Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
St000492: Set partitions ⟶ ℤ
Values
[1,0,1,0] => [1] => [1,0,1,0] => {{1},{2}} => 1
[1,0,1,0,1,0] => [2,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => 3
[1,0,1,1,0,0] => [1,1] => [1,0,1,1,0,0] => {{1},{2,3}} => 1
[1,1,0,0,1,0] => [2] => [1,1,0,0,1,0] => {{1,2},{3}} => 2
[1,1,0,1,0,0] => [1] => [1,0,1,0] => {{1},{2}} => 1
[1,0,1,0,1,0,1,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => 6
[1,0,1,0,1,1,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => 3
[1,0,1,1,0,0,1,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 4
[1,0,1,1,0,1,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => 3
[1,0,1,1,1,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => 1
[1,1,0,0,1,0,1,0] => [3,2] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 5
[1,1,0,0,1,1,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 2
[1,1,0,1,0,0,1,0] => [3,1] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => 4
[1,1,0,1,0,1,0,0] => [2,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => 3
[1,1,0,1,1,0,0,0] => [1,1] => [1,0,1,1,0,0] => {{1},{2,3}} => 1
[1,1,1,0,0,0,1,0] => [3] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 3
[1,1,1,0,0,1,0,0] => [2] => [1,1,0,0,1,0] => {{1,2},{3}} => 2
[1,1,1,0,1,0,0,0] => [1] => [1,0,1,0] => {{1},{2}} => 1
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 10
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 6
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 7
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => 6
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 3
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 8
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 4
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 7
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => 6
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => 3
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => 3
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => 4
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => 1
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 9
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 6
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => 5
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 2
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 8
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => 4
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 7
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => 6
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => 3
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => 5
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 4
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => 3
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => 1
[1,1,1,0,0,0,1,0,1,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 7
[1,1,1,0,0,0,1,1,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 3
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 5
[1,1,1,0,0,1,0,1,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 5
[1,1,1,0,0,1,1,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => 6
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => 4
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => 3
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => {{1},{2,3}} => 1
[1,1,1,1,0,0,0,0,1,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 4
[1,1,1,1,0,0,0,1,0,0] => [3] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 3
[1,1,1,1,0,0,1,0,0,0] => [2] => [1,1,0,0,1,0] => {{1,2},{3}} => 2
[1,1,1,1,0,1,0,0,0,0] => [1] => [1,0,1,0] => {{1},{2}} => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => 15
[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => 10
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 11
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}} => 10
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 6
[1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 7
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,5},{4},{6}} => 11
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}} => 10
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,5,6},{4}} => 6
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 8
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,6},{4,5}} => 6
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => 7
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 13
[1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 8
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,6},{5}} => 8
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5},{6}} => 12
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6}} => 7
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,5},{3},{4},{6}} => 11
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}} => 10
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}} => 6
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,4,5},{3},{6}} => 8
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => 6
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => 7
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}} => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 10
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 5
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,5},{3,4},{6}} => 8
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => 7
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}} => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 9
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => 6
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => 8
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}} => 4
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}} => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}} => 5
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => 1
>>> Load all 1366 entries. <<<[1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => 14
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 10
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4,6},{5}} => 9
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 5
[1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 11
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,5},{4},{6}} => 10
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,6},{4},{5}} => 9
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 7
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => 5
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}} => 6
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}} => 13
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5,6}} => 8
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6}} => 9
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6},{5}} => 8
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}} => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}} => 12
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6}} => 7
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}} => 11
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 10
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 8
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 7
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => {{1,3,4},{2},{5},{6}} => 10
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 8
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 8
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 4
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 9
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 7
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => 6
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => 6
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 12
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 7
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 8
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => 7
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => {{1,4},{2,3},{5},{6}} => 10
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => 5
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 9
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 9
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 6
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 6
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => 5
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 11
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => 6
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 8
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 8
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 10
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 7
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => 7
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => 5
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 9
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 6
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 7
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 7
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 5
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 5
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 8
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => 6
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => {{1},{2,3}} => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [1,1,0,0,1,0] => {{1,2},{3}} => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [1,0,1,0] => {{1},{2}} => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => 21
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => 15
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 16
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,7},{6}} => 15
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 17
