3},{2},{4,10},{5,9},{6,8},{7}} => [2,1,2,2,2,1] => [1,2,2,2,1,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4},{6,8,10},{7},{9}} => [3,1,1,3,1,1] => [1,1,3,1,1,3]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3,5},{2},{4},{6,10},{7,9},{8}} => [3,1,1,2,2,1] => [1,2,2,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,5},{2,4},{3},{6,8,10},{7},{9}} => [2,2,1,3,1,1] => [1,1,3,1,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3},{6,10},{7,9},{8}} => [2,2,1,2,2,1] => [1,2,2,1,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,3,5,7},{2},{4},{6},{8,10},{9}} => [4,1,1,1,2,1] => [1,2,1,1,1,4]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,7},{2},{4,6},{5},{8,10},{9}} => [3,1,2,1,2,1] => [1,2,1,2,1,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,5,7},{2,4},{3},{6},{8,10},{9}} => [3,2,1,1,2,1] => [1,2,1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,7},{2,4,6},{3},{5},{8,10},{9}} => [2,3,1,1,2,1] => [1,2,1,1,3,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,7},{2,6},{3,5},{4},{8,10},{9}} => [2,2,2,1,2,1] => [1,2,1,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => [5,1,1,1,1,1] => [1,1,1,1,1,5]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,3,5,9},{2},{4},{6,8},{7},{10}} => [4,1,1,2,1,1] => [1,1,2,1,1,4]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,3,7,9},{2},{4,6},{5},{8},{10}} => [4,1,2,1,1,1] => [1,1,1,2,1,4]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,3,9},{2},{4,6,8},{5},{7},{10}} => [3,1,3,1,1,1] => [1,1,1,3,1,3]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,3,9},{2},{4,8},{5,7},{6},{10}} => [3,1,2,2,1,1] => [1,1,2,2,1,3]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,5,7,9},{2,4},{3},{6},{8},{10}} => [4,2,1,1,1,1] => [1,1,1,1,2,4]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,5,9},{2,4},{3},{6,8},{7},{10}} => [3,2,1,2,1,1] => [1,1,2,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,7,9},{2,4,6},{3},{5},{8},{10}} => [3,3,1,1,1,1] => [1,1,1,1,3,3]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,7,9},{2,6},{3,5},{4},{8},{10}} => [3,2,2,1,1,1] => [1,1,1,2,2,3]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,9},{2,4,6,8},{3},{5},{7},{10}} => [2,4,1,1,1,1] => [1,1,1,1,4,2]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,9},{2,4,8},{3},{5,7},{6},{10}} => [2,3,1,2,1,1] => [1,1,2,1,3,2]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,9},{2,6,8},{3,5},{4},{7},{10}} => [2,3,2,1,1,1] => [1,1,1,2,3,2]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,9},{2,8},{3,5,7},{4},{6},{10}} => [2,2,3,1,1,1] => [1,1,1,3,2,2]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,9},{2,8},{3,7},{4,6},{5},{10}} => [2,2,2,2,1,1] => [1,1,2,2,2,2]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => {{1},{2,4,6,8,10,12},{3},{5},{7},{9},{11}} => [1,6,1,1,1,1,1] => [1,1,1,1,1,6,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => {{1},{2,4,6,8,12},{3},{5},{7},{9,11},{10}} => [1,5,1,1,1,2,1] => [1,2,1,1,1,5,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => {{1},{2,4,6,10,12},{3},{5},{7,9},{8},{11}} => [1,5,1,1,2,1,1] => [1,1,2,1,1,5,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => {{1},{2,4,6,12},{3},{5},{7,9,11},{8},{10}} => [1,4,1,1,3,1,1] => [1,1,3,1,1,4,1]
