- FindStat

Identifier

Mp00079: Set partitions —shape⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St000074: Gelfand-Tsetlin patterns ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 3756 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{1,4,6,7},{2,5},{3}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,5,7},{3}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,5},{3,7}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,5},{3},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,7},{2,5,6},{3}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,6,7},{3}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,6},{3,7}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,6},{3},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,7},{2,5},{3,6}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,7},{3,6}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5},{3,6,7}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5},{3,6},{7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4},{2,5,7},{3},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4},{2,5},{3},{6,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4,6,7},{2},{3,5}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,7},{3,5}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2},{3,5,7}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2},{3,5},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,7},{2,6},{3,5}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,6,7},{3,5}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,6},{3,5,7}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,6},{3,5},{7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4,7},{2},{3,5,6}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,7},{3,5,6}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,5,6,7}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,5,6},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,7},{2},{3,5},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4},{2},{3,5,7},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4},{2},{3,5},{6,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4},{2},{3,5},{6},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,6},{2},{3,7},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,6},{2},{3},{5,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4},{2,6,7},{3},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4},{2,6},{3},{5,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4,7},{2},{3,6},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4},{2},{3,6,7},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4},{2},{3,6},{5,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4},{2},{3,6},{5},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4,7},{2},{3},{5,6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4},{2,7},{3},{5,6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4},{2},{3,7},{5,6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4},{2},{3},{5,6,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4},{2},{3},{5,6},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4},{2},{3,7},{5},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4},{2},{3},{5,7},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4},{2},{3},{5},{6,7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,5,6,7},{2,4},{3}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,4,7},{3}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,4},{3,7}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5,7},{2,4,6},{3}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,6,7},{3}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,6},{3,7}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,6},{3},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5,7},{2,4},{3,6}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,7},{3,6}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4},{3,6,7}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4},{3,6},{7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2,4,7},{3},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2,4},{3},{6,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6,7},{2,4,5},{3}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,5,7},{3}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,5},{3,7}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,5},{3},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7},{2,4,5,6},{3}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5,6,7},{3}} => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5,6},{3,7}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5,6},{3},{7}} => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7},{2,4,5},{3,6}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5,7},{3,6}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5},{3,6,7}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5},{3,6},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7},{2,4,5},{3},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,5,7},{3},{6}} => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,5},{3,7},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,5},{3},{6,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,5},{3},{6},{7}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,6,7},{2,4},{3,5}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,7},{3,5}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4},{3,5,7}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4},{3,5},{7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7},{2,4,6},{3,5}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,6,7},{3,5}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,6},{3,5,7}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,6},{3,5},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7},{2,4},{3,5,6}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,7},{3,5,6}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,5,6,7}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,5,6},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,4,7},{3,5},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4},{3,5,7},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4},{3,5},{6,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,4},{3,5},{6},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2,4,7},{3},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,6},{2,4},{3},{5,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2,4,6},{3},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,6,7},{3},{5}} => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,6},{3,7},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,6},{3},{5,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,6},{3},{5},{7}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,4,7},{3,6},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4},{3,6,7},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4},{3,6},{5,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,4},{3,6},{5},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2,4},{3},{5,6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,4,7},{3},{5,6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4},{3,7},{5,6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,4},{3},{5,6,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4},{3},{5,6},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,4,7},{3},{5},{6}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2,4},{3,7},{5},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,4},{3},{5,7},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,4},{3},{5},{6,7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,4},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,5,6,7},{2},{3,4}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,7},{3,4}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2},{3,4,7}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2},{3,4},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5,7},{2,6},{3,4}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6,7},{3,4}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6},{3,4,7}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6},{3,4},{7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5,7},{2},{3,4,6}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,7},{3,4,6}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2},{3,4,6,7}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2},{3,4,6},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5,7},{2},{3,4},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2},{3,4,7},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2},{3,4},{6,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2},{3,4},{6},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6,7},{2,5},{3,4}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,5,7},{3,4}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,5},{3,4,7}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7},{2,5,6},{3,4}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,6,7},{3,4}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,6},{3,4,7}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,6},{3,4},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7},{2,5},{3,4,6}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,7},{3,4,6}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,4,6,7}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,4,6},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,5,7},{3,4},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5},{3,4,7},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5},{3,4},{6,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,5},{3,4},{6},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6,7},{2},{3,4,5}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,7},{3,4,5}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,4,5,7}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,4,5},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7},{2,6},{3,4,5}} => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,7},{3,4,5}} => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,4,5,7}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,4,5},{7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7},{2},{3,4,5,6}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,7},{3,4,5,6}} => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,4,5,6,7}} => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,4,5,6},{7}} => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7},{2},{3,4,5},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,7},{3,4,5},{6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,4,5,7},{6}} => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,4,5},{6,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,4,5},{6},{7}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,6,7},{2},{3,4},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,6},{2},{3,4,7},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2},{3,4},{5,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,6},{2},{3,4},{5},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,6,7},{3,4},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,6},{3,4,7},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,6},{3,4},{5,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,6},{3,4},{5},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2},{3,4,6},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,7},{3,4,6},{5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,4,6,7},{5}} => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,4,6},{5,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,4,6},{5},{7}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,7},{2},{3,4},{5,6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,7},{3,4},{5,6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2},{3,4,7},{5,6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,4},{5,6,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,4},{5,6},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2},{3,4},{5},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,7},{3,4},{5},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,4,7},{5},{6}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2},{3,4},{5,7},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,4},{5},{6,7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,4},{5},{6},{7}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5,6},{2},{3,7},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5,6},{2},{3},{4,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2,6,7},{3},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2,6},{3},{4,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5,7},{2},{3,6},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2},{3,6,7},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2},{3,6},{4,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2},{3,6},{4},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5,7},{2},{3},{4,6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2,7},{3},{4,6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2},{3,7},{4,6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2},{3},{4,6,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2},{3},{4,6},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5},{2},{3,7},{4},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5},{2},{3},{4,7},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5},{2},{3},{4},{6,7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2,5,7},{3},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,6},{2,5},{3},{4,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2,5,6},{3},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5,6,7},{3},{4}} => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5,6},{3,7},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5,6},{3},{4,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5,6},{3},{4},{7}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,5,7},{3,6},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5},{3,6,7},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5},{3,6},{4,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,5},{3,6},{4},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2,5},{3},{4,6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,5,7},{3},{4,6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5},{3,7},{4,6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,5},{3},{4,6,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5},{3},{4,6},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,5,7},{3},{4},{6}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2,5},{3,7},{4},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,5},{3},{4,7},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,5},{3},{4},{6,7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,5},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,6,7},{2},{3,5},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,6},{2},{3,5,7},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2},{3,5},{4,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,6},{2},{3,5},{4},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,6,7},{3,5},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,6},{3,5,7},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,6},{3,5},{4,7}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,6},{3,5},{4},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2},{3,5,6},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,7},{3,5,6},{4}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,5,6,7},{4}} => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,5,6},{4,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,5,6},{4},{7}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,7},{2},{3,5},{4,6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,7},{3,5},{4,6}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2},{3,5,7},{4,6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,5},{4,6,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,5},{4,6},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2},{3,5},{4},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,7},{3,5},{4},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,5,7},{4},{6}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2},{3,5},{4,7},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,5},{4},{6,7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,5},{4},{6},{7}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,6,7},{2},{3},{4,5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2,7},{3},{4,5}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,6},{2},{3,7},{4,5}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,6},{2},{3},{4,5,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2},{3},{4,5},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2,6},{3},{4,5}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,6,7},{3},{4,5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,6},{3,7},{4,5}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,6},{3},{4,5,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,6},{3},{4,5},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2},{3,6},{4,5}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,7},{3,6},{4,5}} => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2},{3,6,7},{4,5}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,6},{4,5,7}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,6},{4,5},{7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2},{3},{4,5,6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,7},{3},{4,5,6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,7},{4,5,6}} => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3},{4,5,6,7}} => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3},{4,5,6},{7}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,7},{2},{3},{4,5},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,7},{3},{4,5},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,7},{4,5},{6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4,5,7},{6}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2},{3},{4,5},{6,7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4,5},{6},{7}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6},{2},{3,7},{4},{5}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6},{2},{3},{4,7},{5}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6},{2},{3},{4},{5,7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,6,7},{3},{4},{5}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2,6},{3,7},{4},{5}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,6},{3},{4,7},{5}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,6},{3},{4},{5,7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,6},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,7},{2},{3,6},{4},{5}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,7},{3,6},{4},{5}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,6,7},{4},{5}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2},{3,6},{4,7},{5}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,6},{4},{5,7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,6},{4},{5},{7}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,7},{2},{3},{4,6},{5}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,7},{3},{4,6},{5}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,7},{4,6},{5}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4,6,7},{5}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2},{3},{4,6},{5,7}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4,6},{5},{7}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,7},{2},{3},{4},{5,6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,7},{3},{4},{5,6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,7},{4},{5,6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4,7},{5,6}} => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4},{5,6,7}} => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2},{3},{4},{5,6},{7}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2,7},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3,7},{4},{5},{6}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4,7},{5},{6}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5,7},{6}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5},{6},{7}} => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => 0

{{1,2},{3,4},{5,6},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,4},{5,6},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,3},{5,6},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,3},{4,6},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,3},{4,5},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,3},{4,5},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,4},{3,5},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,4},{3,5},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,4},{3,5},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,4},{3,6},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,5},{3,6},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,5},{4,6},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,2},{3,5},{4,6},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,2},{3,6},{4,5},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,6},{4,5},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,6},{3,5},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,6},{3,4},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,5},{3,4},{7,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,5},{3,4},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,6},{3,4},{5,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,6},{3,4},{5,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,7},{3,4},{5,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,7},{3,4},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,7},{3,5},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,7},{4,5},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,2},{3,7},{4,5},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,2},{3,8},{4,5},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,8},{4,5},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,8},{3,5},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,8},{3,4},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,8},{3,4},{5,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,8},{3,4},{5,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,7},{3,5},{4,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,8},{3,5},{4,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,8},{3,6},{4,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,8},{3,6},{5,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,8},{4,6},{5,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,2},{3,8},{4,6},{5,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,2},{3,7},{4,6},{5,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,7},{4,6},{5,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,7},{3,6},{5,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,7},{3,6},{4,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,7},{3,5},{4,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,6},{3,5},{4,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,6},{3,5},{4,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,5},{3,6},{4,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,5},{3,6},{4,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,5},{3,7},{4,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,2},{3,6},{4,7},{5,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,2},{3,5},{4,7},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,5},{4,7},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,4},{3,7},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,4},{3,7},{5,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,4},{3,6},{5,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,4},{3,6},{5,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,3},{4,6},{5,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,3},{4,6},{5,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,3},{4,7},{5,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,3},{4,7},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,3},{5,7},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,4},{5,7},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,2},{3,4},{5,7},{6,8}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,2},{3,4},{5,8},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,4},{5,8},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,3},{5,8},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,3},{4,8},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,3},{4,8},{5,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,3},{4,8},{5,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,4},{3,8},{5,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,4},{3,8},{5,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,4},{3,8},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,5},{3,8},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,5},{4,8},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,2},{3,5},{4,8},{6,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,2},{3,6},{4,8},{5,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,6},{4,8},{5,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,6},{3,8},{5,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,6},{3,8},{4,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,5},{3,8},{4,7}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,5},{3,8},{4,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,5},{3,7},{4,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,6},{3,7},{4,5}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,6},{3,8},{4,5}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,7},{3,8},{4,5}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,7},{3,8},{4,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,7},{3,8},{5,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,7},{4,8},{5,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,2},{3,7},{4,8},{5,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,2},{3,8},{4,7},{5,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3},{2,8},{4,7},{5,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,8},{3,7},{4,5}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,7},{2,8},{3,6},{4,5}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,6},{2,7},{3,8},{4,9},{5,10}} => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [[2,2,2,2,2,0,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 5