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 11
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4,6},{5},{7}} => 16
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4,7},{5},{6}} => 15
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4,6,7},{5}} => 10
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 12
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4,7},{5,6}} => 10
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4,5,7},{6}} => 11
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 18
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 12
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 13
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5,7},{6}} => 12
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7}} => 17
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,5},{4},{6,7}} => 11
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,6},{4},{5},{7}} => 16
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,7},{4},{5},{6}} => 15
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4},{5}} => 10
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,5,6},{4},{7}} => 12
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,7},{4},{5,6}} => 10
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,5,7},{4},{6}} => 11
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,5,6,7},{4}} => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,6},{4,5},{7}} => 12
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,7},{4,5},{6}} => 11
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4,5}} => 6
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,6},{5},{7}} => 13
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,7},{4,6},{5}} => 10
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,7},{5},{6}} => 12
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,6,7},{5}} => 7
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,7},{4,5,6}} => 6
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,7},{5,6}} => 7
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,7},{6}} => 8
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 19
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 13
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5,7},{6}} => 13
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 15
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4,6},{5},{7}} => 14
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4,7},{5},{6}} => 13
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4,6,7},{5}} => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 10
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4,7},{5,6}} => 8
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4,5,7},{6}} => 9
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7}} => 18
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6,7}} => 12
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5,6},{7}} => 13
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5,7},{6}} => 12
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5,6,7}} => 7
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7}} => 17
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,5},{3},{4},{6,7}} => 11
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,6},{3},{4},{5},{7}} => 16
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,7},{3},{4},{5},{6}} => 15
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4},{5}} => 10
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3},{4},{7}} => 12
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,7},{3},{4},{5,6}} => 10
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3},{4},{6}} => 11
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3},{4}} => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7}} => 14
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,4,5},{3},{6,7}} => 8
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,6},{3},{4,5},{7}} => 12
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,7},{3},{4,5},{6}} => 11
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4,5}} => 6
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,4,6},{3},{5},{7}} => 13
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2,7},{3},{4,6},{5}} => 10
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,4,7},{3},{5},{6}} => 12
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,4,6,7},{3},{5}} => 7
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,4,5,6},{3},{7}} => 9
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,7},{3},{4,5,6}} => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,4,7},{3},{5,6}} => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,4,5,7},{3},{6}} => 8
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,4,5,6,7},{3}} => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 16
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 10
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4},{5,7},{6}} => 10
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7}} => 14
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,5},{3,4},{6,7}} => 8
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,6},{3,4},{5},{7}} => 13
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2,7},{3,4},{5},{6}} => 12
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3,4},{5}} => 7
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3,4},{7}} => 9
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,7},{3,4},{5,6}} => 7
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3,4},{6}} => 8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3,4}} => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7}} => 15
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,5},{4},{6,7}} => 9
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,6},{3,5},{4},{7}} => 12
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,7},{3,5},{4},{6}} => 11
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,5},{4}} => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,6},{4},{5},{7}} => 14
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4},{5}} => 10
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,7},{4},{5},{6}} => 13
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4},{5}} => 8
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,5,6},{4},{7}} => 10
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,7},{3,5,6},{4}} => 6
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,7},{4},{5,6}} => 8
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,5,7},{4},{6}} => 9
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,5,6,7},{4}} => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 12
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 6
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,6},{3,4,5},{7}} => 9
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,7},{3,4,5},{6}} => 8
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,4,5}} => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,6},{4,5},{7}} => 10
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4,5}} => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,7},{4,5},{6}} => 9
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4,5}} => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,6},{5},{7}} => 11
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,7},{3,4,6},{5}} => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,7},{4,6},{5}} => 8
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,7},{5},{6}} => 10
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,6,7},{5}} => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,7},{3,4,5,6}} => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,7},{4,5,6}} => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,7},{5,6}} => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,7},{6}} => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => 20
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 15
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5,7},{6}} => 14
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 9
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 16
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 10
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4,6},{5},{7}} => 15
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4,7},{5},{6}} => 14
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4,6,7},{5}} => 9
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 11
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4,7},{5,6}} => 9
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4,5,7},{6}} => 10
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 17
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 11
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,4},{5,7},{6}} => 11
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7}} => 16
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2},{3,5},{4},{6,7}} => 10
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,2},{3,6},{4},{5},{7}} => 15
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3,7},{4},{5},{6}} => 14
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,2},{3,6,7},{4},{5}} => 9
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3,5,6},{4},{7}} => 11
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3,7},{4},{5,6}} => 9
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2},{3,5,7},{4},{6}} => 10
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3,5,6,7},{4}} => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 13
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3,6},{4,5},{7}} => 11
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3,7},{4,5},{6}} => 10
