- FindStat

Identifier

Mp00311: Plane partitions —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
St001050: Set partitions ⟶ ℤ

Values

[[1]] => [1] => [1,0,1,0] => {{1},{2}} => 2

[[1],[1]] => [1,1] => [1,0,1,1,0,0] => {{1},{2,3}} => 1

[[2]] => [2] => [1,1,0,0,1,0] => {{1,2},{3}} => 2

[[1,1]] => [2] => [1,1,0,0,1,0] => {{1,2},{3}} => 2

[[1],[1],[1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => 1

[[2],[1]] => [2,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => 3

[[1,1],[1]] => [2,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => 3

[[3]] => [3] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 2

[[2,1]] => [3] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 2

[[1,1,1]] => [3] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 2

[[1],[1],[1],[1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => 1

[[2],[1],[1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => 2

[[2],[2]] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 1

[[1,1],[1],[1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => 2

[[1,1],[1,1]] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 1

[[3],[1]] => [3,1] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => 3

[[2,1],[1]] => [3,1] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => 3

[[1,1,1],[1]] => [3,1] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => 3

[[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 2

[[3,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 2

[[2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 2

[[2,1,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 2

[[1,1,1,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 2

[[1],[1],[1],[1],[1]] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => 1

[[2],[1],[1],[1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => 2

[[2],[2],[1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => 1

[[1,1],[1],[1],[1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => 2

[[1,1],[1,1],[1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => 1

[[3],[1],[1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 2

[[3],[2]] => [3,2] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 3

[[2,1],[1],[1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 2

[[2,1],[2]] => [3,2] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 3

[[2,1],[1,1]] => [3,2] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 3

[[1,1,1],[1],[1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 2

[[1,1,1],[1,1]] => [3,2] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 3

[[4],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => 3

[[3,1],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => 3

[[2,2],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => 3

[[2,1,1],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => 3

[[1,1,1,1],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => 3

[[5]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 2

[[4,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 2

[[3,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 2

[[3,1,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 2

[[2,2,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 2

[[2,1,1,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 2

[[1,1,1,1,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 2

[[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => 1

[[2],[1],[1],[1],[1]] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}} => 2

[[2],[2],[1],[1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => 1

[[2],[2],[2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 1

[[1,1],[1],[1],[1],[1]] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}} => 2

[[1,1],[1,1],[1],[1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => 1

[[1,1],[1,1],[1,1]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 1

[[3],[1],[1],[1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => 2

[[3],[2],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => 4

[[3],[3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 1

[[2,1],[1],[1],[1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => 2

[[2,1],[2],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => 4

[[2,1],[1,1],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => 4

[[2,1],[2,1]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 1

[[1,1,1],[1],[1],[1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => 2

[[1,1,1],[1,1],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => 4

[[1,1,1],[1,1,1]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 1

[[4],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => 2

[[4],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 3

[[3,1],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => 2

[[3,1],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 3

[[3,1],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 3

[[2,2],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => 2

[[2,2],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 3

[[2,2],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 3

[[2,1,1],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => 2

[[2,1,1],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 3

[[2,1,1],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 3

[[1,1,1,1],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => 2

[[1,1,1,1],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 3

[[5],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 3

[[4,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 3

[[3,2],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 3

[[3,1,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 3

[[2,2,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 3

[[2,1,1,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 3

[[1,1,1,1,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 3

[[6]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 2

[[5,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 2

[[4,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 2

[[4,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 2

[[3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 2

[[3,2,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 2

[[3,1,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 2

[[2,2,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 2

[[2,2,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 2

[[2,1,1,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 2

[[1,1,1,1,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 2

[[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => 1

[[2],[1],[1],[1],[1],[1]] => [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}} => 2

[[2],[2],[1],[1],[1]] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}} => 1

[[2],[2],[2],[1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 1

[[1,1],[1],[1],[1],[1],[1]] => [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}} => 2

[[1,1],[1,1],[1],[1],[1]] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}} => 1

>>> Load all 1123 entries. <<<

[[1,1],[1,1],[1,1],[1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 1

[[3],[1],[1],[1],[1]] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}} => 2

[[3],[2],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => 3

[[3],[2],[2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => 2

[[3],[3],[1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => 1

[[2,1],[1],[1],[1],[1]] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}} => 2

[[2,1],[2],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => 3

[[2,1],[2],[2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => 2

[[2,1],[1,1],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => 3

[[2,1],[1,1],[1,1]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => 2

[[2,1],[2,1],[1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => 1

[[1,1,1],[1],[1],[1],[1]] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}} => 2

