Identifier
-
Mp00128:
Set partitions
—to composition⟶
Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
St000008: Integer compositions ⟶ ℤ
Values
{{1}} => [1] => [1] => 0
{{1,2}} => [2] => [1,1] => 1
{{1},{2}} => [1,1] => [2] => 0
{{1,2,3}} => [3] => [1,1,1] => 3
{{1,2},{3}} => [2,1] => [2,1] => 2
{{1,3},{2}} => [2,1] => [2,1] => 2
{{1},{2,3}} => [1,2] => [1,2] => 1
{{1},{2},{3}} => [1,1,1] => [3] => 0
{{1,2,3,4}} => [4] => [1,1,1,1] => 6
{{1,2,3},{4}} => [3,1] => [2,1,1] => 5
{{1,2,4},{3}} => [3,1] => [2,1,1] => 5
{{1,2},{3,4}} => [2,2] => [1,2,1] => 4
{{1,2},{3},{4}} => [2,1,1] => [3,1] => 3
{{1,3,4},{2}} => [3,1] => [2,1,1] => 5
{{1,3},{2,4}} => [2,2] => [1,2,1] => 4
{{1,3},{2},{4}} => [2,1,1] => [3,1] => 3
{{1,4},{2,3}} => [2,2] => [1,2,1] => 4
{{1},{2,3,4}} => [1,3] => [1,1,2] => 3
{{1},{2,3},{4}} => [1,2,1] => [2,2] => 2
{{1,4},{2},{3}} => [2,1,1] => [3,1] => 3
{{1},{2,4},{3}} => [1,2,1] => [2,2] => 2
{{1},{2},{3,4}} => [1,1,2] => [1,3] => 1
{{1},{2},{3},{4}} => [1,1,1,1] => [4] => 0
{{1,2,3,4,5}} => [5] => [1,1,1,1,1] => 10
{{1,2,3,4},{5}} => [4,1] => [2,1,1,1] => 9
{{1,2,3,5},{4}} => [4,1] => [2,1,1,1] => 9
{{1,2,3},{4,5}} => [3,2] => [1,2,1,1] => 8
{{1,2,3},{4},{5}} => [3,1,1] => [3,1,1] => 7
{{1,2,4,5},{3}} => [4,1] => [2,1,1,1] => 9
{{1,2,4},{3,5}} => [3,2] => [1,2,1,1] => 8
{{1,2,4},{3},{5}} => [3,1,1] => [3,1,1] => 7
{{1,2,5},{3,4}} => [3,2] => [1,2,1,1] => 8
{{1,2},{3,4,5}} => [2,3] => [1,1,2,1] => 7
{{1,2},{3,4},{5}} => [2,2,1] => [2,2,1] => 6
{{1,2,5},{3},{4}} => [3,1,1] => [3,1,1] => 7
{{1,2},{3,5},{4}} => [2,2,1] => [2,2,1] => 6
{{1,2},{3},{4,5}} => [2,1,2] => [1,3,1] => 5
{{1,2},{3},{4},{5}} => [2,1,1,1] => [4,1] => 4
{{1,3,4,5},{2}} => [4,1] => [2,1,1,1] => 9
{{1,3,4},{2,5}} => [3,2] => [1,2,1,1] => 8
{{1,3,4},{2},{5}} => [3,1,1] => [3,1,1] => 7
{{1,3,5},{2,4}} => [3,2] => [1,2,1,1] => 8
{{1,3},{2,4,5}} => [2,3] => [1,1,2,1] => 7
{{1,3},{2,4},{5}} => [2,2,1] => [2,2,1] => 6
{{1,3,5},{2},{4}} => [3,1,1] => [3,1,1] => 7
{{1,3},{2,5},{4}} => [2,2,1] => [2,2,1] => 6
{{1,3},{2},{4,5}} => [2,1,2] => [1,3,1] => 5
{{1,3},{2},{4},{5}} => [2,1,1,1] => [4,1] => 4
{{1,4,5},{2,3}} => [3,2] => [1,2,1,1] => 8
{{1,4},{2,3,5}} => [2,3] => [1,1,2,1] => 7