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3,6,7},{4,5}} => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3,4,6},{5},{7}} => 12
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3,7},{4,6},{5}} => 9
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3,4,7},{5},{6}} => 11
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2},{3,4,6,7},{5}} => 6
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2},{3,7},{4,5,6}} => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3,4,7},{5,6}} => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3,4,5,7},{6}} => 7
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7}} => 19
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6,7}} => 13
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5,6},{7}} => 14
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5,7},{6}} => 13
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5,6,7}} => 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,3},{2},{4,5},{6},{7}} => 15
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4,5},{6,7}} => 9
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4,6},{5},{7}} => 14
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4,7},{5},{6}} => 13
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4,6,7},{5}} => 8
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4,5,6},{7}} => 10
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4,7},{5,6}} => 8
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,3},{2},{4,5,7},{6}} => 9
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4,5,6,7}} => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7}} => 18
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2},{3},{5},{6,7}} => 12
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5,6},{7}} => 13
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5,7},{6}} => 12
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5,6,7}} => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7}} => 17
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2},{3},{4},{6,7}} => 11
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7}} => 16
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => 15
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => 10
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3},{4},{7}} => 12
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 11
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}} => 10
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7}} => 14
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2},{3},{6,7}} => 8
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2},{3},{4,5},{7}} => 12
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2},{3},{5},{7}} => 13
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,5},{4},{6}} => 11
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}} => 10
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,5,6},{4}} => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2},{3},{7}} => 9
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 8
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,6},{4,5}} => 6
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => 7
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7}} => 16
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6,7}} => 10
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,3,4},{2},{5,6},{7}} => 11
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,3,4},{2},{5,7},{6}} => 10
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,3,4},{2},{5,6,7}} => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7}} => 14
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2},{3,4},{6,7}} => 8
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2},{3,4},{5},{7}} => 13
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 13
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3,4},{7}} => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,6},{5}} => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7}} => 15
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,3,5},{2},{4},{6,7}} => 9
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2},{3,5},{4},{7}} => 12
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5},{6}} => 12
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6}} => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,3,6},{2},{4},{5},{7}} => 14
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,5},{3},{4},{6}} => 11
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}} => 10
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}} => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,3,5,6},{2},{4},{7}} => 10
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,4,5},{3},{6}} => 8
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => 7
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}} => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7}} => 12
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,3,4,5},{2},{6,7}} => 6
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2},{3,4,5},{7}} => 9
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 10
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,3,6},{2},{4,5},{7}} => 10
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,5},{3,4},{6}} => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => 7
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}} => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,3,4,6},{2},{5},{7}} => 11
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 9
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => 6
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => 8
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}} => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,3,4,5,6},{2},{7}} => 7
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}} => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}} => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 18
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 12
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 13
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5,7},{6}} => 12
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 14
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 8
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4,6},{5},{7}} => 13
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3},{4,7},{5},{6}} => 12
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3},{4,6,7},{5}} => 7
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 9
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4,7},{5,6}} => 7
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4,5,7},{6}} => 8
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7}} => 16
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6,7}} => 10
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2,3},{5,6},{7}} => 11
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2,3},{5,7},{6}} => 10
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2,3},{5,6,7}} => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7}} => 15
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2,3},{4},{6,7}} => 9
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2,3},{4},{5},{7}} => 14
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => 14
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3},{4},{7}} => 10
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 10
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4,6},{5}} => 9
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2,3},{6},{7}} => 12
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2,3},{6,7}} => 6
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2,3},{4,5},{7}} => 10
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 11
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2,3},{5},{7}} => 11
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,5},{4},{6}} => 10
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,6},{4},{5}} => 9
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2,3},{7}} => 7
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 7
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => 5
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}} => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7}} => 17
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,4},{3},{5},{6,7}} => 11
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,4},{3},{5,6},{7}} => 12
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,4},{3},{5,7},{6}} => 11
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,4},{3},{5,6,7}} => 6
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7}} => 14
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2,4},{3},{6,7}} => 8
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2,4},{3},{5},{7}} => 13
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}} => 13
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5,6}} => 8
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,4},{3},{7}} => 9
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6}} => 9
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6},{5}} => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}} => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7}} => 16
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3},{4},{6,7}} => 10
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3},{4},{7}} => 12
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}} => 12
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6}} => 7
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3},{4},{5},{7}} => 15
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}} => 11
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 10
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 6