{{1},{2},{3},{4},{5},{6},{7},{8}} => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => 0

{{1},{2},{3},{4},{5},{6},{7,8}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5},{6,8},{7}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5},{6,7,8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2},{3},{4},{5,6},{7},{8}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5,6},{7,8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4},{5,7},{6},{8}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5,8},{6},{7}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5,7,8},{6}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2},{3},{4},{5,6,7},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2},{3},{4},{5,8},{6,7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4},{5,6,8},{7}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2},{3},{4},{5,6,7,8}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3},{4,5},{6},{7,8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4,8},{5},{6},{7}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4,6,7,8},{5}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3},{4,8},{5,6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4,7,8},{5,6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3},{4,8},{5,7},{6}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4,8},{5,6,7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3},{4,5,6,7,8}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,4},{5},{6},{7,8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,4},{5},{6,8},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,4},{5,6,7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,5},{4},{6,7,8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,8},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3,7,8},{4},{5,6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,5,7,8},{4},{6}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,8},{4},{5,6,7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,5,8},{4},{6,7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,5,6,7,8},{4}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,4,5},{6},{7},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2},{3,4,5},{6,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,8},{4,5},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,6,7,8},{4,5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,8},{4,6},{5},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,7,8},{4,6},{5}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,8},{4,7},{5},{6}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,8},{4,6,7},{5}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,4,5,6},{7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,8},{4,5,6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,7,8},{4,5,6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,8},{4,7},{5,6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2},{3,4,5,8},{6},{7}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,4,5,6,7},{8}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,8},{4,5,6,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,4,8},{5,6,7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,4,5,8},{6,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,4,5,6,8},{7}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,4,5,6,7,8}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3},{4},{5},{6},{7,8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,3},{4},{5},{6,8},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,3},{4},{5,6,7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3},{4,5},{6,7},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,3},{4,5},{6,8},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,3},{4,5},{6,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3},{4,6,7},{5},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3},{4,6,8},{5},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3},{4,6,7,8},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3},{4,5,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3},{4,7},{5,6},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,3},{4,8},{5,6},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,3},{4,7,8},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3},{4,8},{5,7},{6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,3},{4,5,8},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3},{4,8},{5,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3},{4,5,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3},{4,5,6,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3},{4,5,6,7,8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,4},{3},{5},{6},{7,8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,4},{3},{5},{6,8},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,4},{3},{5},{6,7,8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4},{3},{5,6},{7,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,4},{3},{5,7,8},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4},{3},{5,8},{6,7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,4},{3},{5,6,7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3},{4},{6,8},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,8},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2,5,8},{3},{4},{6},{7}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2,8},{3},{4},{5,6,7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5,6,8},{3},{4},{7}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5,6,7,8},{3},{4}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5},{3},{6,7},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,5},{3},{6,8},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,5},{3},{6,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3},{4,5},{7,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,6,8},{3},{4,5},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,6,7,8},{3},{4,5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,6},{3},{5},{7,8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,6,7},{3},{5},{8}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,8},{3},{4,6,7},{5}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,8},{3},{5},{6,7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,6,8},{3},{5},{7}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,6,7,8},{3},{5}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,7,8},{3},{4,5,6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,7},{3},{5,6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,8},{3},{4,7},{5,6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,4,8},{3},{5,6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,7,8},{3},{5,6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,8},{3},{5,7},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,5,7,8},{3},{6}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,8},{3},{5,6,7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5,8},{3},{6,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5,6,8},{3},{7}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5,6,7,8},{3}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,4},{5},{6},{7},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2,3,4},{5},{6,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4},{5,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4},{5,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4},{5,6,8},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,4},{6,7},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,5},{3,4},{6,8},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,5},{3,4},{6,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,4},{5},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,6,7},{3,4},{5},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,6,8},{3,4},{5},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,7},{3,4},{5,6},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,8},{3,4},{5,6},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,7,8},{3,4},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,4},{5,7},{6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,8},{3,4},{5,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,8},{3,4},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,6,7,8},{3,4}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,5},{4},{6},{7},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2,3,5},{4},{6,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,5},{4},{7,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,7},{3,5},{4},{6},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,8},{3,5},{4},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,6,7},{3,5},{4},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,8},{3,5},{4},{6,7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,6,8},{3,5},{4},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,6,7,8},{3,5},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,6},{4},{5},{7},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2,3,7},{4},{5},{6},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2,8},{3,7},{4},{5},{6}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,3,8},{4},{5},{6},{7}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2,3,7,8},{4},{5},{6}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3,6,7},{4},{5},{8}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3,6,8},{4},{5},{7}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3,6,7,8},{4},{5}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,7},{3,5,6},{4},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,8},{3,5,6},{4},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3,7},{4},{5,6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,8},{3,7},{4},{5,6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,3,5,7},{4},{6},{8}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,8},{3,5,7},{4},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3,5,8},{4},{6},{7}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3,5,7,8},{4},{6}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,5,6,7},{4},{8}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,5,6,7},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,8},{4},{5,6,7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,5,8},{4},{6,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,5,6,8},{4},{7}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,4,5},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,8},{3,4,5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,8},{3,4,5},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,7,8},{3,4,5}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,6},{4,5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,7},{3,6},{4,5},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,8},{3,6},{4,5},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,7,8},{3,6},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,7},{4,5},{6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,3,8},{4,5},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3,6,7},{4,5},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,6,7},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,8},{4,5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,6,8},{4,5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,6},{5},{7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,4,6},{5},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,7,8},{3,4,6},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,7},{4,6},{5}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,3,8},{4,6},{5},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3,7,8},{4,6},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,8},{5},{6},{7}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3,4,7,8},{5},{6}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,4,6,7},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,8},{4,6,7},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,6,8},{5},{7}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,6,7,8},{5}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,4,5,6},{7},{8}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,5,6},{7,8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,8},{3,4,5,6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,7},{4,5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,8},{4,5,6},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,4,7},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,8},{4,7},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,8},{5,6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,5,7},{6},{8}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,4,5,7},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,8},{4,5,7},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,8},{5,7},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,5,8},{6},{7}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,5,7,8},{6}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,4,8},{5,6,7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,4,5,8},{6,7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,4,5,6,8},{7}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,4,5,6,7,8}} => [7,1] => [[1,2,3,4,5,6,7],[8]] => [[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,2},{3},{4},{5},{6},{7,8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,2},{3},{4},{5},{6,8},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,2},{3},{4},{5,6,7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3},{4,5},{6,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3},{4,6,7,8},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3},{4,5,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3},{4,5,8},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2},{3},{4,5,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3},{4,5,6,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3},{4,5,6,7,8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,4},{5},{6,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4},{5,7,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4},{5,6,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4},{5,6,7,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,5},{4},{6,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,6,7,8},{4},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,5,6},{4},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,7,8},{4},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,5,7,8},{4},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,8},{4},{5,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,5,8},{4},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,5,6,8},{4},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,5,6,7,8},{4}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,4,5},{6},{7},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2},{3,8},{4,5},{6},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,2},{3,7,8},{4,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,6,8},{4,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,6,7,8},{4,5}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,4,6},{5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,7,8},{4,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4,8},{5},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2},{3,4,7,8},{5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,8},{4,6,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4,8},{5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4,6,8},{5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4,6,7,8},{5}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,4,5,6},{7,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,8},{4,5,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4,8},{5,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,8},{4,5,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4,8},{5,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4,5,8},{6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4,5,7,8},{6}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,4,5,6,7},{8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,8},{4,5,6,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,4,8},{5,6,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,4,5,8},{6,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,4,5,6,8},{7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,4,5,6,7,8}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3},{2},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,3},{2},{4},{5},{6},{7,8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,3},{2},{4},{5},{6,8},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,3},{2},{4},{5},{6,7,8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3},{2},{4},{5,7,8},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3},{2},{4},{5,8},{6,7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3},{2},{4},{5,6,7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,5},{6,7},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3},{2},{4,5},{6,8},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3},{2},{4,5},{6,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,6},{5},{7,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3},{2},{4,6,7},{5},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3},{2},{4,8},{5},{6,7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3},{2},{4,6,8},{5},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3},{2},{4,6,7,8},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,5,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,7},{5,6},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3},{2},{4,8},{5,6},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3},{2},{4,7,8},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,8},{5,7},{6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3},{2},{4,5,7,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,8},{5,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,5,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,5,6,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,5,6,7,8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4},{2},{3},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,4},{2},{3},{5},{6,8},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4},{2},{3},{5},{6,7,8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4},{2},{3},{5,6},{7,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4},{2},{3},{5,8},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4},{2},{3},{5,6,7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2},{3},{4},{6},{7},{8}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,5},{2},{3},{4},{6,7,8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2},{3},{4},{5},{7},{8}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,6},{2},{3},{4},{5},{7,8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2},{3},{4},{5},{6},{8}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,7,8},{2},{3},{4},{5},{6}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,8},{2},{3},{4},{5},{6,7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6,8},{2},{3},{4},{5},{7}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,6,7,8},{2},{3},{4},{5}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7},{2},{3},{4},{5,6},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5,7},{2},{3},{4},{6},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,8},{2},{3},{4},{5,7},{6}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5,7,8},{2},{3},{4},{6}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,8},{2},{3},{4},{5,6,7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5,6,8},{2},{3},{4},{7}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5,6,7,8},{2},{3},{4}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2},{3},{6},{7},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,4,5},{2},{3},{6,8},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,5},{2},{3},{6,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3},{4,5},{7},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,8},{2},{3},{4,5},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6,7},{2},{3},{4,5},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6,7,8},{2},{3},{4,5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2},{3},{4,6},{5},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4,6,8},{2},{3},{5},{7}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,5,6},{2},{3},{7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2},{3},{4,5,6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,8},{2},{3},{5,6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,7,8},{2},{3},{5,6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,8},{2},{3},{6},{7}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,5,6,7},{2},{3},{8}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2},{3},{5,6,7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,8},{2},{3},{6,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,6,8},{2},{3},{7}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2},{5},{6},{7},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,3,4},{2},{5},{6},{7,8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,4},{2},{5},{6,8},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,4},{2},{5},{6,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2},{5,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2},{5,7,8},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2},{5,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2},{5,6,8},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2},{5,6,7,8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5},{2},{3,4},{6},{7},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5},{2},{3,4},{6},{7,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2},{3,4},{6,8},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,8},{2},{3,4},{5},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6,7,8},{2},{3,4},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2},{3,4},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7,8},{2},{3,4},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2},{3,4},{6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5,7,8},{2},{3,4},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6,7},{2},{3,4},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2},{3,4},{5,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2},{3,4},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6,8},{2},{3,4},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2},{4},{6},{7},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,3,5},{2},{4},{6},{7,8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,5},{2},{4},{6,7},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,5},{2},{4},{6,8},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,5},{2},{4},{6,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,5},{4},{7},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6},{2},{3,5},{4},{7,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,8},{2},{3,5},{4},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6,8},{2},{3,5},{4},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6,7,8},{2},{3,5},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2},{4},{5},{7},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,3,7},{2},{4},{5},{6},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,3,8},{2},{4},{5},{6},{7}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,3,7,8},{2},{4},{5},{6}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,5,6},{2},{4},{7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2},{3,5,6},{4},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7,8},{2},{3,5,6},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2},{4},{5,6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,5,7},{2},{4},{6},{8}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,5,7,8},{2},{4},{6}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2},{4},{5,6,7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5,8},{2},{4},{6,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5,6,8},{2},{4},{7}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,5},{2},{6},{7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,5},{2},{6,7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,5},{2},{6,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,5},{2},{6,7,8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6},{2},{3,4,5},{7},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2},{3,4,5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2},{3,4,5},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7,8},{2},{3,4,5},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2},{3,4,5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2},{3,4,5},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2},{4,5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2},{3,6},{4,5},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7,8},{2},{3,6},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2},{4,5},{6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,7,8},{2},{4,5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2},{3,6,7},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2},{4,5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6,8},{2},{4,5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,6},{2},{5},{7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2},{4,6},{5},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,7,8},{2},{4,6},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,8},{2},{5},{6},{7}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,4,7,8},{2},{5},{6}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2},{3,4,6,7},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2},{4,6,7},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,6,8},{2},{5},{7}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,5,6},{2},{7},{8}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,5,6},{2},{7,8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,8},{2},{3,4,5,6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2},{4,5,6},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2},{4,5,6},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2},{3,4,7},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2},{4,7},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,8},{2},{5,6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2},{3,4,5,7},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2},{4,5,7},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,8},{2},{5,7},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,5,8},{2},{6},{7}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,5,6,7},{2},{8}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4,5,8},{2},{6,7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4,5,6,8},{2},{7}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4,5,6,7,8},{2}} => [7,1] => [[1,2,3,4,5,6,7],[8]] => [[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,2,3},{4},{5},{6},{7,8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,3},{4},{5},{6,8},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,3},{4,6,7},{5},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3},{4,5,8},{6},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3},{4,5,7,8},{6}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3},{4,5,6,7},{8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3},{4,5,8},{6,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