{{1,4},{2,3},{5}} => [2,2,1] => [2,2,1] => 6
{{1,5},{2,3,4}} => [2,3] => [1,1,2,1] => 7
{{1},{2,3,4,5}} => [1,4] => [1,1,1,2] => 6
{{1},{2,3,4},{5}} => [1,3,1] => [2,1,2] => 5
{{1,5},{2,3},{4}} => [2,2,1] => [2,2,1] => 6
{{1},{2,3,5},{4}} => [1,3,1] => [2,1,2] => 5
{{1},{2,3},{4,5}} => [1,2,2] => [1,2,2] => 4
{{1},{2,3},{4},{5}} => [1,2,1,1] => [3,2] => 3
{{1,4,5},{2},{3}} => [3,1,1] => [3,1,1] => 7
{{1,4},{2,5},{3}} => [2,2,1] => [2,2,1] => 6
{{1,4},{2},{3,5}} => [2,1,2] => [1,3,1] => 5
{{1,4},{2},{3},{5}} => [2,1,1,1] => [4,1] => 4
{{1,5},{2,4},{3}} => [2,2,1] => [2,2,1] => 6
{{1},{2,4,5},{3}} => [1,3,1] => [2,1,2] => 5
{{1},{2,4},{3,5}} => [1,2,2] => [1,2,2] => 4
{{1},{2,4},{3},{5}} => [1,2,1,1] => [3,2] => 3
{{1,5},{2},{3,4}} => [2,1,2] => [1,3,1] => 5
{{1},{2,5},{3,4}} => [1,2,2] => [1,2,2] => 4
{{1},{2},{3,4,5}} => [1,1,3] => [1,1,3] => 3
{{1},{2},{3,4},{5}} => [1,1,2,1] => [2,3] => 2
{{1,5},{2},{3},{4}} => [2,1,1,1] => [4,1] => 4
{{1},{2,5},{3},{4}} => [1,2,1,1] => [3,2] => 3
{{1},{2},{3,5},{4}} => [1,1,2,1] => [2,3] => 2
{{1},{2},{3},{4,5}} => [1,1,1,2] => [1,4] => 1
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [5] => 0
{{1,2,3,4,5,6}} => [6] => [1,1,1,1,1,1] => 15
{{1,2,3,4,5},{6}} => [5,1] => [2,1,1,1,1] => 14
{{1,2,3,4,6},{5}} => [5,1] => [2,1,1,1,1] => 14
{{1,2,3,4},{5,6}} => [4,2] => [1,2,1,1,1] => 13
{{1,2,3,4},{5},{6}} => [4,1,1] => [3,1,1,1] => 12
{{1,2,3,5,6},{4}} => [5,1] => [2,1,1,1,1] => 14
{{1,2,3,5},{4,6}} => [4,2] => [1,2,1,1,1] => 13
{{1,2,3,5},{4},{6}} => [4,1,1] => [3,1,1,1] => 12
{{1,2,3,6},{4,5}} => [4,2] => [1,2,1,1,1] => 13
{{1,2,3},{4,5,6}} => [3,3] => [1,1,2,1,1] => 12
{{1,2,3},{4,5},{6}} => [3,2,1] => [2,2,1,1] => 11
{{1,2,3,6},{4},{5}} => [4,1,1] => [3,1,1,1] => 12
{{1,2,3},{4,6},{5}} => [3,2,1] => [2,2,1,1] => 11
{{1,2,3},{4},{5,6}} => [3,1,2] => [1,3,1,1] => 10
{{1,2,3},{4},{5},{6}} => [3,1,1,1] => [4,1,1] => 9
{{1,2,4,5,6},{3}} => [5,1] => [2,1,1,1,1] => 14
{{1,2,4,5},{3,6}} => [4,2] => [1,2,1,1,1] => 13
{{1,2,4,5},{3},{6}} => [4,1,1] => [3,1,1,1] => 12
{{1,2,4,6},{3,5}} => [4,2] => [1,2,1,1,1] => 13
{{1,2,4},{3,5,6}} => [3,3] => [1,1,2,1,1] => 12
{{1,2,4},{3,5},{6}} => [3,2,1] => [2,2,1,1] => 11
{{1,2,4,6},{3},{5}} => [4,1,1] => [3,1,1,1] => 12