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3},{4},{7}} => 11
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => 6
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7}} => 13
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,4,5},{3},{6,7}} => 7
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2,4,5},{3},{7}} => 9
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => {{1,3,4},{2},{5},{6}} => 10
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3},{4,5},{7}} => 11
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 8
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 4
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,4,6},{3},{5},{7}} => 12
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 9
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => 6
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,4,5,6},{3},{7}} => 8
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => 6
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 15
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 9
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 10
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4},{5,7},{6}} => 9
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7}} => 12
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,5},{2,3,4},{6,7}} => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,6},{2,3,4},{5},{7}} => 11
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 12
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 7
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3,4},{7}} => 7
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 8
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7}} => 13
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3,4},{6,7}} => 7
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3,4},{7}} => 9
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => {{1,4},{2,3},{5},{6}} => 10
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3,4},{5},{7}} => 12
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 9
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 9
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 8
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 6
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => 5
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7}} => 14
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,5},{4},{6,7}} => 8
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,6},{2,3,5},{4},{7}} => 10
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 11
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => 6
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 8
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 8
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 13
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 10
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => 6
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 9
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => 7
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 11
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 7
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 9
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 8
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 6
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 7
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 9
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 5
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 10
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 8
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => 6
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => {{1},{2,3}} => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => {{1,2},{3}} => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => [1,0,1,0] => {{1},{2}} => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 3
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8},{3}} => 3
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,5,6,7,8},{4}} => 4
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,6,7,8},{5}} => 5
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,7,8},{6}} => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8},{7}} => 7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [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
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [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
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => 21
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => 15
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 16
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,7},{6}} => 15
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 10
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 17
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 11
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4,6},{5},{7}} => 16
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4,7},{5},{6}} => 15
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4,6,7},{5}} => 10
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 12
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4,7},{5,6}} => 10
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4,5,7},{6}} => 11
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 6
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 18
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 12
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 13
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5,7},{6}} => 12
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 7
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7}} => 17
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,5},{4},{6,7}} => 11
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,6},{4},{5},{7}} => 16
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,7},{4},{5},{6}} => 15
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4},{5}} => 10
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,5,6},{4},{7}} => 12
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,7},{4},{5,6}} => 10
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,5,7},{4},{6}} => 11
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,5,6,7},{4}} => 6
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 8
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,6},{4,5},{7}} => 12
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,7},{4,5},{6}} => 11
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4,5}} => 6
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,6},{5},{7}} => 13
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,7},{4,6},{5}} => 10
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,7},{5},{6}} => 12
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,6,7},{5}} => 7
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 9
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,7},{4,5,6}} => 6
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,7},{5,6}} => 7
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,7},{6}} => 8
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 19
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 13
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5,7},{6}} => 13
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 8
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 15
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 9
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4,6},{5},{7}} => 14
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4,7},{5},{6}} => 13
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4,6,7},{5}} => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 10
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4,7},{5,6}} => 8
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4,5,7},{6}} => 9
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7}} => 18
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6,7}} => 12
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5,6},{7}} => 13
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5,7},{6}} => 12
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5,6,7}} => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7}} => 17
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,5},{3},{4},{6,7}} => 11
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,6},{3},{4},{5},{7}} => 16
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,7},{3},{4},{5},{6}} => 15
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4},{5}} => 10
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3},{4},{7}} => 12
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,7},{3},{4},{5,6}} => 10
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3},{4},{6}} => 11
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3},{4}} => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7}} => 14
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,4,5},{3},{6,7}} => 8
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,6},{3},{4,5},{7}} => 12
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,7},{3},{4,5},{6}} => 11
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4,5}} => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,4,6},{3},{5},{7}} => 13
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2,7},{3},{4,6},{5}} => 10
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,4,7},{3},{5},{6}} => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,4,6,7},{3},{5}} => 7
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,4,5,6},{3},{7}} => 9
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,7},{3},{4,5,6}} => 6
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,4,7},{3},{5,6}} => 7