3},{4,5,6,7,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,4},{2,3},{5},{6},{7},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4},{2,3},{5,7,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3},{5,6,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3},{5,6,7,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5},{2,3},{4},{6},{7},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5},{2,3},{4},{6,7},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2,3},{4},{6,8},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,6},{2,3},{4},{5},{7,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7},{2,3},{4},{5},{6},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,8},{2,3},{4},{5},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6,8},{2,3},{4},{5},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5,6},{2,3},{4},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3},{4},{5,6},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7,8},{2,3},{4},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,3},{4},{6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5,7,8},{2,3},{4},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6,7},{2,3},{4},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3},{4},{5,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,3},{4},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6,8},{2,3},{4},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2,3},{6,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3},{4,5},{6},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,8},{2,3},{4,5},{6},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7,8},{2,3},{4,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,3},{4,5},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,3},{4,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7,8},{2,3},{4,5}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,6},{2,3},{5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3},{4,6},{5},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7,8},{2,3},{4,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,3},{5},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,7,8},{2,3},{5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6,7},{2,3},{5},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3},{4,6,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,3},{5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6,8},{2,3},{5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6,7,8},{2,3},{5}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5,6},{2,3},{7,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7},{2,3},{4,5,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,3},{5,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,3},{5,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,7},{2,3},{6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3},{4,5,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,3},{5,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,8},{2,3},{6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,6,7},{2,3},{8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,8},{2,3},{5,6,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5,8},{2,3},{6,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5,6,8},{2,3},{7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5,6,7,8},{2,3}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,4},{3},{5},{6},{7},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,2,4},{3},{5,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3},{5,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3},{5,6,8},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3},{5,6,7,8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5},{2,4},{3},{6},{7},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5},{2,4},{3},{6},{7,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2,4},{3},{6,7},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2,4},{3},{6,8},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2,4},{3},{6,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4},{3},{5},{6},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,8},{2,4},{3},{5},{6,7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,6,7,8},{2,4},{3},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,4},{3},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4},{3},{5,6},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7,8},{2,4},{3},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,4},{3},{6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,8},{2,4},{3},{5,7},{6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5,7,8},{2,4},{3},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4},{3},{5,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,4},{3},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6,8},{2,4},{3},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3},{4},{6},{7},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,2,5},{3},{4},{6},{7,8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2,5},{3},{4},{7},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6},{2,5},{3},{4},{7,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7},{2,5},{3},{4},{6},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,8},{2,5},{3},{4},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7,8},{2,5},{3},{4},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6,7,8},{2,5},{3},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3},{4},{5},{7},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,2,6},{3},{4},{5},{7,8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7,8},{2,6},{3},{4},{5}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,7},{3},{4},{5},{6},{8}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,2,7,8},{3},{4},{5},{6}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,5,6},{3},{4},{7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7,8},{2,5,6},{3},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,5,7},{3},{4},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,5,7,8},{3},{4},{6}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,6,7},{3},{4},{8}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,5,6,7},{3},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,6,8},{3},{4},{7}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,5},{3},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,5},{3},{6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7,8},{2,4,5},{3},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,4,5},{3},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4,5},{3},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,4,5},{3},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3},{4,5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,6},{3},{4,5},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7,8},{2,6},{3},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7,8},{3},{4,5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,6,7},{3},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3},{4,5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6,8},{3},{4,5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,6},{3},{5},{7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,6},{3},{5},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7,8},{2,4,6},{3},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7,8},{3},{4,6},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4,7},{3},{5},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,4,8},{3},{5},{6},{7}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,4,7,8},{3},{5},{6}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4,6,7},{3},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3},{4,6,7},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,8},{3},{5},{6,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,6,8},{3},{5},{7}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,6,7,8},{3},{5}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,5,6},{3},{7,8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7},{2,4,5,6},{3},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4,5,6},{3},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,7},{3},{4,5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3},{4,5,6},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,7},{3},{5,6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4,7},{3},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3},{4,7},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,8},{3},{5,6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4,5,7},{3},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3},{4,5,7},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,8},{3},{5,7},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,5,7,8},{3},{6}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,5,8},{3},{6,7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,5,6,8},{3},{7}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,5,6,7,8},{3}} => [7,1] => [[1,2,3,4,5,6,7],[8]] => [[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4},{5},{6},{7},{8}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,3,4},{5},{6,7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,4},{5,6},{7,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4},{5,7,8},{6}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4},{5,6,7},{8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4},{5,8},{6,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4},{5,6,8},{7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4},{5,6,7,8}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,5},{2,3,4},{6},{7},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2,3,4},{6,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3,4},{5},{7},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2,3,4},{5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,4},{5},{6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,8},{2,3,4},{5},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,8},{2,3,4},{5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,3,4},{5},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,3,4},{7},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,4},{5,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,4},{5,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,3,4},{6},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,4},{5,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,3,4},{6},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6,7},{2,3,4},{8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,8},{2,3,4},{6,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,6,8},{2,3,4},{7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,6,7,8},{2,3,4}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,5},{3,4},{6},{7},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,5},{3,4},{6,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,4},{6,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,4},{6,7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7},{2,5},{3,4},{6},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7,8},{2,5},{3,4},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,5},{3,4},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,5},{3,4},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7,8},{2,5},{3,4}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6},{3,4},{5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,6},{3,4},{5},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,8},{2,6},{3,4},{5},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7,8},{2,6},{3,4},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,7},{3,4},{5},{6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,2,8},{3,4},{5},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,7,8},{3,4},{5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,6,7},{3,4},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,4},{5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6,8},{3,4},{5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,6},{3,4},{7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,5,6},{3,4},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7,8},{2,5,6},{3,4}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,7},{3,4},{5,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,4},{5,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,7},{3,4},{6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,5,7},{3,4},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,4},{5,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,8},{3,4},{6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,6,8},{3,4},{7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,5},{4},{6},{7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,5},{4},{6,7,8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6},{2,3,5},{4},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,5},{4},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7,8},{2,3,5},{4},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,3,5},{4},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,5},{4},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,3,5},{4},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3,5},{4},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,6},{3,5},{4},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7,8},{2,6},{3,5},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7,8},{3,5},{4},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,6,7},{3,5},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,5},{4},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6,8},{3,5},{4},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,6},{4},{5},{7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,6},{4},{5},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,7,8},{2,3,6},{4},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7,8},{3,6},{4},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,7},{4},{5},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,3,8},{4},{5},{6},{7}} => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,3,7,8},{4},{5},{6}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,6,7},{4},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,6,7},{4},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,8},{4},{5},{6,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,6,8},{4},{5},{7}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,6,7,8},{4},{5}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,5,6},{4},{7},{8}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,5,6},{4},{7,8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7},{2,3,5,6},{4},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,5,6},{4},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3,5,6},{4},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,7},{3,5,6},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,5,6},{4},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,7},{4},{5,6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,7},{4},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,7},{4},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,8},{4},{5,6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,5,7},{4},{6},{8}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,5,7},{4},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,5,7},{4},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,8},{4},{5,7},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,5,8},{4},{6},{7}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,5,7,8},{4},{6}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,5,6,7},{4},{8}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,8},{2,3,5,6,7},{4}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,5,6,7,8},{4}} => [7,1] => [[1,2,3,4,5,6,7],[8]] => [[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5},{6},{7},{8}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,4,5},{6,7},{8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,5},{6,8},{7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,5},{6,7,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,6},{2,3,4,5},{7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,4,5},{6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7,8},{2,3,4,5}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,6},{3,4,5},{7},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3,4,5},{7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7},{2,6},{3,4,5},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,6},{3,4,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7,8},{2,6},{3,4,5}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,8},{2,7},{3,4,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,4,5},{6,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6,7,8},{3,4,5}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,6},{4,5},{7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,6},{4,5},{7,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,8},{2,3,6},{4,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,6},{4,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,7},{4,5},{6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,7},{4,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,7},{4,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,8},{4,5},{6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,6,7},{4,5},{8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,8},{2,3,6,7},{4,5}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,8},{4,5},{6,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,6,8},{4,5},{7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,6,7,8},{4,5}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,6},{5},{7},{8}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,4,6},{5},{7,8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,8},{2,3,4,6},{5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,7},{3,4,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,4,6},{5},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7,8},{3,4,6},{5}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,7},{4,6},{5},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,7},{4,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,7},{4,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,8},{4,6},{5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,7,8},{4,6},{5}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,7},{5},{6},{8}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,4,7},{5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,4,7},{5},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,8},{4,7},{5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,4,8},{5},{6},{7}} => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,4,7,8},{5},{6}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,6,7},{5},{8}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,8},{2,3,4,6,7},{5}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,6,8},{5},{7}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,6,7,8},{5}} => [7,1] => [[1,2,3,4,5,6,7],[8]] => [[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5,6},{7},{8}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,5,6},{7,8}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,7},{2,3,4,5,6},{8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,8},{2,3,4,5,6},{7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,7},{3,4,5,6},{8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,7,8},{3,4,5,6}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,7},{4,5,6},{8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,8},{2,3,7},{4,5,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,8},{3,7},{4,5,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,8},{4,5,6},{7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,7,8},{4,5,6}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,7},{5,6},{8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,8},{2,3,4,7},{5,6}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,8},{3,4,7},{5,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,8},{4,7},{5,6}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,8},{5,6},{7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,5,7},{6},{8}} => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,8},{2,3,4,5,7},{6}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,8},{3,4,5,7},{6}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,8},{4,5,7},{6}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,8},{5,7},{6}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,5,7,8},{6}} => [7,1] => [[1,2,3,4,5,6,7],[8]] => [[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5,6,7},{8}} => [7,1] => [[1,2,3,4,5,6,7],[8]] => [[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,8},{2,3,4,5,6,7}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,8},{3,4,5,6,7}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,8},{4,5,6,7}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,8},{5,6,7}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5,8},{6,7}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5,6,8},{7}} => [7,1] => [[1,2,3,4,5,6,7],[8]] => [[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5,6,7,8}} => [8] => [[1,2,3,4,5,6,7,8]] => [[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,3,5,6,7,8},{2,4}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4,6,7,8},{2,5}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,4,6,7,8},{3,5}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,4,5,7,8},{3,6}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,5,7,8},{4,6}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,4,5,6,8},{3,7}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,5,6,8},{4,7}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,6,8},{5,7}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,4,5,6,7},{3,8}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,5,7,8},{2,4,6}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,5,7,8},{3,4,6}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4,7,8},{2,5,6}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,4,7,8},{3,5,6}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,5,6,8},{3,4,7}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4,6,8},{2,5,7}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,4,6,8},{3,5,7}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,6,8},{4,5,7}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,5,8},{4,6,7}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,6,7},{4,5,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4,5,7},{2,6,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,7},{5,6,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,4,5,6},{3,7,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,5,6},{4,7,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,6},{5,7,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,6,7,8},{2,4},{5}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4,7,8},{2,6},{5}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,7,8},{3,6},{5}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4,5,8},{2,7},{6}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4,6,7},{2,8},{5}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,6,7},{3,8},{5}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4,5,7},{2,8},{6}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,5,7},{4,8},{6}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4,5,6},{2,8},{7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,5,6},{4,8},{7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,6},{5,8},{7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5,6,7},{2,4},{8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,5,7},{4,6},{8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,5,6},{4,7},{8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,6},{5,7},{8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5,7},{2,4,6,8}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,5,7},{3,4,6,8}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4,7},{2,5,6,8}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,7},{4,5,6,8}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,5,6},{2,4,7,8}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,5,6},{3,4,7,8}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,4,6},{3,5,7,8}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,6},{4,5,7,8}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,6,8},{2,5,7},{4}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6,8},{3,5,7},{4}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5,8},{3,6,7},{4}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5,8},{3,4,6},{7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,8},{3,5,6},{7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,7},{3,6,8},{5}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5,7},{2,4,8},{6}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,7},{3,5,8},{6}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4,5},{2,7,8},{6}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,5},{3,7,8},{6}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5,6},{2,4,8},{7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,6},{4,5,8},{7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,5},{4,6,7},{8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,7,8},{3,5},{4,6}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6,8},{3,5},{4,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,6,8},{2,4},{5,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5,8},{2,6},{4,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5,8},{2,4},{6,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,8},{3,5},{6,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5,7},{2,6},{3,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5,7},{2,6},{4,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5,6},{2,4},{7,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,6},{3,5},{7,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,7,8},{2,6},{3},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7,8},{2,6},{3},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7,8},{2,6},{4},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7,8},{2,5},{4},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7,8},{2,4},{5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6,8},{2,7},{3},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6,8},{2,7},{3},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6,8},{2,7},{4},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6,8},{3,7},{4},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,8},{2,7},{3},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5,8},{2,7},{4},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,8},{3,7},{4},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,8},{2,7},{5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,8},{3,7},{5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6,8},{2,5},{3},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6,8},{2,5},{4},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6,8},{2,4},{5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,8},{2,6},{3},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5,8},{2,6},{4},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,8},{3,6},{4},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,8},{2,6},{5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,8},{3,