[[1,1,1],[1,1],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => 3

[[1,1,1],[1,1],[1,1]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => 2

[[1,1,1],[1,1,1],[1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => 1

[[4],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 2

[[4],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 4

[[4],[3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3

[[3,1],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 2

[[3,1],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 4

[[3,1],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 4

[[3,1],[3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3

[[3,1],[2,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3

[[2,2],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 2

[[2,2],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 4

[[2,2],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 4

[[2,2],[2,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3

[[2,1,1],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 2

[[2,1,1],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 4

[[2,1,1],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 4

[[2,1,1],[2,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3

[[2,1,1],[1,1,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3

[[1,1,1,1],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 2

[[1,1,1,1],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 4

[[1,1,1,1],[1,1,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3

[[5],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => 2

[[5],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 3

[[4,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => 2

[[4,1],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 3

[[4,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 3

[[3,2],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => 2

[[3,2],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 3

[[3,2],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 3

[[3,1,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => 2

[[3,1,1],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 3

[[3,1,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 3

[[2,2,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => 2

[[2,2,1],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 3

[[2,2,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 3

[[2,1,1,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => 2

[[2,1,1,1],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 3

[[2,1,1,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 3

[[1,1,1,1,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => 2

[[1,1,1,1,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 3

[[6],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 3

[[5,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 3

[[4,2],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 3

[[4,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 3

[[3,3],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 3

[[3,2,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 3

[[3,1,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 3

[[2,2,2],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 3

[[2,2,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 3

[[2,1,1,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 3

[[1,1,1,1,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 3

[[7]] => [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}} => 2

[[6,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => 2

[[5,2]] => [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}} => 2

[[5,1,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => 2

[[4,3]] => [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}} => 2

[[4,2,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => 2

[[4,1,1,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => 2

[[3,3,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => 2

[[3,2,2]] => [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}} => 2

[[3,2,1,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => 2

[[3,1,1,1,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => 2

[[2,2,2,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => 2

[[2,2,1,1,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => 2

[[2,1,1,1,1,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => 2

[[1,1,1,1,1,1,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => 2

[[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9}} => 1

[[2],[1],[1],[1],[1],[1],[1]] => [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}} => 2

[[2],[2],[1],[1],[1],[1]] => [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}} => 1

[[2],[2],[2],[1],[1]] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}} => 1

[[2],[2],[2],[2]] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 1

[[1,1],[1],[1],[1],[1],[1],[1]] => [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}} => 2

[[1,1],[1,1],[1],[1],[1],[1]] => [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}} => 1

[[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}} => 1

[[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 1

[[3],[1],[1],[1],[1],[1]] => [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}} => 2

[[3],[2],[1],[1],[1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => 3

[[3],[2],[2],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => 2

[[3],[3],[1],[1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 1

[[3],[3],[2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 1

[[2,1],[1],[1],[1],[1],[1]] => [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}} => 2

[[2,1],[2],[1],[1],[1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => 3

[[2,1],[2],[2],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => 2

[[2,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => 3

[[2,1],[1,1],[1,1],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => 2

[[2,1],[2,1],[1],[1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 1

[[2,1],[2,1],[2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 1

[[2,1],[2,1],[1,1]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 1

[[1,1,1],[1],[1],[1],[1],[1]] => [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}} => 2