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,4,5,7},{3},{6}} => 8
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,4,5,6,7},{3}} => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 16
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 10
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 11
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4},{5,7},{6}} => 10
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 5
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7}} => 14
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,5},{3,4},{6,7}} => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,6},{3,4},{5},{7}} => 13
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2,7},{3,4},{5},{6}} => 12
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3,4},{5}} => 7
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3,4},{7}} => 9
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,7},{3,4},{5,6}} => 7
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3,4},{6}} => 8
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3,4}} => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7}} => 15
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,5},{4},{6,7}} => 9
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,6},{3,5},{4},{7}} => 12
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,7},{3,5},{4},{6}} => 11
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,5},{4}} => 6
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,6},{4},{5},{7}} => 14
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4},{5}} => 10
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,7},{4},{5},{6}} => 13
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4},{5}} => 8
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,5,6},{4},{7}} => 10
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,7},{3,5,6},{4}} => 6
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,7},{4},{5,6}} => 8
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,5,7},{4},{6}} => 9
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,5,6,7},{4}} => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 12
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 6
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,6},{3,4,5},{7}} => 9
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,7},{3,4,5},{6}} => 8
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,4,5}} => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,6},{4,5},{7}} => 10
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4,5}} => 6
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,7},{4,5},{6}} => 9
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4,5}} => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,6},{5},{7}} => 11
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,7},{3,4,6},{5}} => 7
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,7},{4,6},{5}} => 8
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,7},{5},{6}} => 10
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,6,7},{5}} => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,7},{3,4,5,6}} => 3
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,7},{4,5,6}} => 4
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,7},{5,6}} => 5
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,7},{6}} => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => 20
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 15
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5,7},{6}} => 14
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 9
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 16
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 10
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4,6},{5},{7}} => 15
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4,7},{5},{6}} => 14
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4,6,7},{5}} => 9
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 11
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4,7},{5,6}} => 9
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4,5,7},{6}} => 10
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 17
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 11
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 12
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,4},{5,7},{6}} => 11
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 6
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7}} => 16
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2},{3,5},{4},{6,7}} => 10
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,2},{3,6},{4},{5},{7}} => 15
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3,7},{4},{5},{6}} => 14
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,2},{3,6,7},{4},{5}} => 9
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3,5,6},{4},{7}} => 11
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3,7},{4},{5,6}} => 9
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2},{3,5,7},{4},{6}} => 10
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3,5,6,7},{4}} => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 13
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3,6},{4,5},{7}} => 11
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3,7},{4,5},{6}} => 10
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3,6,7},{4,5}} => 5
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3,4,6},{5},{7}} => 12
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3,7},{4,6},{5}} => 9
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3,4,7},{5},{6}} => 11
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2},{3,4,6,7},{5}} => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 8
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2},{3,7},{4,5,6}} => 5
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3,4,7},{5,6}} => 6
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3,4,5,7},{6}} => 7
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7}} => 19
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6,7}} => 13
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5,6},{7}} => 14
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5,7},{6}} => 13
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5,6,7}} => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,3},{2},{4,5},{6},{7}} => 15
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4,5},{6,7}} => 9
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4,6},{5},{7}} => 14
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4,7},{5},{6}} => 13
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4,6,7},{5}} => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4,5,6},{7}} => 10
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4,7},{5,6}} => 8
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,3},{2},{4,5,7},{6}} => 9
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4,5,6,7}} => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7}} => 18
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2},{3},{5},{6,7}} => 12
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5,6},{7}} => 13
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5,7},{6}} => 12
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5,6,7}} => 7
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7}} => 17
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2},{3},{4},{6,7}} => 11
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7}} => 16
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => 15
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => 10
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3},{4},{7}} => 12
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 11
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}} => 10
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 6
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7}} => 14
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2},{3},{6,7}} => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2},{3},{4,5},{7}} => 12
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2},{3},{5},{7}} => 13
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,5},{4},{6}} => 11
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}} => 10
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,5,6},{4}} => 6
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2},{3},{7}} => 9
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 8
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,6},{4,5}} => 6
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => 7
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7}} => 16
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6,7}} => 10
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,3,4},{2},{5,6},{7}} => 11
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,3,4},{2},{5,7},{6}} => 10
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,3,4},{2},{5,6,7}} => 5
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7}} => 14
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2},{3,4},{6,7}} => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2},{3,4},{5},{7}} => 13
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 13
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 8
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3,4},{7}} => 9
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,6},{5}} => 8
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7}} => 15
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,3,5},{2},{4},{6,7}} => 9
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2},{3,5},{4},{7}} => 12
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5},{6}} => 12