6},{5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,8},{2,5},{6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,8},{3,5},{6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6,7},{2,8},{3},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6,7},{2,8},{3},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6,7},{2,8},{4},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6,7},{3,8},{4},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,7},{2,8},{3},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5,7},{2,8},{4},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,7},{3,8},{4},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,7},{2,8},{5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,7},{3,8},{5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,6},{2,8},{3},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5,6},{2,8},{4},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,6},{3,8},{4},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,6},{2,8},{5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,6},{3,8},{5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,6},{4,8},{5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,5},{2,8},{6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,5},{3,8},{6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,5},{4,8},{6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6,7},{2,5},{3},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6,7},{2,5},{4},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,7},{2,6},{3},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5,7},{2,6},{4},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,7},{3,6},{4},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,7},{2,6},{5},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,7},{3,6},{5},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5,7},{2,4},{6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,7},{3,5},{6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,6},{2,7},{3},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,6},{2,7},{5},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,6},{3,7},{5},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,6},{4,7},{5},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,5},{2,7},{6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,5},{3,7},{6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,5},{4,7},{6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,6},{3,5},{7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,5},{2,6},{7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,5},{3,6},{7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,5},{4,6},{7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,4,8},{5,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5},{2,6,8},{3,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4},{2,6,8},{5,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5},{2,4,8},{6,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5},{3,4,8},{6,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4},{2,5,8},{6,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4},{3,5,8},{6,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,6},{2,5,7},{3,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5},{3,4,6},{7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4},{2,5,6},{7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4},{3,5,6},{7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,7},{2,6,8},{3},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,6,8},{3},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,6,8},{4},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3,6,8},{4},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,5,8},{3},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,5,8},{4},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3,5,8},{4},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,4,8},{5},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3,4,8},{5},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,7,8},{3},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,7,8},{3},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,7,8},{4},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3,7,8},{4},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2,7,8},{3},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2,7,8},{4},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,7,8},{4},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2,7,8},{5},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3,7,8},{5},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,5,8},{3},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,5,8},{4},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3,5,8},{4},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,4,8},{5},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3,4,8},{5},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2,6,8},{3},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2,6,8},{4},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,6,8},{4},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2,6,8},{5},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3,6,8},{5},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,4,8},{6},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3,5,8},{6},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,5,7},{3},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,5,7},{4},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3,5,7},{4},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,4,7},{5},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2,6,7},{4},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,6,7},{4},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2,6,7},{5},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2,4,7},{6},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,4,7},{6},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3,5,7},{6},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,4,6},{7},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,6},{3,7},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,6},{3,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,6},{4,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,6},{4,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,5},{3,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,5},{4,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,5},{4,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,4},{5,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,5},{3,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,5},{4,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,5},{4,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,4},{5,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,6},{3,8},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,6},{3,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,6},{4,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3,6},{4,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,5},{3,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,5},{4,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3,5},{4,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,4},{5,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3,4},{5,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,7},{3,8},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,7},{3,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,7},{4,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3,7},{4,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2,7},{3,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2,7},{4,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,7},{4,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2,7},{5,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3,7},{5,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,5},{3,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,5},{4,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3,5},{4,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,4},{5,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3,4},{5,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2,6},{3,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2,6},{4,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,6},{4,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2,6},{5,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3,6},{5,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3},{4,6},{5,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2,4},{6,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2,5},{6,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,5},{3,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,5},{4,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,4},{5,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3,4},{5,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2,6},{3,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2,6},{5,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3,6},{5,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3},{4,6},{5,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2,5},{6,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,4},{5},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6,7},{2,8},{3},{4},{5}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,4},{2,8},{5},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,7},{2,6},{3},{5},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,7},{2,5},{3},{6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,7},{2,4},{5},{6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,6},{2,7},{3},{5},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,5},{2,4},{6},{7},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2,6},{3,7},{4},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3},{2,6},{4,7},{5},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3},{2,5},{4,7},{6},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4},{2,5},{3,6},{7},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3},{2,5},{4,6},{7},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4},{2,8},{3},{5},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,3},{2,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5},{2,6},{3},{4},{7},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4},{2,5},{3},{6},{7},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,3},{2,4},{5},{6},{7},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,3,5,8},{2},{4,6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5,7},{2},{4},{6,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,4},{3},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,8},{3},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,4},{3,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,4},{3,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,5,8},{4,6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,6},{3,4},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,6},{3,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,8},{3},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,5},{3},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,6,7},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,6},{5,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,7},{5,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,5,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2},{3,4,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3},{4,7,8},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,7},{3},{4,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,5,7},{4},{6,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2},{3,4},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2},{3,5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,8},{5,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2},{3,8},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2},{3,7},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,4,7},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3,7},{4},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,6,7},{4,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,6},{4,7,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3},{4},{5,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,4},{5,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,7},{3,4},{5,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3},{4},{5,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,7},{4,6,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,5,8},{4,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,8},{4,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,4,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,5,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,7},{5,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,6},{5,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,6,7},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,6,7},{4},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,6},{4},{5,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,7},{4},{5,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,7,8},{4,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,4,7},{5},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,3,7},{5},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,3,8},{5},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,8},{4,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,8},{4},{5,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,8},{4},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,7},{4},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,6},{3,7},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,6},{3,8},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,8},{5,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,7},{3,5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,7},{3,4},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,4,6},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,6},{4},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3,8},{4,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,6},{4},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,7},{3,4,6},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,6,8},{4,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,5,7},{4,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,7},{4,5,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,7},{3},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,8},{4},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,8},{4,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2},{4,5,8},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3},{4,5,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,8},{4,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,8},{4},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7,8},{2,5},{3,6},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,6,8},{3},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,5},{3,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,5},{3},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7,8},{2},{3,6},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,7},{3,6},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,5,7},{3,6},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,6,7},{3},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,7},{2},{3,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2,6},{4},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,8},{4,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6,8},{2},{3,7},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4,6},{3,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,5},{3},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2,8},{4},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,3,8},{4},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,6},{3,4,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2},{3,4,7},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,4},{3,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3,8},{4,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3,7,8},{4},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,3,7},{4,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,3,6},{4},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,4},{3,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,4,8},{3},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,5,7},{3},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,7},{3,5},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,7},{3},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,8},{3,4},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2},{3,4,8},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,5},{3,4,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,6,8},{3,4},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,3,6},{5},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,8},{3,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,7},{3,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,8},{3,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,8},{3,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,5},{3,4,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3,5},{4,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,3,6},{4,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6},{3,4,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,7},{3,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,8},{3,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,8},{3,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,8},{3,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,8},{3,4,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,3,8},{4,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,8},{4,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,7},{3,4,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,7},{3,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,6},{3,4,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,6},{4,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,6},{4,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,5},{4,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,5},{3,4,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4,7},{3,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4,7},{3,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,8},{3,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2,8},{4,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,7},{4,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,8},{3,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,7},{3,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,6},{3,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,8},{3,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,5},{4,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3,8},{4,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,8},{3,4,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,8},{3,4,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3,7},{4,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,7},{3,4,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2},{4,6,8},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4,6,8},{5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,6,8},{3},{5,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,6,8},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2},{4,8},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2},{4,7},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2},{4,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5,7},{2},{4,6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2},{4,6,8},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2},{4,6},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5,7},{2},{4,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4,8},{5,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,8},{3,5,7},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,8},{3,5,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,7},{3,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,5,7},{4,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,7},{4,6,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,4,6},{5},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,6},{3},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,4,8},{3},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,5,7},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,6},{3,5},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,6},{3,5},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,8},{3,7},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,8},{3,6},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,8},{3,6},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,6,8},{3,5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,6,8},{3,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5},{3,6,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,5},{4,6,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,6,8},{3},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4},{3,6,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,8},{3,5,7},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,8},{3,5,7},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,8},{3},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,7},{3},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,7},{3},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,4,6},{3},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,4},{3,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,8},{3,5},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,6,8},{3,7},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,7},{3,5,8},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2,7},{4},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,6,8},{3,5},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,6},{3,5,8},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4,6},{5,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,6},{4,5,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,5,6},{4,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,6},{3},{4,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3},{4,5,8},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3},{4,5,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,3},{4,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,3,8},{4},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,8},{3,4},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,8},{3,4,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,3,8},{4,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3,5,8},{4},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,8},{4,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3,6},{5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,6},{3},{5,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3,8},{5,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3,8},{5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,8},{5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2,8},{5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2,8},{5,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,8},{5,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,3},{5,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,6},{5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,6,8},{5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,6},{5,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4,5},{3,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,6},{4,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2,6},{5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,5,8},{3,4},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,5},{3,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2,8},{3,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,5,6},{4},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,5},{4},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4},{3,7,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,4},{3,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,8},{3,5,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,7,8},{3,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,8},{3},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,8},{3,4},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,3,8},{4},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,7},{4},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,3,7},{4},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2,7},{3},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,7},{3},{5,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,6,7},{3},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,6},{3},{5,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,5,7,8},{3},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,5,8},{3},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,5,6,8},{3},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,6,8},{3},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,6,8},{4},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3,6},{4},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,6},{3},{4,5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,5,6},{3},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,5},{3},{4,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7,8},{2,5},{3},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4},{3,6,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7,8},{2,4},{3,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,7},{5,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,7},{4,5,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,6,7},{4,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,6},{4,7,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,7,8},{3},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,8},{3},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,5,8},{3},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,5,8},{3,4},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,5,8},{4},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3},{4,6},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2},{3,4,6},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2},{3,6},{4,5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2},{3,5,6},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2},{3,5},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,5},{4,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2},{3,7,8},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2},{3,8},{4,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2},{3,8},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,8},{4,5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,4,8},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3},{4,8},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6,8},{3},{4,7},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,3},{4,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2},{3,7},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6,8},{2},{3,7},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2},{3,6,7},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3},{4},{5},{6},{7},{8},{9}} => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [[1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => 0