[[1,1,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => 3

[[1,1,1],[1,1],[1,1],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => 2

[[1,1,1],[1,1,1],[1],[1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 1

[[1,1,1],[1,1,1],[1,1]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 1

[[4],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => 2

[[4],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 3

[[4],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 2

[[4],[3],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 4

[[4],[4]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 1

[[3,1],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => 2

[[3,1],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 3

[[3,1],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 2

[[3,1],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 3

[[3,1],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 2

[[3,1],[3],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 4

[[3,1],[2,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 4

[[3,1],[3,1]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 1

[[2,2],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => 2

[[2,2],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 3

[[2,2],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 2

[[2,2],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 3

[[2,2],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 2

[[2,2],[2,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 4

[[2,2],[2,2]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 1

[[2,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => 2

[[2,1,1],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 3

[[2,1,1],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 2

[[2,1,1],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 3

[[2,1,1],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 2

[[2,1,1],[2,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 4

[[2,1,1],[1,1,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 4

[[2,1,1],[2,1,1]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 1

[[1,1,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => 2

[[1,1,1,1],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 3

[[1,1,1,1],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 2

[[1,1,1,1],[1,1,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 4

[[1,1,1,1],[1,1,1,1]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 1

[[5],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => 2

[[5],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 4

[[5],[3]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 3

[[4,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => 2

[[4,1],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 4

[[4,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 4

[[4,1],[3]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 3

[[4,1],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 3

[[3,2],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => 2

[[3,2],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 4

[[3,2],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 4

[[3,2],[3]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 3

[[3,2],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 3

[[3,1,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => 2

[[3,1,1],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 4

[[3,1,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 4

[[3,1,1],[3]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 3

[[3,1,1],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 3

[[3,1,1],[1,1,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 3

[[2,2,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => 2

[[2,2,1],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 4

[[2,2,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 4

[[2,2,1],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 3

[[2,2,1],[1,1,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 3

[[2,1,1,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => 2

[[2,1,1,1],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 4

[[2,1,1,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 4

[[2,1,1,1],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 3

[[2,1,1,1],[1,1,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 3

[[1,1,1,1,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => 2

[[1,1,1,1,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 4

[[1,1,1,1,1],[1,1,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 3

[[6],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 2

[[6],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[5,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 2

[[5,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[5,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[4,2],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 2

[[4,2],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[4,2],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[4,1,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 2

[[4,1,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[4,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[3,3],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 2

[[3,3],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[3,3],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[3,2,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 2

[[3,2,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[3,2,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[3,1,1,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 2

[[3,1,1,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[3,1,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[2,2,2],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 2

[[2,2,2],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[2,2,2],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[2,2,1,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 2

[[2,2,1,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[2,2,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[2,1,1,1,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 2

[[2,1,1,1,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[2,1,1,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[1,1,1,1,1,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 2

[[1,1,1,1,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3

[[7],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[6,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[5,2],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[5,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[4,3],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[4,2,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[4,1,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[3,3,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[3,2,2],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[3,2,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[3,1,1,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[2,2,2,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[2,2,1,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[2,1,1,1,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[1,1,1,1,1,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3

[[8]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[7,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[6,2]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[6,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[5,3]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[5,2,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[5,1,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[4,4]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[4,3,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[4,2,2]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[4,2,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[4,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[3,3,2]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[3,3,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[3,2,2,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[3,2,1,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[3,1,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[2,2,2,2]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[2,2,2,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[2,2,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[2,1,1,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[1,1,1,1,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2

[[1],[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => 1

[[2],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,9},{8}} => 2

[[2],[2],[1],[1],[1],[1],[1]] => [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}} => 1

[[2],[2],[2],[1],[1],[1]] => [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}} => 1

[[2],[2],[2],[2],[1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 1

[[1,1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,9},{8}} => 2

[[1,1],[1,1],[1],[1],[1],[1],[1]] => [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}} => 1

[[1,1],[1,1],[1,1],[1],[1],[1]] => [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}} => 1

[[1,1],[1,1],[1,1],[1,1],[1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 1

[[3],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6,7}} => 2

[[3],[2],[1],[1],[1],[1]] => [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}} => 3

[[3],[2],[2],[1],[1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => 2

[[3],[2],[2],[2]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}} => 2

[[3],[3],[1],[1],[1]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}} => 1

[[3],[3],[2],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 1

[[3],[3],[3]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 1

[[2,1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6,7}} => 2

[[2,1],[2],[1],[1],[1],[1]] => [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}} => 3

[[2,1],[2],[2],[1],[1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => 2

[[2,1],[2],[2],[2]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}} => 2

[[2,1],[1,1],[1],[1],[1],[1]] => [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}} => 3

[[2,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => 2

[[2,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}} => 2

[[2,1],[2,1],[1],[1],[1]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}} => 1

[[2,1],[2,1],[2],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 1

[[2,1],[2,1],[1,1],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 1

[[2,1],[2,1],[2,1]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 1

[[1,1,1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6,7}} => 2

[[1,1,1],[1,1],[1],[1],[1],[1]] => [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}} => 3

[[1,1,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => 2

[[1,1,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}} => 2

[[1,1,1],[1,1,1],[1],[1],[1]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}} => 1

[[1,1,1],[1,1,1],[1,1],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 1

[[1,1,1],[1,1,1],[1,1,1]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 1

[[4],[1],[1],[1],[1],[1]] => [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}} => 2

[[4],[2],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => 3

[[4],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 2

[[4],[3],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 3

[[4],[3],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 4

[[4],[4],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => 1

[[3,1],[1],[1],[1],[1],[1]] => [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}} => 2