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6}} => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,3,6},{2},{4},{5},{7}} => 14
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,5},{3},{4},{6}} => 11
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}} => 10
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}} => 6
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,3,5,6},{2},{4},{7}} => 10
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,4,5},{3},{6}} => 8
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => 6
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => 7
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}} => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7}} => 12
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,3,4,5},{2},{6,7}} => 6
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2},{3,4,5},{7}} => 9
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 10
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,3,6},{2},{4,5},{7}} => 10
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,5},{3,4},{6}} => 8
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => 7
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}} => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,3,4,6},{2},{5},{7}} => 11
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 9
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => 6
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => 8
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}} => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,3,4,5,6},{2},{7}} => 7
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => 3
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}} => 4
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}} => 5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 18
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 12
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 13
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5,7},{6}} => 12
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 14
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 8
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4,6},{5},{7}} => 13
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3},{4,7},{5},{6}} => 12
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3},{4,6,7},{5}} => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 9
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4,7},{5,6}} => 7
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4,5,7},{6}} => 8
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7}} => 16
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6,7}} => 10
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2,3},{5,6},{7}} => 11
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2,3},{5,7},{6}} => 10
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2,3},{5,6,7}} => 5
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7}} => 15
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2,3},{4},{6,7}} => 9
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2,3},{4},{5},{7}} => 14
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => 14
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3},{4},{7}} => 10
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 10
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4,6},{5}} => 9
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 5
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2,3},{6},{7}} => 12
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2,3},{6,7}} => 6
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2,3},{4,5},{7}} => 10
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 11
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2,3},{5},{7}} => 11
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,5},{4},{6}} => 10
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,6},{4},{5}} => 9
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => 5
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2,3},{7}} => 7
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 7
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => 5
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}} => 6
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7}} => 17
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,4},{3},{5},{6,7}} => 11
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,4},{3},{5,6},{7}} => 12
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,4},{3},{5,7},{6}} => 11
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,4},{3},{5,6,7}} => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7}} => 14
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2,4},{3},{6,7}} => 8
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2,4},{3},{5},{7}} => 13
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}} => 13
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5,6}} => 8
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,4},{3},{7}} => 9
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6}} => 9
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6},{5}} => 8
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}} => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7}} => 16
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3},{4},{6,7}} => 10
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3},{4},{7}} => 12
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}} => 12
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6}} => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3},{4},{5},{7}} => 15
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}} => 11
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 10
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 6
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3},{4},{7}} => 11
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 8
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 7
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => 6
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7}} => 13
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,4,5},{3},{6,7}} => 7
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2,4,5},{3},{7}} => 9
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => {{1,3,4},{2},{5},{6}} => 10
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3},{4,5},{7}} => 11
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 8
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 8
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,4,6},{3},{5},{7}} => 12
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 9
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 7
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => 6
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,4,5,6},{3},{7}} => 8
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => 6
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => 3
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 15
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 9
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 10
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4},{5,7},{6}} => 9
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7}} => 12
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,5},{2,3,4},{6,7}} => 6
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,6},{2,3,4},{5},{7}} => 11
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 12
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 7
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3,4},{7}} => 7
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 8
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => 7
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7}} => 13
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3,4},{6,7}} => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3,4},{7}} => 9
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => {{1,4},{2,3},{5},{6}} => 10
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => 5
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3,4},{5},{7}} => 12
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 9
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 9
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 8
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 6
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 6
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => 5
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7}} => 14
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,5},{4},{6,7}} => 8
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,6},{2,3,5},{4},{7}} => 10
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 11
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => 6
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 11
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 8
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 8
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 13
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 10
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 7
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => 6
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 9
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => 7
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => 5
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 4
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => [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
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 11
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 7
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 9
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 8