{{1},{2},{3},{4},{5},{6},{7},{8,9}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5},{6},{7,9},{8}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5},{6,9},{7},{8}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5,9},{6},{7},{8}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4,9},{5},{6},{7},{8}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3,9},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2,9},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,9},{2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => 0

{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5},{6},{7,8,9}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2},{3},{4},{5},{6},{7},{8,10},{9}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5},{6,9},{7,8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4},{5},{6},{7,10},{8},{9}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5,9},{6,7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4},{5},{6,10},{7},{8},{9}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4,9},{5,6},{7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4},{5,10},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3,9},{4,5},{6},{7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4,10},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2,9},{3,4},{5},{6},{7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,10},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,9},{2,3},{4},{5},{6},{7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,10},{3},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,2,3,4,5,6,7,8},{9}} => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1},{2,3,4,5,6,7,8,9}} => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,3,4,5,6,7,8,9},{10}} => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1,2,3,4,5,6,8},{7},{9}} => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,3,4,5,6,7,9},{8}} => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,3,4,5,6,7,8,9,10}} => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1,2,3,4,5,6,7,9},{8},{10}} => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[8,1,1,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,3,4,5,8},{6,7},{9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5,7,8},{6},{9}} => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,3,4,5,6,9},{7,8}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,3,4,5,6,8,9},{7}} => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,3,4,5,6,7,8,10},{9}} => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[8,1,1,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,4,6,8},{2},{3,5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,3},{4,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2},{3,6},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2},{4,6},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7,8},{2},{3,6},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6,7},{2},{3,5},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2},{3,7},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2},{3,7},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2},{3,6},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,3},{5,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,5,8},{4,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,7,8},{3},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4,8},{5,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,5,8},{4,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4},{3,5,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,6},{3,5,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,6},{3,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,6,7},{3,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,6},{4},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3,7},{5,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2,7},{5,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,8},{3},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,3},{4,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,3},{5,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,6},{5,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,7},{5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3,7},{5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2,7},{5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3},{4},{5,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,4},{5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4},{3,6,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,7},{3,6,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,6},{3,5,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4},{3,5,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,7,8},{3},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4},{3,5,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,5},{3,7,8},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6},{3,7,8},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,8},{3,6,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4,5,6,7,8}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,4},{2,3,5,6,7,8}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,5},{2,3,4,6,7,8}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,4},{2,6},{3,5,7,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5},{2,6},{3,4,7,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5},{2,4,6,8},{3,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5,8},{2,3,6,7}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,4},{2},{3,5,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2},{3,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2},{3,4,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,4,7,8},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2},{3,4,7,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2},{3,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2},{3,4,8},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2},{3,4,8},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6,7},{2},{3,8},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2},{3,7,8},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2},{4},{5,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,6},{4},{5,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,5,7,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4},{3},{5,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,3},{4},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4},{3},{5,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,4},{3},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,6,7},{4},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6,7},{2},{4},{5,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2},{4},{5,6,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,7},{4},{5,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2},{3,8},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,5},{3},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4,5},{3,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4},{3,5,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,3},{4,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,5},{3,4,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2},{3,5,6},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,6,8},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,3},{4},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2},{3},{5,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,6},{3,7},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,6},{3},{4,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,7},{4,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,6,7},{4,5,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,6,7},{4},{5,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,6},{4,8},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,4,6,8},{5,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,6},{4,5,7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3},{4,6,7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,6},{4,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,6,7},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,5,6,7},{4,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,5,6},{4,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,5},{4,6,7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,8},{3,5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,6,8},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,7},{3,6},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,8},{4,5,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4,7,8},{5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,4,8},{5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,7},{3},{5,6,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2},{3,4,5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,7},{4,8},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,7},{4,5,6,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,5,7},{4,6,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,5},{4,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,5,7},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2},{3,6,7},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2},{3,6},{4,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2},{3},{4,6,7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3},{4,5,7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,4},{5,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3},{4,7,8},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,4,7},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,7},{4,5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2},{3,7},{4,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6},{3},{4,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,5},{4},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,6},{3},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2,6},{3},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,7},{3,4},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2,8},{3},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,8},{3,5},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,8},{3},{4,5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,5,8},{3},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,5,8},{3},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,7},{3},{4,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,5},{3,6,8},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,6},{3,5,7},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,3},{4,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3},{4,6,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,3},{4,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,5,6},{3,7},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,6},{4},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,5},{3,8},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6,7},{3},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,7},{4,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,4,8},{3},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,8},{3},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2},{3,6,8},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2},{3,6,8},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,5},{3},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6,8},{3},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,6},{3},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,5,7},{3},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2},{3,6},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2},{3,8},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2},{3,7},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,6},{3},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,5,8},{3,6},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,5,8},{3},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,5,6},{3},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,5},{3},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,5},{3},{4,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,7},{3},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,7},{3},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,5,8},{3,7},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,8},{3,7},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,8},{3,6,7},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,7,8},{3,6},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,5},{3,6,7},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,5,7},{3},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,8},{3,6},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,7},{3,6,8},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,5},{3},{4,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,5},{3,7},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6,8},{3,7},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,5,7},{3,8},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,8},{3},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,8},{3},{4,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,7,8},{3,5},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,8},{3,5,6},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,5,6},{3,8},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6,7},{3,8},{4}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,4,6},{5},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,5},{4,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4,6},{3,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,8},{3,4,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3,8},{4,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2},{4,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2},{4,7,8},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,7,8},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2},{3,8},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6,7},{2},{4,8},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2},{3,6,7},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2},{3,4,8},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,5,7,8},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2},{3,5,8},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,6,8},{3},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4,6},{3},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2},{3,6,8},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2},{3,5,7},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,5,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,5,7},{4},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2},{3,4,7},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4,7},{5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3},{4,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,8},{3},{4,7},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4,7},{5,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,5},{4,6,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3},{4,7},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,6},{4},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3,7},{4},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3},{4,6,8},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3},{4,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,5,6},{4,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,8},{4,5,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2,8},{4,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3,8},{4,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,7},{3},{5,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,5},{4},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3,4},{5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,7},{3},{5},{6,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3},{5,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4},{5,6,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4,7},{5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,8},{3,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,4},{5,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4,7},{5,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4,6},{5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2,8},{5,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3,4,8},{5},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,6},{3,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,8},{3,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,8},{3,4,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,7},{3},{4},{6,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,8},{3},{4,6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,8},{4,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2},{3,5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,5,8},{4,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,5,7},{4},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3,5},{4},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,4},{5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,7},{5},{6,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,7},{3},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4,6},{5,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4},{5,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5},{3,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,5},{4,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,5},{4,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,8},{3,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5},{3,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,4,5},{6,7,8,9,10}} => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1,6},{2,4},{3,7,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,3,4,7,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,5,7},{2,4,6,8},{3}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,6},{2,3,4,8},{7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5},{2,3},{4,7,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4},{3,5,7,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6},{2,5},{3,4,7,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,7},{2},{4,8},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2},{4,7},{5},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3},{2},{4,7},{5,8},{6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,4,7},{3},{5,8},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,7},{3,4,5,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3,4,7},{5},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,6,7},{3},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,8},{3},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4},{3,5,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,3,7},{4},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,8},{3,7},{4},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,7},{3,5,8},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,7},{3,5},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,5},{3,4,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,6},{4,5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3,7},{4,5},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,7},{3,4,8},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6,8},{3,4},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,7},{3},{6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4},{2,5},{3},{6,8},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2,3,6,8},{4},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,6,8},{4},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5,6,7},{3,8},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,5},{4,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,7},{3,4,8},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,3,7},{4},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,7},{4,8},{5}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,6},{3,7},{4},{5},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6,7},{2,3,8},{4},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,6},{3,5,7},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2},{3,5,8},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,8},{4},{5},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5},{2},{3},{4,8},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2},{3,4},{5,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2},{3,4},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3},{4,5,8},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2},{3,4},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2},{3,4,6},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,8},{3,7},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,7},{4},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,7,8},{4},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,7,8},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,6,8},{4},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,8},{3,4},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,3},{4},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,7},{3,4},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,6,8},{4,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6,8},{2},{4,7},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,6},{3},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,4,7},{3},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,7},{2},{3},{6,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4},{2},{5,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4},{5,7,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,6},{3},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6,7,8},{3},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2},{3,6,7,8},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,8},{2},{3,7},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,6},{3,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2},{3,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,7},{3,8},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3,8},{4},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,4,8},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3},{4,5,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3},{4,6,8},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,5,6},{4,7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,5,7},{4,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,7},{4,6},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,6},{4,7},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,5,8},{4,6,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5},{2},{3,4,6,7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6,7},{3,4},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,5,7,8},{4,6}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5,7},{2},{3,6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,5,6,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2},{3,5,7},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,5,7},{4},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,5,6,8},{4},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2,6},{4,5},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2,4,7},{3},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,4},{3},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,6},{3},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2},{3,4,6,8},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,7},{3,4,5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,4,5,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,4,5,7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,7},{3,4,5},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4},{3,5,6,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4},{2,7},{3,5,6,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,8},{2,6},{3,5,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6,8},{2,4},{3,5,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,8},{2,5,7},{4,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5},{2,7},{3,4,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,8},{3,5,6},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,5},{3,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,7},{3,8},{4},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,7},{3,5,6},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,8},{3,6,7},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,5,6},{3},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,8},{3,4,7},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,3,6},{4},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,6},{4,5,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,3,8},{5},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,8},{5,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,5},{4,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2},{4,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6,7},{2},{3,4,8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5},{3},{4,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3},{4,8},{6,7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5,8},{2,4},{3,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,7},{3,5,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,6},{3,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3,5},{4,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,7},{3},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,8},{4,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,7},{4,8},{5},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,7},{2,3},{5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,7,8},{5},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5,7},{3,4,8},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,4},{3,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,5},{6,7},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,4,8},{3,5},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,6},{3,5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,6},{4},{7,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,5,7},{3,6,8},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,7},{3,8},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,4},{3,5,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,4},{3,5},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,6},{4,7},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,5},{3,6,8},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,6,7},{4,8},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5,8},{2},{4,7},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2},{3,7,8},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2},{3,5,8},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,6,8},{3,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,3,7,8},{4},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,6,8},{4},{5,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3},{4,6},{5,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,6,8},{3},{4,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,5,6,8},{4,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5,7},{3,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,4,6,7},{5,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,7,8},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,7},{3,5},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,6,8},{4,5,7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3},{4,7},{5,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7,8},{2,4},{3,5},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6,8},{2},{3},{5,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,6},{3,7,8},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,6},{5,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,6,7},{3},{5,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,7,8},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2},{3,6,8},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4,5},{6,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,8},{4,6,7},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4,5},{6,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,7,8},{3},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,7,8},{5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,8},{2,4},{5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2},{3},{4,5,7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,3,7},{4,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,6,7},{5},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,3,7},{5},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,5,7},{3},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,5},{3,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6,7},{2},{3},{4,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,6},{3,4},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,7},{3,5,8},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,6,7},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,5,8},{3,4,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,6,7},{2,4,5,8}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,8},{3,5,6},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,6,7},{3},{4,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,7,8},{3,4},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,7},{3,4,6,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7},{2},{3,8},{4,5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,5},{3,6,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,6,8},{3,7},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5,8},{3,7},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5},{3,7,8},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,8},{4,5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,6},{2},{3,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5,6},{2},{4,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,6,7},{3,8},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,7,8},{3,4},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2},{4,7,8},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,5},{4,7,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,6},{3},{4,5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,7,8},{4,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2,8},{3,7},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,4},{5},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2},{4,5,8},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,5},{4,7,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,7},{5,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,5,7},{3},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,6},{5,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5,8},{3,6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,4,5,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,6},{5,8},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3},{2},{4,6},{5,8},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3},{2,5},{4},{6,8},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,4,5,6},{3,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,5},{4,8},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2,4},{3,7},{6},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2,4,6,7},{3},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,5,7,8},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,5},{4,7},{6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7},{2,4},{3,6},{5},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,5,7,8},{3,6},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,4,7},{3},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,5,6,7},{4},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,6,7,8},{4},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,6,7,8},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,8},{5,7},{6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3},{2,7},{4,6},{5},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,4,7},{3,6,8},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,3,5},{6},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2,3,6},{5},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,3,6,7},{4},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,7},{5,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,8},{3,4,6},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,7},{3,4,6},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,6},{4,5,7},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3},{4,5,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2},{4,5,7},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,5},{6,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,5,7},{3,4},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,5},{6,8},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,6},{4,5,8},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,8},{3,4,7},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,7},{4,6,8},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,7},{4,5,8},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2},{3,5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2},{3,5},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,5,8},{6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6,8},{3},{4},{5,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,6,8},{4},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,3},{2},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,4},{2},{3},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,5},{2},{3},{4},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,6},{2},{3},{4},{5},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,7},{2},{3},{4},{5},{6},{8},{9}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,8},{2},{3},{4},{5},{6},{7},{9}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,2,3},{4},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,3,4},{2},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,4},{2},{3},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,5},{2},{3},{4},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,6},{2},{3},{4},{5},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,7},{2},{3},{4},{5},{6},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,8},{2},{3},{4},{5},{6},{7},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,8,9},{2},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,8},{2},{3,6},{4,5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2},{3,5,6},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2},{3,4,6},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4,8},{5},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6},{3,4,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4},{3,6,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,3,6},{4,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,3,4,6},{7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,3},{4,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3,8},{5,6},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,4,5,6,7,8,9}} => [9] => [[1,2,3,4,5,6,7,8,9]] => [[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1,2,3,4,5,6,7},{8,9}} => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,3,4,5,6,7},{8},{9}} => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5,6},{7,8,9}} => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,3,4,5,6},{7,8},{9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5,6},{7},{8},{9}} => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,5},{6,7,8,9}} => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,3,4,5},{6,7,8},{9}} => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5},{6},{7},{8},{9}} => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,4},{5},{6},{7},{8},{9}} => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,3,4,5,6,7,8,9,10}} => [10] => [[1,2,3,4,5,6,7,8,9,10]] => [[10,0,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 9