[[3,1],[2],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => 3

[[3,1],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 2

[[3,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => 3

[[3,1],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 2

[[3,1],[3],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 3

[[3,1],[3],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 4

[[3,1],[2,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 3

[[3,1],[2,1],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 4

[[3,1],[2,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 4

[[3,1],[3,1],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => 1

[[2,2],[1],[1],[1],[1],[1]] => [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}} => 2

[[2,2],[2],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => 3

[[2,2],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 2

[[2,2],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => 3

[[2,2],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 2

[[2,2],[2,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 3

[[2,2],[2,1],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 4

[[2,2],[2,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 4

[[2,2],[2,2],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => 1

[[2,1,1],[1],[1],[1],[1],[1]] => [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}} => 2

[[2,1,1],[2],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => 3

[[2,1,1],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 2

[[2,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => 3

[[2,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 2

[[2,1,1],[2,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 3

[[2,1,1],[2,1],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 4

[[2,1,1],[2,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 4

[[2,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 3

[[2,1,1],[1,1,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 4

[[2,1,1],[2,1,1],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => 1

[[1,1,1,1],[1],[1],[1],[1],[1]] => [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}} => 2

[[1,1,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => 3

[[1,1,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 2

[[1,1,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 3

[[1,1,1,1],[1,1,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 4

[[1,1,1,1],[1,1,1,1],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => 1

[[5],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 2

[[5],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 3

[[5],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 2

[[5],[3],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 4

[[5],[4]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3

[[4,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 2

[[4,1],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 3

[[4,1],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 2

[[4,1],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 3

[[4,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 2

[[4,1],[3],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 4

[[4,1],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 4

[[4,1],[4]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3

[[4,1],[3,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3

[[3,2],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 2

[[3,2],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 3

[[3,2],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 2

[[3,2],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 3

[[3,2],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 2

[[3,2],[3],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 4

[[3,2],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 4

[[3,2],[3,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3

[[3,2],[2,2]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3

[[3,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 2

[[3,1,1],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 3

[[3,1,1],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 2

[[3,1,1],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 3

[[3,1,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 2

[[3,1,1],[3],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 4

[[3,1,1],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 4

[[3,1,1],[1,1,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 4

[[3,1,1],[3,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3

[[3,1,1],[2,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3

[[2,2,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 2

[[2,2,1],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 3

[[2,2,1],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 2

[[2,2,1],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 3

[[2,2,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 2

[[2,2,1],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 4

[[2,2,1],[1,1,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 4

[[2,2,1],[2,2]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3

[[2,2,1],[2,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3

[[2,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 2

[[2,1,1,1],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 3

[[2,1,1,1],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 2

[[2,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 3

[[2,1,1,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 2

[[2,1,1,1],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 4

[[2,1,1,1],[1,1,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 4

[[2,1,1,1],[2,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3

[[2,1,1,1],[1,1,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3

[[1,1,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 2

[[1,1,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 3

[[1,1,1,1,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 2

[[1,1,1,1,1],[1,1,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 4

[[1,1,1,1,1],[1,1,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3

[[6],[1],[1],[1]] => [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}} => 2

[[6],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[6],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[5,1],[1],[1],[1]] => [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}} => 2

[[5,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[5,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[5,1],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[5,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[4,2],[1],[1],[1]] => [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}} => 2

[[4,2],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[4,2],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[4,2],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[4,2],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[4,1,1],[1],[1],[1]] => [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}} => 2

[[4,1,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[4,1,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[4,1,1],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[4,1,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[4,1,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[3,3],[1],[1],[1]] => [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}} => 2

[[3,3],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[3,3],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[3,3],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[3,3],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[3,2,1],[1],[1],[1]] => [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}} => 2

[[3,2,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[3,2,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[3,2,1],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[3,2,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[3,2,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[3,1,1,1],[1],[1],[1]] => [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}} => 2

[[3,1,1,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[3,1,1,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[3,1,1,1],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[3,1,1,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[3,1,1,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[2,2,2],[1],[1],[1]] => [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}} => 2

[[2,2,2],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[2,2,2],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[2,2,2],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[2,2,2],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[2,2,1,1],[1],[1],[1]] => [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}} => 2

[[2,2,1,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[2,2,1,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[2,2,1,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[2,2,1,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[2,1,1,1,1],[1],[1],[1]] => [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}} => 2

[[2,1,1,1,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[2,1,1,1,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[2,1,1,1,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[2,1,1,1,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[1,1,1,1,1,1],[1],[1],[1]] => [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}} => 2