{{1,2,4},{3,6},{5}} => [3,2,1] => [2,2,1,1] => 11
{{1,2,4},{3},{5,6}} => [3,1,2] => [1,3,1,1] => 10
{{1,2,4},{3},{5},{6}} => [3,1,1,1] => [4,1,1] => 9
{{1,2,5,6},{3,4}} => [4,2] => [1,2,1,1,1] => 13
>>> Load all 3870 entries. <<<{{1,2,5},{3,4,6}} => [3,3] => [1,1,2,1,1] => 12
{{1,2,5},{3,4},{6}} => [3,2,1] => [2,2,1,1] => 11
{{1,2,6},{3,4,5}} => [3,3] => [1,1,2,1,1] => 12
{{1,2},{3,4,5,6}} => [2,4] => [1,1,1,2,1] => 11
{{1,2},{3,4,5},{6}} => [2,3,1] => [2,1,2,1] => 10
{{1,2,6},{3,4},{5}} => [3,2,1] => [2,2,1,1] => 11
{{1,2},{3,4,6},{5}} => [2,3,1] => [2,1,2,1] => 10
{{1,2},{3,4},{5,6}} => [2,2,2] => [1,2,2,1] => 9
{{1,2},{3,4},{5},{6}} => [2,2,1,1] => [3,2,1] => 8
{{1,2,5,6},{3},{4}} => [4,1,1] => [3,1,1,1] => 12
{{1,2,5},{3,6},{4}} => [3,2,1] => [2,2,1,1] => 11
{{1,2,5},{3},{4,6}} => [3,1,2] => [1,3,1,1] => 10
{{1,2,5},{3},{4},{6}} => [3,1,1,1] => [4,1,1] => 9
{{1,2,6},{3,5},{4}} => [3,2,1] => [2,2,1,1] => 11
{{1,2},{3,5,6},{4}} => [2,3,1] => [2,1,2,1] => 10
{{1,2},{3,5},{4,6}} => [2,2,2] => [1,2,2,1] => 9
{{1,2},{3,5},{4},{6}} => [2,2,1,1] => [3,2,1] => 8
{{1,2,6},{3},{4,5}} => [3,1,2] => [1,3,1,1] => 10
{{1,2},{3,6},{4,5}} => [2,2,2] => [1,2,2,1] => 9
{{1,2},{3},{4,5,6}} => [2,1,3] => [1,1,3,1] => 8
{{1,2},{3},{4,5},{6}} => [2,1,2,1] => [2,3,1] => 7
{{1,2,6},{3},{4},{5}} => [3,1,1,1] => [4,1,1] => 9
{{1,2},{3,6},{4},{5}} => [2,2,1,1] => [3,2,1] => 8
{{1,2},{3},{4,6},{5}} => [2,1,2,1] => [2,3,1] => 7
{{1,2},{3},{4},{5,6}} => [2,1,1,2] => [1,4,1] => 6
{{1,2},{3},{4},{5},{6}} => [2,1,1,1,1] => [5,1] => 5
{{1,3,4,5,6},{2}} => [5,1] => [2,1,1,1,1] => 14
{{1,3,4,5},{2,6}} => [4,2] => [1,2,1,1,1] => 13
{{1,3,4,5},{2},{6}} => [4,1,1] => [3,1,1,1] => 12
{{1,3,4,6},{2,5}} => [4,2] => [1,2,1,1,1] => 13
{{1,3,4},{2,5,6}} => [3,3] => [1,1,2,1,1] => 12
{{1,3,4},{2,5},{6}} => [3,2,1] => [2,2,1,1] => 11
{{1,3,4,6},{2},{5}} => [4,1,1] => [3,1,1,1] => 12
{{1,3,4},{2,6},{5}} => [3,2,1] => [2,2,1,1] => 11
{{1,3,4},{2},{5,6}} => [3,1,2] => [1,3,1,1] => 10
{{1,3,4},{2},{5},{6}} => [3,1,1,1] => [4,1,1] => 9
{{1,3,5,6},{2,4}} => [4,2] => [1,2,1,1,1] => 13
{{1,3,5},{2,4,6}} => [3,3] => [1,1,2,1,1] => 12
{{1,3,5},{2,4},{6}} => [3,2,1] => [2,2,1,1] => 11
{{1,3,6},{2,4,5}} => [3,3] => [1,1,2,1,1] => 12