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => {{1},{2,4,6,12},{3},{5},{7,11},{8,10},{9}} => [1,4,1,1,2,2,1] => [1,2,2,1,1,4,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,4,8,10,12},{3},{5,7},{6},{9},{11}} => [1,5,1,2,1,1,1] => [1,1,1,2,1,5,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,4,8,12},{3},{5,7},{6},{9,11},{10}} => [1,4,1,2,1,2,1] => [1,2,1,2,1,4,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => {{1},{2,4,10,12},{3},{5,7,9},{6},{8},{11}} => [1,4,1,3,1,1,1] => [1,1,1,3,1,4,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,4,10,12},{3},{5,9},{6,8},{7},{11}} => [1,4,1,2,2,1,1] => [1,1,2,2,1,4,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,7,9,11},{6},{8},{10}} => [1,3,1,4,1,1,1] => [1,1,1,4,1,3,1]
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,7,11},{6},{8,10},{9}} => [1,3,1,3,1,2,1] => [1,2,1,3,1,3,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,9,11},{6,8},{7},{10}} => [1,3,1,3,2,1,1] => [1,1,2,3,1,3,1]
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,11},{6,8,10},{7},{9}} => [1,3,1,2,3,1,1] => [1,1,3,2,1,3,1]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,11},{6,10},{7,9},{8}} => [1,3,1,2,2,2,1] => [1,2,2,2,1,3,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,6,8,10,12},{3,5},{4},{7},{9},{11}} => [1,5,2,1,1,1,1] => [1,1,1,1,2,5,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,6,8,12},{3,5},{4},{7},{9,11},{10}} => [1,4,2,1,1,2,1] => [1,2,1,1,2,4,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,6,10,12},{3,5},{4},{7,9},{8},{11}} => [1,4,2,1,2,1,1] => [1,1,2,1,2,4,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,6,12},{3,5},{4},{7,9,11},{8},{10}} => [1,3,2,1,3,1,1] => [1,1,3,1,2,3,1]
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1},{2,6,12},{3,5},{4},{7,11},{8,10},{9}} => [1,3,2,1,2,2,1] => [1,2,2,1,2,3,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,8,10,12},{3,5,7},{4},{6},{9},{11}} => [1,4,3,1,1,1,1] => [1,1,1,1,3,4,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,8,12},{3,5,7},{4},{6},{9,11},{10}} => [1,3,3,1,1,2,1] => [1,2,1,1,3,3,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,8,10,12},{3,7},{4,6},{5},{9},{11}} => [1,4,2,2,1,1,1] => [1,1,1,2,2,4,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,8,12},{3,7},{4,6},{5},{9,11},{10}} => [1,3,2,2,1,2,1] => [1,2,1,2,2,3,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,5,7,9},{4},{6},{8},{11}} => [1,3,4,1,1,1,1] => [1,1,1,1,4,3,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,5,9},{4},{6,8},{7},{11}} => [1,3,3,1,2,1,1] => [1,1,2,1,3,3,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,7,9},{4,6},{5},{8},{11}} => [1,3,3,2,1,1,1] => [1,1,1,2,3,3,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,9},{4,6,8},{5},{7},{11}} => [1,3,2,3,1,1,1] => [1,1,1,3,2,3,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,9},{4,8},{5,7},{6},{11}} => [1,3,2,2,2,1,1] => [1,1,2,2,2,3,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => {{1},{2,12},{3,5,7,9,11},{4},{6},{8},{10}} => [1,2,5,1,1,1,1] => [1,1,1,1,5,2,1]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => {{1},{2,12},{3,5,7,11},{4},{6},{8,10},{9}} => [1,2,4,1,1,2,1] => [1,2,1,1,4,2,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,12},{3,5,9,11},{4},{6,8},{7},{10}} => [1,2,4,1,2,1,1] => [1,1,2,1,4,2,1]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,5,11},{4},{6,8,10},{7},{9}} => [1,2,3,1,3,1,1] => [1,1,3,1,3,2,1]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,5,11},{4},{6,10},{7,9},{8}} => [1,2,3,1,2,2,1] => [1,2,2,1,3,2,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,12},{3,7,9,11},{4,6},{5},{8},{10}} => [1,2,4,2,1,1,1] => [1,1,1,2,4,2,1]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,7,11},{4,6},{5},{8,10},{9}} => [1,2,3,2,1,2,1] => [1,2,1,2,3,2,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,9,11},{4,6,8},{5},{7},{10}} => [1,2,3,3,1,1,1] => [1,1,1,3,3,2,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