[[1,1,1,1,1,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4

[[1,1,1,1,1,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3

[[7],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[7],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[6,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[6,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[6,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[5,2],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[5,2],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[5,2],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[5,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[5,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[5,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[4,3],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[4,3],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[4,3],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[4,2,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[4,2,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[4,2,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[4,1,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[4,1,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[4,1,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[3,3,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[3,3,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[3,3,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[3,2,2],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[3,2,2],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[3,2,2],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[3,2,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[3,2,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[3,2,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[3,1,1,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[3,1,1,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[3,1,1,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[2,2,2,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[2,2,2,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[2,2,2,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[2,2,1,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[2,2,1,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[2,2,1,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[2,1,1,1,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[2,1,1,1,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[2,1,1,1,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[1,1,1,1,1,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2

[[1,1,1,1,1,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3

[[8],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[7,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[6,2],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[6,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[5,3],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[5,2,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[5,1,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[4,4],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[4,3,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[4,2,2],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[4,2,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[4,1,1,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[3,3,2],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[3,3,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[3,2,2,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[3,2,1,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[3,1,1,1,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[2,2,2,2],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[2,2,2,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[2,2,1,1,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[2,1,1,1,1,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[1,1,1,1,1,1,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3

[[9]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[8,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[7,2]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[7,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[6,3]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[6,2,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[6,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[5,4]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[5,3,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[5,2,2]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[5,2,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[5,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[4,4,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[4,3,2]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[4,3,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[4,2,2,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[4,2,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[4,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[3,3,3]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[3,3,2,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[3,3,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[3,2,2,2]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[3,2,2,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[3,2,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[3,1,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[2,2,2,2,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[2,2,2,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[2,2,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[2,1,1,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[1,1,1,1,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => 1

[[2],[1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,10},{9}} => 2

[[2],[2],[1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8,9},{7}} => 1

[[2],[2],[2],[1],[1],[1],[1]] => [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}} => 1

[[2],[2],[2],[2],[1],[1]] => [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}} => 1

[[2],[2],[2],[2],[2]] => [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}} => 1

[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,10},{9}} => 2

[[1,1],[1,1],[1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8,9},{7}} => 1

[[1,1],[1,1],[1,1],[1],[1],[1],[1]] => [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}} => 1

[[1,1],[1,1],[1,1],[1,1],[1],[1]] => [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}} => 1

[[1,1],[1,1],[1,1],[1,1],[1,1]] => [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}} => 1

[[3],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,9},{7,8}} => 2

[[3],[2],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6},{7}} => 3

[[3],[2],[2],[1],[1],[1]] => [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}} => 2

[[3],[2],[2],[2],[1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => 2

[[3],[3],[1],[1],[1],[1]] => [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}} => 1

[[3],[3],[2],[1],[1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}} => 1

[[3],[3],[2],[2]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => 1

[[3],[3],[3],[1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}} => 1

[[2,1],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,9},{7,8}} => 2

[[2,1],[2],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6},{7}} => 3

[[2,1],[2],[2],[1],[1],[1]] => [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}} => 2

[[2,1],[2],[2],[2],[1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => 2

[[2,1],[1,1],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6},{7}} => 3

[[2,1],[1,1],[1,1],[1],[1],[1]] => [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}} => 2

[[2,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => 2

[[2,1],[2,1],[1],[1],[1],[1]] => [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}} => 1

[[2,1],[2,1],[2],[1],[1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}} => 1

[[2,1],[2,1],[2],[2]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => 1

[[2,1],[2,1],[1,1],[1],[1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}} => 1

[[2,1],[2,1],[1,1],[1,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => 1

[[2,1],[2,1],[2,1],[1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}} => 1

[[1,1,1],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,9},{7,8}} => 2

[[1,1,1],[1,1],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6},{7}} => 3

[[1,1,1],[1,1],[1,1],[1],[1],[1]] => [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}} => 2

[[1,1,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => 2

[[1,1,1],[1,1,1],[1],[1],[1],[1]] => [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}} => 1

[[1,1,1],[1,1,1],[1,1],[1],[1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}} => 1

[[1,1,1],[1,1,1],[1,1],[1,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => 1

[[1,1,1],[1,1,1],[1,1,1],[1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}} => 1

[[4],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6,7}} => 2

[[4],[2],[1],[1],[1],[1]] => [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}} => 3

[[4],[2],[2],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => 2

[[4],[2],[2],[2]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => 2

[[4],[3],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => 3

[[4],[3],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 5

[[4],[3],[3]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => 2

[[4],[4],[1],[1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => 1

[[4],[4],[2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => 1

[[3,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6,7}} => 2

[[3,1],[2],[1],[1],[1],[1]] => [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}} => 3