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 6
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 7
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 9
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 7
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 5
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 5
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 10
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 8
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => 4
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => {{1},{2,3}} => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [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
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 6
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 5
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => {{1,2},{3}} => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => {{1},{2}} => 1
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 3
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8},{3}} => 3
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,6,7,8},{5}} => 5
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,7,8},{6}} => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8},{7}} => 7
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [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
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [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
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => 21
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => 15
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 16
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,7},{6}} => 15
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 10
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4,7},{5},{6}} => 15
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 6
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,6},{4},{5},{7}} => 16
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,7},{4},{5},{6}} => 15
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,6},{5},{7}} => 13
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,7},{5},{6}} => 12
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 9
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 3
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 19
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 9
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4,6,7},{5}} => 8
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7}} => 17
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,5},{3},{4},{6,7}} => 11
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,6},{3},{4},{5},{7}} => 16
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,7},{3},{4},{5},{6}} => 15
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4},{5}} => 10
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,4,5,6,7},{3}} => 3
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 16
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4},{5,7},{6}} => 10
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 5
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7}} => 15
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,6},{3,5},{4},{7}} => 12
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,6},{4},{5},{7}} => 14
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4},{5}} => 10
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,7},{4},{5},{6}} => 13
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4},{5}} => 8
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,7},{3,5,6},{4}} => 6
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,5,6,7},{4}} => 4
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 12
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 6
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,7},{3,4,5},{6}} => 8
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,4,5}} => 3
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,7},{4,5},{6}} => 9
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,6},{5},{7}} => 11
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,7},{5},{6}} => 10
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,6,7},{5}} => 5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,7},{3,4,5,6}} => 3
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,7},{4,5,6}} => 4
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,7},{5,6}} => 5
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,7},{6}} => 6
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => 20
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5,7},{6}} => 14
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 9
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 10
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4,6},{5},{7}} => 15
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4,6,7},{5}} => 9
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 11
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3,7},{4},{5},{6}} => 14
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3,4,7},{5},{6}} => 11
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 8
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3,4,7},{5,6}} => 6
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3,4,5,7},{6}} => 7
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7}} => 19
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5,7},{6}} => 13
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4,5,6,7}} => 4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7}} => 18
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5,6,7}} => 7
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7}} => 17
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2},{3},{4},{6,7}} => 11
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7}} => 16
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => 15
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => 10
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 11
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}} => 10
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 6
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,5},{4},{6}} => 11
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}} => 10
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => 7
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 3
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 8
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5},{6}} => 12
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,3,6},{2},{4},{5},{7}} => 14
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}} => 10
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => 7
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}} => 3
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7}} => 12
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 10
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 5
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,3,6},{2},{4,5},{7}} => 10
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => 7
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}} => 3
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 9
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => 8
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}} => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,3,4,5,6},{2},{7}} => 7
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}} => 5
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 18
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 12
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 13
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 8
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4,5,7},{6}} => 8
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7}} => 16
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2,3},{4},{5},{7}} => 14
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => 14
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3},{4},{7}} => 10
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => 5
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 7
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7}} => 14
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}} => 13
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,4},{3},{7}} => 9
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6},{5}} => 8
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}} => 4
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7}} => 16
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}} => 12
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6}} => 7
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3},{4},{5},{7}} => 15
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}} => 11
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 10
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 6
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 7
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => 6
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 3
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7}} => 13
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 8
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 4
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 7
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => 6
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,4,5,6},{3},{7}} => 8
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => 6
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => 3
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => 4
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4},{5,7},{6}} => 9
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 4