,9,11},{4,8},{5,7},{6},{10}} => [1,2,3,2,2,1,1] => [1,1,2,2,3,2,1]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,6,8,10},{5},{7},{9}} => [1,2,2,4,1,1,1] => [1,1,1,4,2,2,1]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,6,10},{5},{7,9},{8}} => [1,2,2,3,1,2,1] => [1,2,1,3,2,2,1]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,8,10},{5,7},{6},{9}} => [1,2,2,3,2,1,1] => [1,1,2,3,2,2,1]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,10},{5,7,9},{6},{8}} => [1,2,2,2,3,1,1] => [1,1,3,2,2,2,1]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,10},{5,9},{6,8},{7}} => [1,2,2,2,2,2,1] => [1,2,2,2,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,3},{2},{4,6,8,10,12},{5},{7},{9},{11}} => [2,1,5,1,1,1,1] => [1,1,1,1,5,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,3},{2},{4,6,8,12},{5},{7},{9,11},{10}} => [2,1,4,1,1,2,1] => [1,2,1,1,4,1,2]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,6,10,12},{5},{7,9},{8},{11}} => [2,1,4,1,2,1,1] => [1,1,2,1,4,1,2]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1,3},{2},{4,6,12},{5},{7,9,11},{8},{10}} => [2,1,3,1,3,1,1] => [1,1,3,1,3,1,2]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1,3},{2},{4,6,12},{5},{7,11},{8,10},{9}} => [2,1,3,1,2,2,1] => [1,2,2,1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,8,10,12},{5,7},{6},{9},{11}} => [2,1,4,2,1,1,1] => [1,1,1,2,4,1,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3},{2},{4,8,12},{5,7},{6},{9,11},{10}} => [2,1,3,2,1,2,1] => [1,2,1,2,3,1,2]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,10,12},{5,7,9},{6},{8},{11}} => [2,1,3,3,1,1,1] => [1,1,1,3,3,1,2]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,10,12},{5,9},{6,8},{7},{11}} => [2,1,3,2,2,1,1] => [1,1,2,2,3,1,2]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,3},{2},{4,12},{5,7,9,11},{6},{8},{10}} => [2,1,2,4,1,1,1] => [1,1,1,4,2,1,2]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,3},{2},{4,12},{5,7,11},{6},{8,10},{9}} => [2,1,2,3,1,2,1] => [1,2,1,3,2,1,2]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1,3},{2},{4,12},{5,9,11},{6,8},{7},{10}} => [2,1,2,3,2,1,1] => [1,1,2,3,2,1,2]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,3},{2},{4,12},{5,11},{6,8,10},{7},{9}} => [2,1,2,2,3,1,1] => [1,1,3,2,2,1,2]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,3},{2},{4,12},{5,11},{6,10},{7,9},{8}} => [2,1,2,2,2,2,1] => [1,2,2,2,2,1,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3,5},{2},{4},{6,8,10,12},{7},{9},{11}} => [3,1,1,4,1,1,1] => [1,1,1,4,1,1,3]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3,5},{2},{4},{6,8,12},{7},{9,11},{10}} => [3,1,1,3,1,2,1] => [1,2,1,3,1,1,3]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4},{6,10,12},{7,9},{8},{11}} => [3,1,1,3,2,1,1] => [1,1,2,3,1,1,3]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,3,5},{2},{4},{6,12},{7,9,11},{8},{10}} => [3,1,1,2,3,1,1] => [1,1,3,2,1,1,3]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,3,5},{2},{4},{6,12},{7,11},{8,10},{9}} => [3,1,1,2,2,2,1] => [1,2,2,2,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,5},{2,4},{3},{6,8,10,12},{7},{9},{11}} => [2,2,1,4,1,1,1] => [1,1,1,4,1,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,5},{2,4},{3},{6,8,12},{7},{9,11},{10}} => [2,2,1,3,1,2,1] => [1,2,1,3,1,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,5},{2,4},{3},{6,10,12},{7,9},{8},{11}} => [2,2,1,3,2,1,1] => [1,1,2,3,1,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,5},{2,4},{3},{6,12},{7,9,11},{8},{10}} => [2,2,1,2,3,1,1] => [1,1,3,2,1,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