[[3,1],[2],[2],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => 2

[[3,1],[2],[2],[2]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => 2

[[3,1],[1,1],[1],[1],[1],[1]] => [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}} => 3

[[3,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => 2

[[3,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => 2

[[3,1],[3],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => 3

[[3,1],[3],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 5

[[3,1],[3],[3]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => 2

[[3,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => 3

[[3,1],[2,1],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 5

[[3,1],[2,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 5

[[3,1],[2,1],[2,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => 2

[[3,1],[3,1],[1],[1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => 1

[[3,1],[3,1],[2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => 1

[[3,1],[3,1],[1,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => 1

[[2,2],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6,7}} => 2

[[2,2],[2],[1],[1],[1],[1]] => [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}} => 3

[[2,2],[2],[2],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => 2

[[2,2],[2],[2],[2]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => 2

[[2,2],[1,1],[1],[1],[1],[1]] => [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}} => 3

[[2,2],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => 2

[[2,2],[1,1],[1,1],[1,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => 2

[[2,2],[2,1],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => 3

[[2,2],[2,1],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 5

[[2,2],[2,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 5

[[2,2],[2,1],[2,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => 2

[[2,2],[2,2],[1],[1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => 1

[[2,2],[2,2],[2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => 1

[[2,2],[2,2],[1,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => 1

[[2,1,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6,7}} => 2

[[2,1,1],[2],[1],[1],[1],[1]] => [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}} => 3

[[2,1,1],[2],[2],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => 2

[[2,1,1],[2],[2],[2]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => 2

[[2,1,1],[1,1],[1],[1],[1],[1]] => [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}} => 3

[[2,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => 2

[[2,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => 2

[[2,1,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => 3

[[2,1,1],[2,1],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 5

[[2,1,1],[2,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 5

[[2,1,1],[2,1],[2,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => 2

[[2,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => 3

[[2,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 5

[[2,1,1],[1,1,1],[1,1,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => 2

[[2,1,1],[2,1,1],[1],[1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => 1

[[2,1,1],[2,1,1],[2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => 1

[[2,1,1],[2,1,1],[1,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => 1

[[1,1,1,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6,7}} => 2

[[1,1,1,1],[1,1],[1],[1],[1],[1]] => [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}} => 3

[[1,1,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => 2

[[1,1,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => 2

[[1,1,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => 3

[[1,1,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 5

[[1,1,1,1],[1,1,1],[1,1,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => 2

[[1,1,1,1],[1,1,1,1],[1],[1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => 1

[[1,1,1,1],[1,1,1,1],[1,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => 1

[[5],[1],[1],[1],[1],[1]] => [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}} => 2

[[5],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 3

[[5],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 2

[[5],[3],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 3

[[5],[3],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[5],[4],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 4

[[5],[5]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 1

[[4,1],[1],[1],[1],[1],[1]] => [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}} => 2

[[4,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 3

[[4,1],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 2

[[4,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 3

[[4,1],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 2

[[4,1],[3],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 3

[[4,1],[3],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[4,1],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 3

[[4,1],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[4,1],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[4,1],[4],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 4

[[4,1],[3,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 4

[[4,1],[4,1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 1

[[3,2],[1],[1],[1],[1],[1]] => [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}} => 2

[[3,2],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 3

[[3,2],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 2

[[3,2],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 3

[[3,2],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 2

[[3,2],[3],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 3

[[3,2],[3],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[3,2],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 3

[[3,2],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[3,2],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[3,2],[3,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 4

[[3,2],[2,2],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 4

[[3,2],[3,2]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 1

[[3,1,1],[1],[1],[1],[1],[1]] => [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}} => 2

[[3,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 3

[[3,1,1],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 2

[[3,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 3

[[3,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 2

[[3,1,1],[3],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 3

[[3,1,1],[3],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[3,1,1],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 3

[[3,1,1],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[3,1,1],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[3,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 3

[[3,1,1],[1,1,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[3,1,1],[3,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 4

[[3,1,1],[2,1,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 4

[[3,1,1],[3,1,1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 1

[[2,2,1],[1],[1],[1],[1],[1]] => [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}} => 2

[[2,2,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 3

[[2,2,1],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 2

[[2,2,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 3

[[2,2,1],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 2

[[2,2,1],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 3

[[2,2,1],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[2,2,1],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[2,2,1],[1,1,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 3