{{1,2,3,4,5,6,7,8},{9,10}} => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => [[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1,2,3,4,5,6,7,8},{9},{10}} => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[8,1,1,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,3,4,5,6,7},{8,9,10}} => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [[7,3,0,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1,2,3,4,5,6,7},{8,9},{10}} => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,3,4,5,6,7},{8},{9},{10}} => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[7,1,1,1,0,0,0,0,0,0],[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5,6},{7,8,9,10}} => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1,2,3,4,5,6},{7},{8},{9},{10}} => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[6,1,1,1,1,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,5},{6},{7},{8},{9},{10}} => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[5,1,1,1,1,1,0,0,0,0],[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,4},{5},{6},{7},{8},{9},{10}} => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[4,1,1,1,1,1,1,0,0,0],[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[3,1,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,4},{2,3},{5},{6},{7},{8},{9}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5},{2},{3,4},{6},{7},{8},{9}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6},{2},{3},{4,5},{7},{8},{9}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2},{3},{4},{5,6},{8},{9}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,8},{2},{3},{4},{5},{6,7},{9}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,9},{2},{3},{4},{5},{6},{7,8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,2,3},{4,7},{5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3},{4,6,7},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3},{4,8},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5},{3,8},{4},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,7,8},{3},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3},{4,5,7},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,6},{3},{4,7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3,4,7,8},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,7},{5,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,6,7,8},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,7},{4},{5,6,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,6},{4},{5,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3},{4,6,7},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3},{4,6},{5,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,6},{3,7,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,5,6},{4,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,5},{4,7,8},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,4,7,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2},{3,6},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,8},{3,6,7},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,6},{4,7,8},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,7},{2,3,6,8}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,5},{2,3,7},{4,6,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5},{2,3,6,8},{4,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,5},{3,4,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,6,8},{3,4,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,7},{2,6},{3,4,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6},{2,5,7},{3,4,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,7},{2,3,6},{4,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,7},{2,3,8},{4,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,7},{3,6},{4,5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,5,8},{3,6}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7},{2,5,8},{3,4,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6},{2,5},{3,4,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,5,8},{3,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5},{2,7},{3,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5,7},{3,6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,7},{2,8},{3,6}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5},{2,7},{3,6,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7},{2,5},{3,4,6,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,6},{3,4,5,7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,7},{3,6,8},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,4,5,7},{3,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,7},{2,8},{3,4,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,6},{2,7},{4,5},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,8},{3},{4,7},{5}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3},{2},{4,7},{5},{6,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,3,4,7},{2},{5},{6,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,5},{6,8},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5,7},{2},{3,6},{4},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,7},{3,5},{4},{6,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,6},{2,4},{3},{5,7},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,7},{3,5,6,8},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8},{3,6},{4},{5,7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7},{2,5},{3},{4,6},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,7},{3,4,6,8},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3,5,7},{4},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,8},{2},{3,6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,6},{2},{5,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6},{3},{4,8},{5,7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2},{3,7},{4,6},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,6},{3,5,8},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4,7},{3,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,4,6,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,5,7},{6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,6,8},{3,7},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,7},{3,5},{4,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,3,7},{4},{6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2,3,8},{4},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5,8},{2,3,6},{4},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3,8},{4},{5},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2,4,8},{3},{5},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6,8},{2,3,7},{4},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,3},{4,7},{5},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,6},{2,3},{4,7,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3},{4,8},{5},{6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,7},{2,4},{3,8},{5},{6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2},{3,4,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,5,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,5},{3},{4,8},{6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5,8},{2,4,6},{3},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,3,5},{6},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,5,7},{6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4},{3,5,8},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,7},{3,5,6},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,3,5},{4},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5},{3,8},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,8},{4,6},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5,7},{3},{6,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2},{4,5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,7},{3,5,8},{6}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,5,7,8},{4,6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,5,8},{4,6,7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,7},{3,6},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7,8},{2},{3},{4,6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,7,8},{3},{4,6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,5,6,7,8,9},{2}} => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,7,8,9},{2},{3},{4},{5},{6}} => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,4,5,6,7,8,9,10},{2}} => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1,8,9,10},{2},{3},{4},{5},{6},{7}} => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[4,1,1,1,1,1,1,0,0,0],[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,9,10},{2},{3},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[3,1,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,5,6,7},{2},{3,8},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7,8},{2},{3,5},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6,8},{2},{3},{4,7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5,6,7,8,9},{3}} => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4,5,6,7,8},{2},{9}} => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,4,5,6,7,8,9,10},{3}} => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[8,1,1,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1},{2,5,6,7,8,9},{3,4}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,4,5,6,7,8},{2,3},{9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4,5,6,7,8,9},{2},{10}} => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[8,1,1,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1},{2,3,5},{4,6,7,8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,5},{4,6,8},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3,4,5,6,7,8,9,10}} => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => [[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1,2,3,4},{5,6,7,8,9,10}} => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1,3},{2,5,6},{4},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5},{3,7,8},{6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,7},{4,5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2},{3,5},{4,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,5,7,8},{4},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2},{3,5,6,8},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,5,7},{4,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2},{3,5,7},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,3,5},{7},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,8},{2},{3},{4,6,7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2},{3,4,7},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,4,5},{7},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3},{4},{5},{6,7},{8,9}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,3,7},{4,5},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,5,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3},{4,5,7},{6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,4,6},{5,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2},{3,4,7},{5,6,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3},{4,6,8},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3},{4,6,7},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,4},{5},{6,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5},{3},{6,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,5},{4},{6,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,8},{3},{4,5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,8},{3},{5,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,7},{3},{4,5,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,8},{2,5,6},{3},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,8},{2,7},{3,4},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7},{2,4},{3,8},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,5},{6,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,8},{3,6},{5,10},{7},{9}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6},{2,7},{3},{4,5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,6},{5,7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,7,8},{3,5},{4,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6},{2,7},{3,4},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2,7,8},{3},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2},{3,5},{4,6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3,5,8},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,8,9},{4},{5},{6},{7}} => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,9},{4,5},{6},{7},{8}} => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,4,9,10},{5},{6},{7},{8}} => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[6,1,1,1,1,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,8,9},{5},{6},{7}} => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,9},{5,6},{7},{8}} => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,10},{5,6},{7},{8},{9}} => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,9,10},{4},{5},{6},{7},{8}} => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[5,1,1,1,1,1,0,0,0,0],[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8,9},{3,7},{4},{5},{6}} => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,8,9},{3},{5},{6},{7}} => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,9},{3,8},{4,5},{6},{7}} => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,5,9},{3,4},{6},{7},{8}} => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,10},{4,5},{6},{7},{8},{9}} => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,8},{3},{4,5,7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,7},{3,8},{4,5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,6},{3,8},{4,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,9},{2,3,4,5,6,7,8}} => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,8},{2,3,4,5,6,7},{9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,7},{2,3,4,5,6},{8},{9}} => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6},{2,3,4,5},{7},{8},{9}} => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,3,4},{6},{7},{8},{9}} => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,8},{2,6,7},{4},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,7},{3,6},{4},{5,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,8},{3},{4,6},{5,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,10},{2,3,4,5,6,7,8,9}} => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => [[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1,9},{2,3,4,5,6,8},{7}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,10},{2,3,4,5,6,7,9},{8}} => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,9},{2,3,4,5,8},{6,7}} => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,9},{2,3,4,5,7,8},{6}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3},{2,5,6},{4,7},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2,7},{4,5,6},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,8},{3},{4,6,7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,6,7},{3,5},{8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,7,8},{3,6},{5}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5},{3,6,7},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5},{3,6,8},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,6},{3,7,8},{4}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,5,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6},{2,3,8},{5,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4},{2},{3,5,6,7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,7},{4,5,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,9},{2,8},{3,7},{4,6},{5},{10}} => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[2,2,2,2,1,1,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1},{2,10},{3,9},{4,8},{5,7},{6}} => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[2,2,2,2,1,1,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,4,6},{2,3,5,7,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,4,6},{3},{5,7,8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,4,6,7,8},{3,5}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6},{3,4,5,7,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,3,5,8},{4,7},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,3,4,5,6,7,9},{8}} => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,3,4,5,6,7,8,10},{9}} => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1,2},{3,4,5,6,7,8},{9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4,5,6,7,9},{2},{8}} => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,5,7,8},{2,3,4,6}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,6,8},{2,4,5,7}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,6,8},{3,4,5,7}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,6},{2,3,4,5,7,8}} => [6,2] => [[1,2,3,4,5,6],[7,8]] => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,6},{3,4,5,8},{7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,8},{2,3,5,6},{7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5},{2,3,4,8},{6,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,8},{2,3,5},{6,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4},{3,5,6,7,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,5,8},{2,3,4,6,7}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4},{2,5,6,7,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,4,6,7},{2,3,8},{5}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,8},{2,4,6,7},{5}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5},{2,8},{4,6,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,7,8},{2,3,6},{5}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6},{2,3,5},{4,7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6},{3,5},{4,7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5},{3,6},{4,7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5},{2,3,6},{4,7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,7,8},{2,6},{3,5}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7,8},{2,3,5},{4,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7,8},{2,5},{3,4,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7,8},{2,4,6},{3,5}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,8},{2,3,5,7},{6}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5},{3,4,6,7,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2},{3},{4},{5},{6,9},{7},{8},{10}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,8},{2,3},{4},{5},{6},{7},{9}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,2},{3},{4},{5},{6},{7},{8,9}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,3,4,5,6,7},{2,9},{8}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5,7},{6,8},{9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4,5,6,8},{2,9},{7}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4,5,6,9},{2,8},{7}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4,5,6,7,8},{2,10},{9}} => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2},{3,4,5,6,7,8,9}} => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,3},{4,5,6,7,8,9}} => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,3,4},{5,6,7,8,9}} => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1},{2},{3,4,5,6,7,8,9}} => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2},{3,5,6,7,8,9},{4}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,4,5,6,7},{3},{8,9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3},{4,5,6,7,8,9,10}} => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [[7,3,0,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1,2,3},{4,5,7,8,9},{6}} => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,5,6},{4},{7,8,9}} => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4},{5,6,7,9},{8}} => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2},{3},{4},{5,7},{6,8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4,6},{5,8},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,5},{4,8},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,4},{3,8},{5},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4},{5},{6,8},{7,9}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4,7},{5,8},{6}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4},{5,7},{6,9},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,6},{4,8},{5},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3},{4,6,7},{5,8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3},{4,6},{5,9},{7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,5},{3,8},{4},{6},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,5,6},{4,8},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,5},{4,9},{6},{7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,4,5},{3,8},{6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4},{3,9},{5},{6},{7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,3},{2,9},{4},{5},{6},{7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4,6,7,8},{2,3,5}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,6,7,8},{2,4,5}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,5},{2,6},{4,7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5,7,8},{2,3,6}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,7},{2,4,5,8},{6}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,8},{2,4,6},{3,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5,8},{3,4,6,7}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,3,5,7},{4,6},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,5,7},{6,8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,5,8},{4,6,7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3},{2,6,8},{4,5},{7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,6,7},{2},{3},{5,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7,8},{2},{3,5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,7,8},{3,5},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,7,8},{3,6},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3,7,8},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,6,8},{5,7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,4,5,6,8},{7,9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,5,6},{2,3},{4,7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,9},{4},{5},{6},{7},{8}} => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,9},{3},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,2,3,10},{4},{5},{6},{7},{8},{9}} => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[4,1,1,1,1,1,1,0,0,0],[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3},{2,4,5,6,8},{7}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6,7},{2,3,4,5,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,7},{2,3,4},{5,6,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5},{2,3,7,8},{6}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,6,8},{2,3,5,7}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,4,8},{2,3,6,7},{5}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,7},{2,6},{4,5,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6},{3,7},{4,5,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,4,6},{5,7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3},{4,7},{5,6,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5},{2,6,7,8},{3,4}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7},{2,6,8},{3,4,5}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6},{3,5,7,8},{4}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,6},{4,5,7,8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7,8},{2,4},{3,5,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,9},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,2,3,4,5,6,8,9},{7}} => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,4,5,6,7,8,9},{3}} => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,3,4,5,6,7,9,10},{8}} => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1,2},{3,5},{4},{6},{7},{8},{9}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,9},{2,4},{3},{5},{6},{7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,9},{2},{3,4},{5},{6},{7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,10},{2,3},{4},{5},{6},{7},{8},{9}} => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[2,2,1,1,1,1,1,1,0,0],[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,3},{2,5,8},{4},{6,7}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,9},{2,8},{3},{4},{5},{6},{7}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,3,9},{2},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,10},{2,9},{3},{4},{5},{6},{7},{8}} => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[2,2,1,1,1,1,1,1,0,0],[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,9},{3,8},{4},{5},{6},{7}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,2,7},{3},{4},{5},{6},{8,9}} => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2},{3,4,9},{5},{6},{7},{8}} => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,8},{2},{4},{5},{6},{7},{9}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,3,10},{2},{4},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[3,1,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2,4},{3,5,6,7,8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,6},{2},{3},{4,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2},{4,6},{7},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,7},{2},{4},{5},{6,8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,6},{2},{4},{5,8},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,7},{4,8},{5},{6}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2},{3},{4},{5},{6,8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6},{2},{3},{4},{5,8},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4},{2,6},{3},{5,8},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2,6},{3},{4,8},{7}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5,7},{2},{3},{4},{6,8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2},{3},{4,6},{7},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4},{2},{3,6},{5},{7},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,5},{3,6},{4},{7},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4,6},{2},{3,5,7},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3},{4,7},{5},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6},{2},{3},{4,7},{5,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2},{3},{4,7},{6,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5,7},{2},{3},{4,6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,7},{2},{3,6},{5},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4},{2},{3,7},{5},{6,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2},{3,7},{4,8},{6}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,5},{2},{3,7},{4},{6},{8}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2,5},{3,6},{4},{8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,6},{3},{4,8},{5},{7}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5},{2,3,4,8},{6},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2,3,8},{6},{7}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,3,4,6},{5,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7},{2,3},{4,5,6,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7},{2,3,5,6},{4,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,7,8},{2,3,5,6}} => [4,4] => [[1,2,3,4],[5,6,7,8]] => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,5,7,8},{2,3},{4,6}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,6,8},{2,3},{4,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5},{2},{3,4,6,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6},{2},{3},{4,5,7,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,6,7,8},{3},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,6,7,8},{4}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,7},{2},{5,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,9},{3,6},{5,10},{7},{8}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,8},{3,7},{5,10},{6},{9}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,9},{3,7},{5,10},{6},{8}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,9},{3,8},{5,10},{6},{7}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5,10},{3,6},{4,8},{7},{9}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5,10},{3,6},{4,9},{7},{8}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5,10},{3,7},{4,8},{6},{9}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5,10},{3,7},{4,9},{6},{8}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5,10},{3,8},{4,9},{6},{7}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6},{3,7},{4,8},{5,10},{9}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6},{3,7},{4,9},{5,10},{8}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6},{3,8},{4,9},{5,10},{7}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,7},{3,8},{4,9},{5,10},{6}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,6},{2,4,8},{5,10},{7},{9}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,6},{2,4,9},{5,10},{7},{8}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,7},{2,4,8},{5,10},{6},{9}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,7},{2,4,9},{5,10},{6},{8}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,8},{2,4,9},{5,10},{6},{7}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,6},{2,5,10},{4,8},{7},{9}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,6},{2,5,10},{4,9},{7},{8}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,7},{2,5,10},{4,8},{6},{9}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,7},{2,5,10},{4,9},{6},{8}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,8},{2,5,10},{4,9},{6},{7}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,7},{2,6},{4,8},{5,10},{9}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,7},{2,6},{4,9},{5,10},{8}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,8},{2,6},{4,9},{5,10},{7}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,8},{2,7},{4,9},{5,10},{6}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,8},{2,5,10},{3,6},{7},{9}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,9},{2,5,10},{3,6},{7},{8}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,8},{2,5,10},{3,7},{6},{9}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,9},{2,5,10},{3,7},{6},{8}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,9},{2,5,10},{3,8},{6},{7}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,8},{2,6},{3,7},{5,10},{9}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,9},{2,6},{3,7},{5,10},{8}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,9},{2,6},{3,8},{5,10},{7}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,9},{2,7},{3,8},{5,10},{6}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,10},{2,6},{3,7},{4,8},{9}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,10},{2,6},{3,7},{4,9},{8}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,10},{2,6},{3,8},{4,9},{7}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,10},{2,7},{3,8},{4,9},{6}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,6},{2,3,5},{7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,6,8},{4,5,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,4},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,6,9},{2},{3},{4},{5},{7},{8}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,5,9},{2},{3},{4},{6},{7},{8}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,6,7,9},{2},{3},{4},{5},{8}} => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3},{2,4,5,6,7},{8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,4},{3,5,6,7,8,9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,5},{3,4,6,7,8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4},{2,3,5,6,7},{8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4},{3,5,6,7},{8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3},{2,4,5,6,7,8},{9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,4},{3,5,6,7,8,9,10}} => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1},{2,5},{3,4,6,7,8,9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,3,5},{4,6,7,8,9}} => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,6},{3,4,5,7,8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,4,6},{5,7,8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5},{2,3,4,6,7},{8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4},{2,3,5,6,7,8},{9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,4},{3,5,6,7,8},{9}} => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3},{2,4,5,6,7,8,9},{10}} => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,7},{3},{4,6,8},{5}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4,6,8,10},{3},{5},{7},{9}} => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[6,1,1,1,1,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,6,9},{3,10},{5},{7},{8}} => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,7,10},{3,8},{5},{6},{9}} => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,7,9},{3},{5,10},{6},{8}} => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4,8},{3,9},{5,10},{6},{7}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5,8,10},{3,6},{4},{7},{9}} => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5,9},{3,6,10},{4},{7},{8}} => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[4,3,1,1,1,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5,7,10},{3},{4,8},{6},{9}} => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5,7,9},{3},{4},{6,10},{8}} => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5,8},{3,9},{4},{6,10},{7}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6,10},{3,7},{4,8},{5},{9}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6,9},{3,7},{4},{5,10},{8}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6,8},{3},{4,9},{5,10},{7}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,6,8,10},{2,4},{5},{7},{9}} => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,6,9},{2,4,10},{5},{7},{8}} => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[4,3,1,1,1,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,7,10},{2,4,8},{5},{6},{9}} => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[4,3,1,1,1,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,7,9},{2,4},{5,10},{6},{8}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5,8,10},{2},{4,6},{7},{9}} => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5,9},{2},{4,6,10},{7},{8}} => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => [[4,3,1,1,1,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5,7,10},{2},{4},{6,8},{9}} => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5,7,9},{2},{4},{6},{8,10}} => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5,8},{2,9},{4},{6},{7,10}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,6,10},{2,7},{4},{5,8},{9}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,6,9},{2,7},{4},{5},{8,10}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,6,8},{2},{4,9},{5},{7,10}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,7},{2,8},{4,9},{5},{6,10}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,8,10},{2,5},{3,6},{7},{9}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,7,10},{2,5},{3},{6,8},{9}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,7,9},{2,5},{3},{6},{8,10}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,8},{2,5,9},{3},{6},{7,10}} => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => [[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,6,10},{2},{3,7},{5,8},{9}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,6,9},{2},{3,7},{5},{8,10}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,6,8},{2},{3},{5,9},{7,10}} => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => [[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,7},{2,8},{3},{5,9},{6,10}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,9},{2,6},{3,7},{4},{8,10}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,8},{2,6},{3},{4,9},{7,10}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,7},{2},{3,8},{4,9},{6,10}} => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,4,6},{3},{5,7,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5,7},{3},{4,6,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,8},{2,9},{3},{4},{5},{6},{7}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,7},{3,8},{4},{5},{6}} => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,7},{2},{3,9},{4},{5},{6},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,6},{2},{3},{4,9},{5},{7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,5,6},{2},{3,8},{4},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2},{3},{4},{6,9},{7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,4},{2},{3},{5},{6},{7,9},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,3},{2},{4},{5},{6},{7},{8,9}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,2,3,4,5,6,9},{7,8}} => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,3,4,5,6,7,10},{8,9}} => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => [[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 8