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 12
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 7
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3,4},{7}} => 7
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => 7
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3,4},{7}} => 9
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => {{1,4},{2,3},{5},{6}} => 10
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => 5
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 9
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 9
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 6
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => 5
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7}} => 14
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 11
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 11
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 8
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 8
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => 4
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 13
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 10
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 7
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => 6
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 9
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => 5
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 4
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => 3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => [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
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 5
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 4
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 7
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 3
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 5
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 5
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 10
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 8
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => 6
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => 4
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => 3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => {{1},{2,3}} => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [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
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 5
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 4
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 3
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => {{1,2},{3}} => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => {{1},{2}} => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => 10
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => 14
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => 15
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => 15
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => 20
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => 20
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => {{1},{2,3}} => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => {{1,2},{3}} => 2
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => {{1},{2,3}} => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => 3
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 5
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => {{1,2},{3}} => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => {{1},{2}} => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => 1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => 1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [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
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => {{1},{2}} => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => 21
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [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
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 5
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 4
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 3
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 2
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 3
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 4
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => 3
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => 15
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 9
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => [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
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,7},{6}} => 6
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,7},{5,6}} => 5
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,7},{4,5,6}} => 4
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,7},{3,4,5,6}} => 3
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => 3
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => 3
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 10
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => 6
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 3
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 10
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 6
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 3
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,7},{3},{4},{5},{6}} => 15
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}} => 11
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}} => 12
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}} => 13
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => 4
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 5
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,7},{6}} => 15
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 3
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7}} => 16
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7}} => 16
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3},{4},{5},{7}} => 15
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,7},{4},{5},{6}} => 13
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,7},{3},{4},{5},{6}} => 15
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}} => 10
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}} => 10
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}} => 10
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => 21
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7}} => 14
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 11
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 8
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 2
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3,7},{4},{5},{6}} => 14
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7}} => 19
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [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
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => 6
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => 4
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}} => 5
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8},{7}} => 7
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 18
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 19
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => 3
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => 6
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => 1
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,6},{3},{4},{5},{7}} => 16
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,6},{4},{5},{7}} => 14
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 4
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => 3
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => 6
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => 15
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4,5,7},{6}} => 11
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,7},{5},{6}} => 12
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 3
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 3
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => {{1},{2,3}} => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2},{3},{4},{6,7}} => 11
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7}} => 17
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 12
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 5
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 4
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 8
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 3
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
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Description
The rob statistic of a set partition.
Let $S = B_1,\ldots,B_k$ be a set partition with ordered blocks $B_i$ and with $\operatorname{min} B_a < \operatorname{min} B_b$ for $a < b$.
According to [1, Definition 3], a rob (right-opener-bigger) of $S$ is given by a pair $i < j$ such that $j = \operatorname{min} B_b$ and $i \in B_a$ for $a < b$.
This is also the number of occurrences of the pattern {{1}, {2}}, such that 2 is the minimal element of a block.
Let $S = B_1,\ldots,B_k$ be a set partition with ordered blocks $B_i$ and with $\operatorname{min} B_a < \operatorname{min} B_b$ for $a < b$.
According to [1, Definition 3], a rob (right-opener-bigger) of $S$ is given by a pair $i < j$ such that $j = \operatorname{min} B_b$ and $i \in B_a$ for $a < b$.
This is also the number of occurrences of the pattern {{1}, {2}}, such that 2 is the minimal element of a block.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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