[[2,2,1],[1,1,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[2,2,1],[2,2],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 4

[[2,2,1],[2,1,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 4

[[2,2,1],[2,2,1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 1

[[2,1,1,1],[1],[1],[1],[1],[1]] => [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}} => 2

[[2,1,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 3

[[2,1,1,1],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 2

[[2,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 3

[[2,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 2

[[2,1,1,1],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 3

[[2,1,1,1],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[2,1,1,1],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[2,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 3

[[2,1,1,1],[1,1,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[2,1,1,1],[2,1,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 4

[[2,1,1,1],[1,1,1,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 4

[[2,1,1,1],[2,1,1,1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 1

[[1,1,1,1,1],[1],[1],[1],[1],[1]] => [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}} => 2

[[1,1,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 3

[[1,1,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 2

[[1,1,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 3

[[1,1,1,1,1],[1,1,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4

[[1,1,1,1,1],[1,1,1,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 4

[[1,1,1,1,1],[1,1,1,1,1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 1

[[6],[1],[1],[1],[1]] => [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}} => 2

[[6],[2],[1],[1]] => [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}} => 3

[[6],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[6],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[6],[4]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[5,1],[1],[1],[1],[1]] => [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}} => 2

[[5,1],[2],[1],[1]] => [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}} => 3

[[5,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[5,1],[1,1],[1],[1]] => [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}} => 3

[[5,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[5,1],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[5,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[5,1],[4]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[5,1],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[4,2],[1],[1],[1],[1]] => [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}} => 2

[[4,2],[2],[1],[1]] => [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}} => 3

[[4,2],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[4,2],[1,1],[1],[1]] => [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}} => 3

[[4,2],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[4,2],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[4,2],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[4,2],[4]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[4,2],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[4,2],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[4,1,1],[1],[1],[1],[1]] => [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}} => 2

[[4,1,1],[2],[1],[1]] => [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}} => 3

[[4,1,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[4,1,1],[1,1],[1],[1]] => [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}} => 3

[[4,1,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[4,1,1],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[4,1,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[4,1,1],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[4,1,1],[4]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[4,1,1],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[4,1,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[3,3],[1],[1],[1],[1]] => [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}} => 2

[[3,3],[2],[1],[1]] => [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}} => 3

[[3,3],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[3,3],[1,1],[1],[1]] => [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}} => 3

[[3,3],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[3,3],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[3,3],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[3,3],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[3,3],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[3,2,1],[1],[1],[1],[1]] => [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}} => 2

[[3,2,1],[2],[1],[1]] => [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}} => 3

[[3,2,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[3,2,1],[1,1],[1],[1]] => [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}} => 3

[[3,2,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[3,2,1],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[3,2,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[3,2,1],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[3,2,1],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[3,2,1],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[3,2,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[3,1,1,1],[1],[1],[1],[1]] => [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}} => 2

[[3,1,1,1],[2],[1],[1]] => [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}} => 3

[[3,1,1,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[3,1,1,1],[1,1],[1],[1]] => [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}} => 3

[[3,1,1,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[3,1,1,1],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[3,1,1,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[3,1,1,1],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[3,1,1,1],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[3,1,1,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[3,1,1,1],[1,1,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[2,2,2],[1],[1],[1],[1]] => [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}} => 2

[[2,2,2],[2],[1],[1]] => [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}} => 3

[[2,2,2],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[2,2,2],[1,1],[1],[1]] => [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}} => 3

[[2,2,2],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[2,2,2],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[2,2,2],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[2,2,2],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[2,2,2],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[2,2,1,1],[1],[1],[1],[1]] => [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}} => 2

[[2,2,1,1],[2],[1],[1]] => [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}} => 3

[[2,2,1,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[2,2,1,1],[1,1],[1],[1]] => [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}} => 3

[[2,2,1,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[2,2,1,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[2,2,1,1],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[2,2,1,1],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[2,2,1,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[2,2,1,1],[1,1,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[2,1,1,1,1],[1],[1],[1],[1]] => [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}} => 2

[[2,1,1,1,1],[2],[1],[1]] => [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}} => 3

[[2,1,1,1,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[2,1,1,1,1],[1,1],[1],[1]] => [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}} => 3

[[2,1,1,1,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[2,1,1,1,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[2,1,1,1,1],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[2,1,1,1,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[2,1,1,1,1],[1,1,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[1,1,1,1,1,1],[1],[1],[1],[1]] => [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}} => 2

[[1,1,1,1,1,1],[1,1],[1],[1]] => [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}} => 3