{{1},{2,3,4,5,6,7,10},{8,9}} => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,3,4,5,6,9},{2},{7,8}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2},{3},{4,6,8},{5,7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3,5,8},{4,6},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2,8},{3},{4},{5},{6},{7},{9}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,2,7},{3},{4},{5},{6},{8},{9}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,2,9},{3,4,5,6,7,8}} => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1},{2,3,4,5,6,7},{8,9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,3,4,5,6,9},{7},{8}} => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,4,5,9},{6},{7},{8}} => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,9},{5},{6},{7},{8}} => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3,4,5,6,7,10},{8},{9}} => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[7,1,1,1,0,0,0,0,0,0],[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,3,4,5,9},{6,7},{8}} => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,4,5,6,10},{7},{8},{9}} => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[6,1,1,1,1,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,4,9},{5,6},{7},{8}} => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,4,5,10},{6},{7},{8},{9}} => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[5,1,1,1,1,1,0,0,0,0],[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,3,9},{4,5},{6},{7},{8}} => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3,4,10},{5},{6},{7},{8},{9}} => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[4,1,1,1,1,1,1,0,0,0],[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3,10},{4},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[3,1,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2,3},{4},{5},{6},{7,9},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,2,7},{3,8},{4},{5,6}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6,7},{3},{4,8},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,4},{3,6},{5,7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,5},{3},{4,7},{6,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1,4,8},{2,3,7},{5,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,4,7},{5,6,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,7},{2,3},{5,6,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,7},{2,4},{5,6,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,7},{2,6,8},{4,5}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7},{2,3,5,8},{4,6}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6},{3,8},{4,5,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,8},{3,4,6},{5,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,5,7,8},{4,6}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,7,8},{2,6},{3,4}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,8},{2,7},{3,4,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6,8},{2,3},{4,5,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6,8},{2,5,7},{3,4}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6,8},{2,4,7},{3,5}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,4},{3,5},{6,7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,6,8},{3},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6,9},{2},{3},{4},{7},{8}} => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,5,9},{2},{3},{6},{7},{8}} => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,4,9},{2},{5},{6},{7},{8}} => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,6},{2},{3},{4},{5},{7,8,9}} => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2},{3},{4},{6,7,8,9}} => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7,8,10},{2},{3},{4},{5},{6},{9}} => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[4,1,1,1,1,1,1,0,0,0],[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4},{2},{3},{5,6,7,9},{8}} => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,6,7,10},{2},{3},{4},{5},{8},{9}} => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[4,1,1,1,1,1,1,0,0,0],[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3},{2},{4,5,6,9},{7},{8}} => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,6,10},{2},{3},{4},{7},{8},{9}} => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[4,1,1,1,1,1,1,0,0,0],[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2},{3,4,5,9},{6},{7},{8}} => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5,10},{2},{3},{6},{7},{8},{9}} => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[4,1,1,1,1,1,1,0,0,0],[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,3,4,10},{2},{5},{6},{7},{8},{9}} => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[4,1,1,1,1,1,1,0,0,0],[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2,3,4,6},{7,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4},{2,8},{5,6,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,6,7},{2,8},{4,5}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,8},{2,3,6},{4,5,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,7},{3,4,5,6,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2},{3,5,6},{4,7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,6},{2,7,8},{3,4}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5},{2,7,8},{3,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7},{2,6},{3,4,5,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,7},{4,5,6,8}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,7},{2,5,6,8},{3,4}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,7},{4},{5,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,4,5,6,7},{2},{8,9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4},{2,6},{5,7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4,5,6},{2,8,9},{7}} => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4,5,6},{2},{7,8,9}} => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,3,4,5,6,7,8},{2},{9,10}} => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,7},{2},{3,4,5,8},{6}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,3,5,6},{7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2,4},{6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2,5,6,7},{3},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2,6},{3},{4},{5},{7},{8},{9}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,2,5},{3},{4},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1,2,4},{3},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 2