,5},{2,4},{3},{6,12},{7,11},{8,10},{9}} => [2,2,1,2,2,2,1] => [1,2,2,2,1,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3,5,7},{2},{4},{6},{8,10,12},{9},{11}} => [4,1,1,1,3,1,1] => [1,1,3,1,1,1,4]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3,5,7},{2},{4},{6},{8,12},{9,11},{10}} => [4,1,1,1,2,2,1] => [1,2,2,1,1,1,4]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3,7},{2},{4,6},{5},{8,10,12},{9},{11}} => [3,1,2,1,3,1,1] => [1,1,3,1,2,1,3]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3,7},{2},{4,6},{5},{8,12},{9,11},{10}} => [3,1,2,1,2,2,1] => [1,2,2,1,2,1,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2,4},{3},{6},{8,10,12},{9},{11}} => [3,2,1,1,3,1,1] => [1,1,3,1,1,2,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,5,7},{2,4},{3},{6},{8,12},{9,11},{10}} => [3,2,1,1,2,2,1] => [1,2,2,1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,7},{2,4,6},{3},{5},{8,10,12},{9},{11}} => [2,3,1,1,3,1,1] => [1,1,3,1,1,3,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,7},{2,4,6},{3},{5},{8,12},{9,11},{10}} => [2,3,1,1,2,2,1] => [1,2,2,1,1,3,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,7},{2,6},{3,5},{4},{8,10,12},{9},{11}} => [2,2,2,1,3,1,1] => [1,1,3,1,2,2,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,5},{4},{8,12},{9,11},{10}} => [2,2,2,1,2,2,1] => [1,2,2,1,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => {{1,3,5,7,9},{2},{4},{6},{8},{10,12},{11}} => [5,1,1,1,1,2,1] => [1,2,1,1,1,1,5]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,3,5,9},{2},{4},{6,8},{7},{10,12},{11}} => [4,1,1,2,1,2,1] => [1,2,1,2,1,1,4]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,3,7,9},{2},{4,6},{5},{8},{10,12},{11}} => [4,1,2,1,1,2,1] => [1,2,1,1,2,1,4]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,9},{2},{4,6,8},{5},{7},{10,12},{11}} => [3,1,3,1,1,2,1] => [1,2,1,1,3,1,3]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,9},{2},{4,8},{5,7},{6},{10,12},{11}} => [3,1,2,2,1,2,1] => [1,2,1,2,2,1,3]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,5,7,9},{2,4},{3},{6},{8},{10,12},{11}} => [4,2,1,1,1,2,1] => [1,2,1,1,1,2,4]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,5,9},{2,4},{3},{6,8},{7},{10,12},{11}} => [3,2,1,2,1,2,1] => [1,2,1,2,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,7,9},{2,4,6},{3},{5},{8},{10,12},{11}} => [3,3,1,1,1,2,1] => [1,2,1,1,1,3,3]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,7,9},{2,6},{3,5},{4},{8},{10,12},{11}} => [3,2,2,1,1,2,1] => [1,2,1,1,2,2,3]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,4,6,8},{3},{5},{7},{10,12},{11}} => [2,4,1,1,1,2,1] => [1,2,1,1,1,4,2]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,4,8},{3},{5,7},{6},{10,12},{11}} => [2,3,1,2,1,2,1] => [1,2,1,2,1,3,2]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,6,8},{3,5},{4},{7},{10,12},{11}} => [2,3,2,1,1,2,1] => [1,2,1,1,2,3,2]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,8},{3,5,7},{4},{6},{10,12},{11}} => [2,2,3,1,1,2,1] => [1,2,1,1,3,2,2]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,8},{3,7},{4,6},{5},{10,12},{11}} => [2,2,2,2,1,2,1] => [1,2,1,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,3,5,7,9,11},{2},{4},{6},{8},{10},{12}} => [6,1,1,1,1,1,1] => [1,1,1,1,1,1,6]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => {{1,3,5,7,11},{2},{4},{6},{8,10},{9},{12}} => [5,1,1,1,2,1,1] => [1,1,2,1,1,1,5]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,3,5,9,11},{2},{4},{6,8},{7},{10},{12}} => [5,1,1,2,1,1,1] => [1,1,1,2,1,1,5]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => {{1,3,5,11},{2},{4},{6,8,10},{7},{9},{12}} => [4,1,1,3,1,1,1] => [1,1,1,3,1,1,4]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => {{1,3,5,11},{2},{4},{6,10},{7,9},{8},{12}} => [4,1,1,2,2,1,1] => [1,1,2,2,1,1,4]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,3,7,9,11},{2},{4,6},{5},{8},{10},{12}} => [5,1,2,1,1,1,1] => [1,1,1,1,2,1,5]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,3,7,11},{2},{4,6},{5},{8,10},{9},{12}} => [4,1,2,1,2,1,1] => [1,1,2,1,2,1,4]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,3,9,11},{2},{4,6,8},{5},{7},{10},{12}} => [4,1,3,1,1,1,1] => [1,1,1,1,3,1,4]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,3,9,11},{2},{4,8},{5,7},{6},{10},{12}} => [4,1,2,2,1,1,1] => [1,1,1,2,2,1,4]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,6,8,10},{5},{7},{9},{12}} => [3,1,4,1,1,1,1] => [1,1,1,1,4,1,3]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,6,10},{5},{7,9},{8},{12}} => [3,1,3,1,2,1,1] => [1,1,2,1,3,1,3]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,8,10},{5,7},{6},{9},{12}} => [3,1,3,2,1,1,1] => [1,1,1,2,3,1,3]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,10},{5,7,9},{6},{8},{12}} => [3,1,2,3,1,1,1] => [1,1,1,3,2,1,3]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,10},{5,9},{6,8},{7},{12}} => [3,1,2,2,2,1,1] => [1,1,2,2,2,1,3]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,5,7,9,11},{2,4},{3},{6},{8},{10},{12}} => [5,2,1,1,1,1,1] => [1,1,1,1,1,2,5]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,5,7,11},{2,4},{3},{6},{8,10},{9},{12}} => [4,2,1,1,2,1,1] => [1,1,2,1,1,2,4]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,5,9,11},{2,4},{3},{6,8},{7},{10},{12}} => [4,2,1,2,1,1,1] => [1,1,1,2,1,2,4]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,5,11},{2,4},{3},{6,8,10},{7},{9},{12}} => [3,2,1,3,1,1,1] => [1,1,1,3,1,2,3]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,5,11},{2,4},{3},{6,10},{7,9},{8},{12}} => [3,2,1,2,2,1,1] => [1,1,2,2,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,7,9,11},{2,4,6},{3},{5},{8},{10},{12}} => [4,3,1,1,1,1,1] => [1,1,1,1,1,3,4]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,7,11},{2,4,6},{3},{5},{8,10},{9},{12}} => [3,3,1,1,2,1,1] => [1,1,2,1,1,3,3]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,7,9,11},{2,6},{3,5},{4},{8},{10},{12}} => [4,2,2,1,1,1,1] => [1,1,1,1,2,2,4]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,7,11},{2,6},{3,5},{4},{8,10},{9},{12}} => [3,2,2,1,2,1,1] => [1,1,2,1,2,2,3]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,4,6,8},{3},{5},{7},{10},{12}} => [3,4,1,1,1,1,1] => [1,1,1,1,1,4,3]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,4,8},{3},{5,7},{6},{10},{12}} => [3,3,1,2,1,1,1] => [1,1,1,2,1,3,3]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,6,8},{3,5},{4},{7},{10},{12}} => [3,3,2,1,1,1,1] => [1,1,1,1,2,3,3]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,8},{3,5,7},{4},{6},{10},{12}} => [3,2,3,1,1,1,1] => [1,1,1,1,3,2,3]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,8},{3,7},{4,6},{5},{10},{12}} => [3,2,2,2,1,1,1] => [1,1,1,2,2,2,3]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => {{1,11},{2,4,6,8,10},{3},{5},{7},{9},{12}} => [2,5,1,1,1,1,1] => [1,1,1,1,1,5,2]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => {{1,11},{2,4,6,10},{3},{5},{7,9},{8},{12}} => [2,4,1,1,2,1,1] => [1,1,2,1,1,4,2]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,11},{2,4,8,10},{3},{5,7},{6},{9},{12}} => [2,4,1,2,1,1,1] => [1,1,1,2,1,4,2]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,4,10},{3},{5,7,