[[1,1,1,1,1,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2

[[1,1,1,1,1,1],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4

[[1,1,1,1,1,1],[1,1,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3

[[7],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[7],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[7],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[6,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[6,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[6,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[6,1],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[6,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[5,2],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[5,2],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[5,2],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[5,2],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[5,2],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[5,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[5,1,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[5,1,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[5,1,1],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[5,1,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[5,1,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[4,3],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[4,3],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[4,3],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[4,3],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[4,3],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[4,2,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[4,2,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[4,2,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[4,2,1],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[4,2,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[4,2,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[4,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[4,1,1,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[4,1,1,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[4,1,1,1],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[4,1,1,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[4,1,1,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[3,3,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[3,3,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[3,3,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[3,3,1],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[3,3,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[3,3,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[3,2,2],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[3,2,2],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[3,2,2],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[3,2,2],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[3,2,2],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[3,2,2],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[3,2,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[3,2,1,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[3,2,1,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[3,2,1,1],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[3,2,1,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[3,2,1,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[3,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[3,1,1,1,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[3,1,1,1,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[3,1,1,1,1],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[3,1,1,1,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[3,1,1,1,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[2,2,2,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[2,2,2,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[2,2,2,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[2,2,2,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[2,2,2,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[2,2,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[2,2,1,1,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[2,2,1,1,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[2,2,1,1,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[2,2,1,1,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[2,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[2,1,1,1,1,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[2,1,1,1,1,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[2,1,1,1,1,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[2,1,1,1,1,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[1,1,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2

[[1,1,1,1,1,1,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4

[[1,1,1,1,1,1,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3

[[8],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[8],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[7,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[7,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[7,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[6,2],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[6,2],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[6,2],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[6,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[6,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[6,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[5,3],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[5,3],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[5,3],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[5,2,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[5,2,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[5,2,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[5,1,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[5,1,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[5,1,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[4,4],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[4,4],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[4,4],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[4,3,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[4,3,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[4,3,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[4,2,2],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[4,2,2],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[4,2,2],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[4,2,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[4,2,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[4,2,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[4,1,1,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[4,1,1,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[4,1,1,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[3,3,2],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[3,3,2],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[3,3,2],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[3,3,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[3,3,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[3,3,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[3,2,2,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[3,2,2,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[3,2,2,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[3,2,1,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[3,2,1,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[3,2,1,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[3,1,1,1,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[3,1,1,1,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[3,1,1,1,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[2,2,2,2],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[2,2,2,2],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[2,2,2,2],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[2,2,2,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[2,2,2,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[2,2,2,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[2,2,1,1,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[2,2,1,1,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[2,2,1,1,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[2,1,1,1,1,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[2,1,1,1,1,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[2,1,1,1,1,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[1,1,1,1,1,1,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2

[[1,1,1,1,1,1,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3

[[9],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[8,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[7,2],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[7,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[6,3],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[6,2,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[6,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[5,4],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[5,3,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[5,2,2],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[5,2,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[5,1,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[4,4,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[4,3,2],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[4,3,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[4,2,2,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[4,2,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[4,1,1,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[3,3,3],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[3,3,2,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[3,3,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[3,2,2,2],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[3,2,2,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[3,2,1,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[3,1,1,1,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[2,2,2,2,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[2,2,2,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[2,2,1,1,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[2,1,1,1,1,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[1,1,1,1,1,1,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3

[[10]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[9,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[8,2]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[8,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[7,3]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[7,2,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[7,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[6,4]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[6,3,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[6,2,2]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[6,2,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[6,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[5,5]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[5,4,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[5,3,2]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[5,3,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[5,2,2,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[5,2,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[5,1,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[4,4,2]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[4,4,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[4,3,3]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[4,3,2,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[4,3,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[4,2,2,2]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[4,2,2,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[4,2,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[4,1,1,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[3,3,3,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[3,3,2,2]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[3,3,2,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[3,3,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[3,2,2,2,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[3,2,2,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[3,2,1,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[3,1,1,1,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[2,2,2,2,2]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[2,2,2,2,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[2,2,2,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[2,2,1,1,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[2,1,1,1,1,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

[[1,1,1,1,1,1,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2

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Description

The number of terminal closers of a set partition.
A closer of a set partition is a number that is maximal in its block. In particular, a singleton is a closer. This statistic counts the number of terminal closers. In other words, this is the number of closers such that all larger elements are also closers.

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Description

The underlying integer partition of a plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.

Map

to noncrossing partition

Description

Biane's map to noncrossing set partitions.

Map

to Dyck path

Description

Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.