{{1},{2},{3,4,5,7},{6,8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,7},{2},{3},{5,6,8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4,5},{2},{3,6,7},{8}} => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,4,6,7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,5,6},{3,7},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3},{4},{5},{6},{7,9},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,2},{3},{4},{5},{6},{7},{8,10},{9}} => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[2,2,1,1,1,1,1,1,0,0],[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,3},{2},{4},{5},{6},{7,9},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,3},{4},{5},{6},{7},{8,9}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,2},{3},{4},{5},{6},{7},{8},{9,10}} => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[2,2,1,1,1,1,1,1,0,0],[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,3,6},{4},{5,8},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,3,7},{4},{5,8},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4},{3,7},{5},{6,8}} => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 3

{{1},{2,5},{3},{4,6,8},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5},{3},{4,6,7},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,2},{3,4,6,8},{5,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,5,8,9},{6},{7}} => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5,9},{6,7},{8}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5,6,9,10},{7},{8}} => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[8,1,1,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,2,3,4,8,9},{5,7},{6}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,6,8,9},{5},{7}} => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,9},{5,8},{6,7}} => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,7,9},{5,6},{8}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,5,6,10},{7,8},{9}} => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 7

{{1,4,6,7,8},{2},{3,5}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5},{2,3,6,7,8}} => [5,3] => [[1,2,3,4,5],[6,7,8]] => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,4,5},{2,3,6},{7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5},{2,3,8},{6,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,7},{2,3,8},{5,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4},{2,7},{5,6,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,6,8},{2,7},{4,5}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2},{3,6,7},{4,5,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6,7},{2,3},{4,5,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6,7},{2,5,8},{3,4}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,5,6},{2,8},{3,4,7}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6,7},{2,4,5},{3,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,4,6,8,10},{3},{5},{7},{9}} => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[5,1,1,1,1,1,0,0,0,0],[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,6,10},{3},{5},{7,9},{8}} => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,8,10},{3},{5,7},{6},{9}} => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,10},{3},{5,7,9},{6},{8}} => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[3,3,1,1,1,1,0,0,0,0],[3,3,1,1,1,0,0,0,0],[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4,10},{3},{5,9},{6,8},{7}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,8,10},{3,5},{4},{7},{9}} => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,6,10},{3,5},{4},{7,9},{8}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8,10},{3,5,7},{4},{6},{9}} => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[3,3,1,1,1,1,0,0,0,0],[3,3,1,1,1,0,0,0,0],[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,8,10},{3,7},{4,6},{5},{9}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,10},{3,5,7,9},{4},{6},{8}} => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,10},{3,5,9},{4},{6,8},{7}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,10},{3,7,9},{4,6},{5},{8}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,10},{3,9},{4,6,8},{5},{7}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,6,8,10},{5},{7},{9}} => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,6,10},{5},{7,9},{8}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,8,10},{5,7},{6},{9}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,10},{5,7,9},{6},{8}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,10},{5,9},{6,8},{7}} => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[2,2,2,2,1,1,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3,5},{2},{4},{6,8,10},{7},{9}} => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[3,3,1,1,1,1,0,0,0,0],[3,3,1,1,1,0,0,0,0],[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5},{2},{4},{6,10},{7,9},{8}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4},{3},{6,8,10},{7},{9}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5},{2,4},{3},{6,10},{7,9},{8}} => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[2,2,2,2,1,1,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3,5,7},{2},{4},{6},{8,10},{9}} => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7},{2},{4,6},{5},{8,10},{9}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7},{2,4},{3},{6},{8,10},{9}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,4,6},{3},{5},{8,10},{9}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7},{2,6},{3,5},{4},{8,10},{9}} => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[2,2,2,2,1,1,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 4

{{1,3,5,7,9},{2},{4},{6},{8},{10}} => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[5,1,1,1,1,1,0,0,0,0],[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,5,9},{2},{4},{6,8},{7},{10}} => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,7,9},{2},{4,6},{5},{8},{10}} => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,9},{2},{4,6,8},{5},{7},{10}} => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[3,3,1,1,1,1,0,0,0,0],[3,3,1,1,1,0,0,0,0],[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,9},{2},{4,8},{5,7},{6},{10}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,7,9},{2,4},{3},{6},{8},{10}} => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,5,9},{2,4},{3},{6,8},{7},{10}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7,9},{2,4,6},{3},{5},{8},{10}} => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[3,3,1,1,1,1,0,0,0,0],[3,3,1,1,1,0,0,0,0],[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,7,9},{2,6},{3,5},{4},{8},{10}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,9},{2,4,6,8},{3},{5},{7},{10}} => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,9},{2,4,8},{3},{5,7},{6},{10}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,9},{2,6,8},{3,5},{4},{7},{10}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,9},{2,8},{3,5,7},{4},{6},{10}} => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,9},{2},{3},{4},{5},{6,7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,9},{2},{3},{4},{5},{6,8},{7}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,5},{3},{4},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3,5},{4},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4,5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1},{2},{3},{4},{5},{6,7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,9},{2},{3},{4},{5},{6,7,8}} => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2},{3},{4},{5},{6,8},{7},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,6,8,9},{2},{3},{4},{5},{7}} => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 3

{{1,5},{2},{3},{4},{6},{7},{8,9}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,2,9},{3,6},{4},{5},{7},{8}} => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,10},{2,6},{3},{4},{5},{7},{8},{9}} => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[2,2,1,1,1,1,1,1,0,0],[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,10},{2},{3,6},{4},{5},{7},{8},{9}} => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[2,2,1,1,1,1,1,1,0,0],[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,3},{4,5},{6},{7},{8},{9}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,10},{2},{3},{4,6},{5},{7},{8},{9}} => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[2,2,1,1,1,1,1,1,0,0],[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2},{3,4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 1

{{1,10},{2},{3},{4},{5,6},{7},{8},{9}} => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[2,2,1,1,1,1,1,1,0,0],[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1,2,4},{3,6,7,8},{5}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,4},{3,5,6,8},{7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,6},{4},{5,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,4},{3,5,6,8},{7}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1},{2,5},{3,4,6},{7,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,2},{3},{4,7},{5,6,8}} => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 4

{{1,4},{2},{3},{5},{6,9},{7},{8}} => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 2

{{1},{2,4,6},{3},{5,7},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1,4,6},{2,3,5,8},{7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,6},{2,3,5,8},{4,7}} => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,5},{2,7,8},{4,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,3,4},{2,5,7,8},{6}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,5,6},{2},{3,7,8}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,5,7,8},{3},{4,6}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,6,8},{4,7},{5}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3,6},{2,4},{5,7,8}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,8},{2,5,7},{3,6}} => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,6,8},{3},{4,5,7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,4,6,8},{2,3,5},{7}} => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1},{2,3,4,6,7},{5,8}} => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5

{{1,2,3,4,5,7},{6},{8,9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1},{2,3,6},{4,7},{5},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,7},{3,8},{5},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5,7},{3},{4,8},{6}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,7},{3,5},{6},{8}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,5,8},{3,6},{4},{7}} => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 3

{{1},{2,4,6,7},{3,5},{8}} => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 4

{{1,3},{2},{4,5,6,7,8,9}} => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,4},{3},{5,6,7,8,9}} => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,5},{4},{6,7,8,9}} => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

{{1,2,3,4,6},{5},{7,8,9}} => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 6

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Description

The number of special entries.
An entry $a_{i,j}$ of a Gelfand-Tsetlin pattern is special if $a_{i-1,j-i} > a_{i,j} > a_{i-1,j}$. That is, it is neither boxed nor circled.

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shape

Description

Sends a set partition to the integer partition obtained by the sizes of the blocks.

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to Gelfand-Tsetlin pattern

Description

Sends a tableau to its corresponding Gelfand-Tsetlin pattern.
To obtain this Gelfand-Tsetlin pattern, fill in the first row of the pattern with the shape of the tableau.
Then remove the maximal entry from the tableau to obtain a smaller tableau, and repeat the process until the tableau is empty.

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initial tableau

Description

Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.