{{1,3},{2,4,5,6}} => [2,4] => [1,1,1,2,1] => 11
{{1,3},{2,4,5},{6}} => [2,3,1] => [2,1,2,1] => 10
{{1,3,6},{2,4},{5}} => [3,2,1] => [2,2,1,1] => 11
{{1,3},{2,4,6},{5}} => [2,3,1] => [2,1,2,1] => 10
{{1,3},{2,4},{5,6}} => [2,2,2] => [1,2,2,1] => 9
{{1,3},{2,4},{5},{6}} => [2,2,1,1] => [3,2,1] => 8
{{1,3,5,6},{2},{4}} => [4,1,1] => [3,1,1,1] => 12
{{1,3,5},{2,6},{4}} => [3,2,1] => [2,2,1,1] => 11
{{1,3,5},{2},{4,6}} => [3,1,2] => [1,3,1,1] => 10
{{1,3,5},{2},{4},{6}} => [3,1,1,1] => [4,1,1] => 9
{{1,3,6},{2,5},{4}} => [3,2,1] => [2,2,1,1] => 11
{{1,3},{2,5,6},{4}} => [2,3,1] => [2,1,2,1] => 10
{{1,3},{2,5},{4,6}} => [2,2,2] => [1,2,2,1] => 9
{{1,3},{2,5},{4},{6}} => [2,2,1,1] => [3,2,1] => 8
{{1,3,6},{2},{4,5}} => [3,1,2] => [1,3,1,1] => 10
{{1,3},{2,6},{4,5}} => [2,2,2] => [1,2,2,1] => 9
{{1,3},{2},{4,5,6}} => [2,1,3] => [1,1,3,1] => 8
{{1,3},{2},{4,5},{6}} => [2,1,2,1] => [2,3,1] => 7
{{1,3,6},{2},{4},{5}} => [3,1,1,1] => [4,1,1] => 9
{{1,3},{2,6},{4},{5}} => [2,2,1,1] => [3,2,1] => 8
{{1,3},{2},{4,6},{5}} => [2,1,2,1] => [2,3,1] => 7
{{1,3},{2},{4},{5,6}} => [2,1,1,2] => [1,4,1] => 6
{{1,3},{2},{4},{5},{6}} => [2,1,1,1,1] => [5,1] => 5
{{1,4,5,6},{2,3}} => [4,2] => [1,2,1,1,1] => 13
{{1,4,5},{2,3,6}} => [3,3] => [1,1,2,1,1] => 12
{{1,4,5},{2,3},{6}} => [3,2,1] => [2,2,1,1] => 11
{{1,4,6},{2,3,5}} => [3,3] => [1,1,2,1,1] => 12
{{1,4},{2,3,5,6}} => [2,4] => [1,1,1,2,1] => 11
{{1,4},{2,3,5},{6}} => [2,3,1] => [2,1,2,1] => 10
{{1,4,6},{2,3},{5}} => [3,2,1] => [2,2,1,1] => 11
{{1,4},{2,3,6},{5}} => [2,3,1] => [2,1,2,1] => 10
{{1,4},{2,3},{5,6}} => [2,2,2] => [1,2,2,1] => 9
{{1,4},{2,3},{5},{6}} => [2,2,1,1] => [3,2,1] => 8
{{1,5,6},{2,3,4}} => [3,3] => [1,1,2,1,1] => 12
{{1,5},{2,3,4,6}} => [2,4] => [1,1,1,2,1] => 11
{{1,5},{2,3,4},{6}} => [2,3,1] => [2,1,2,1] => 10
{{1,6},{2,3,4,5}} => [2,4] => [1,1,1,2,1] => 11
{{1},{2,3,4,5,6}} => [1,5] => [1,1,1,1,2] => 10
{{1},{2,3,4,5},{6}} => [1,4,1] => [2,1,1,2] => 9
{{1,6},{2,3,4},{5}} => [2,3,1] => [2,1,2,1] => 10
{{1},{2,3,4,6},{5}} => [1,4,1] => [2,1,1,2] => 9
{{1},{2,3,4},{5,6}} => [1,3,2] => [1,2,1,2] => 8
{{1},{2,3,4},{5},{6}} => [1,3,1,1] => [3,1,2] => 7
{{1,5,6},{2,3},{4}} => [3,2,1] => [2,2,1,1] => 11
{{1,5},{2,3,6},{4}} => [2,3,1] => [2,1,2,1] => 10