9},{6},{8},{12}} => [2,3,1,3,1,1,1] => [1,1,1,3,1,3,2]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,4,10},{3},{5,9},{6,8},{7},{12}} => [2,3,1,2,2,1,1] => [1,1,2,2,1,3,2]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,11},{2,6,8,10},{3,5},{4},{7},{9},{12}} => [2,4,2,1,1,1,1] => [1,1,1,1,2,4,2]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,6,10},{3,5},{4},{7,9},{8},{12}} => [2,3,2,1,2,1,1] => [1,1,2,1,2,3,2]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,8,10},{3,5,7},{4},{6},{9},{12}} => [2,3,3,1,1,1,1] => [1,1,1,1,3,3,2]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,8,10},{3,7},{4,6},{5},{9},{12}} => [2,3,2,2,1,1,1] => [1,1,1,2,2,3,2]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,5,7,9},{4},{6},{8},{12}} => [2,2,4,1,1,1,1] => [1,1,1,1,4,2,2]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,5,9},{4},{6,8},{7},{12}} => [2,2,3,1,2,1,1] => [1,1,2,1,3,2,2]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,7,9},{4,6},{5},{8},{12}} => [2,2,3,2,1,1,1] => [1,1,1,2,3,2,2]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,9},{4,6,8},{5},{7},{12}} => [2,2,2,3,1,1,1] => [1,1,1,3,2,2,2]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,9},{4,8},{5,7},{6},{12}} => [2,2,2,2,2,1,1] => [1,1,2,2,2,2,2]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8,9,10,11},{2}} => [10,1] => [1,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => {{1,8,9,10},{2,3,4,5,6,7}} => [4,6] => [6,4]
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,5,6,7,8,9},{3,4}} => [1,6,2] => [2,6,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => {{1,9,10},{2,3,4,5,6,7,8}} => [3,7] => [7,3]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,6,7,8,9,10},{2,3,4,5}} => [6,4] => [4,6]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,5,6,7,8,9,10},{2,3,4}} => [7,3] => [3,7]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,4,5,6,7,8,9,10},{2,3}} => [8,2] => [2,8]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,8},{2},{3},{4},{5},{6,7},{9}} => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7},{8},{9}} => [2,1,2,1,1,1,1] => [1,1,1,1,2,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5},{6},{7,9},{8}} => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,4,5,6,7,8},{2,3},{9}} => [6,2,1] => [1,2,6]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => {{1,2,4,6,8,10},{3},{5},{7},{9}} => [6,1,1,1,1] => [1,1,1,1,6]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,5},{2},{3},{4},{6,9},{7},{8}} => [2,1,1,1,2,1,1] => [1,1,2,1,1,1,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,3,4,5,6},{2},{7,8,9}} => [5,1,3] => [3,1,5]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,7},{2},{3},{4},{5,6},{8},{9}} => [2,1,1,1,2,1,1] => [1,1,2,1,1,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,6},{2},{3},{4,5},{7},{8},{9}} => [2,1,1,2,1,1,1] => [1,1,1,2,1,1,2]
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
Map
to composition
Description
The integer composition of block sizes of a set partition.
For a set partition of $\{1,2,\dots,n\}$, this is the integer composition of $n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.
For a set partition of $\{1,2,\dots,n\}$, this is the integer composition of $n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.
Map
reverse
Description
Return the reversal of a composition.
That is, the composition $(i_1, i_2, \ldots, i_k)$ is sent to $(i_k, i_{k-1}, \ldots, i_1)$.
That is, the composition $(i_1, i_2, \ldots, i_k)$ is sent to $(i_k, i_{k-1}, \ldots, i_1)$.
searching the database
Sorry, this map was not found in the database.