{{1,5},{2,3},{4,6}} => [2,2,2] => [1,2,2,1] => 9
{{1,5},{2,3},{4},{6}} => [2,2,1,1] => [3,2,1] => 8
{{1,6},{2,3,5},{4}} => [2,3,1] => [2,1,2,1] => 10
{{1},{2,3,5,6},{4}} => [1,4,1] => [2,1,1,2] => 9
{{1},{2,3,5},{4,6}} => [1,3,2] => [1,2,1,2] => 8
{{1},{2,3,5},{4},{6}} => [1,3,1,1] => [3,1,2] => 7
{{1,6},{2,3},{4,5}} => [2,2,2] => [1,2,2,1] => 9
{{1},{2,3,6},{4,5}} => [1,3,2] => [1,2,1,2] => 8
{{1},{2,3},{4,5,6}} => [1,2,3] => [1,1,2,2] => 7
{{1},{2,3},{4,5},{6}} => [1,2,2,1] => [2,2,2] => 6
{{1,6},{2,3},{4},{5}} => [2,2,1,1] => [3,2,1] => 8
{{1},{2,3,6},{4},{5}} => [1,3,1,1] => [3,1,2] => 7
{{1},{2,3},{4,6},{5}} => [1,2,2,1] => [2,2,2] => 6
{{1},{2,3},{4},{5,6}} => [1,2,1,2] => [1,3,2] => 5
{{1},{2,3},{4},{5},{6}} => [1,2,1,1,1] => [4,2] => 4
{{1,4,5,6},{2},{3}} => [4,1,1] => [3,1,1,1] => 12
{{1,4,5},{2,6},{3}} => [3,2,1] => [2,2,1,1] => 11
{{1,4,5},{2},{3,6}} => [3,1,2] => [1,3,1,1] => 10
{{1,4,5},{2},{3},{6}} => [3,1,1,1] => [4,1,1] => 9
{{1,4,6},{2,5},{3}} => [3,2,1] => [2,2,1,1] => 11
{{1,4},{2,5,6},{3}} => [2,3,1] => [2,1,2,1] => 10
{{1,4},{2,5},{3,6}} => [2,2,2] => [1,2,2,1] => 9
{{1,4},{2,5},{3},{6}} => [2,2,1,1] => [3,2,1] => 8
{{1,4,6},{2},{3,5}} => [3,1,2] => [1,3,1,1] => 10
{{1,4},{2,6},{3,5}} => [2,2,2] => [1,2,2,1] => 9
{{1,4},{2},{3,5,6}} => [2,1,3] => [1,1,3,1] => 8
{{1,4},{2},{3,5},{6}} => [2,1,2,1] => [2,3,1] => 7
{{1,4,6},{2},{3},{5}} => [3,1,1,1] => [4,1,1] => 9
{{1,4},{2,6},{3},{5}} => [2,2,1,1] => [3,2,1] => 8
{{1,4},{2},{3,6},{5}} => [2,1,2,1] => [2,3,1] => 7
{{1,4},{2},{3},{5,6}} => [2,1,1,2] => [1,4,1] => 6
{{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => [5,1] => 5
{{1,5,6},{2,4},{3}} => [3,2,1] => [2,2,1,1] => 11
{{1,5},{2,4,6},{3}} => [2,3,1] => [2,1,2,1] => 10
{{1,5},{2,4},{3,6}} => [2,2,2] => [1,2,2,1] => 9
{{1,5},{2,4},{3},{6}} => [2,2,1,1] => [3,2,1] => 8
{{1,6},{2,4,5},{3}} => [2,3,1] => [2,1,2,1] => 10
{{1},{2,4,5,6},{3}} => [1,4,1] => [2,1,1,2] => 9
{{1},{2,4,5},{3,6}} => [1,3,2] => [1,2,1,2] => 8
{{1},{2,4,5},{3},{6}} => [1,3,1,1] => [3,1,2] => 7
{{1,6},{2,4},{3,5}} => [2,2,2] => [1,2,2,1] => 9
{{1},{2,4,6},{3,5}} => [1,3,2] => [1,2,1,2] => 8
{{1},{2,4},{3,5,6}} => [1,2,3] => [1,1,2,2] => 7
{{1},{2,4},{3,5},{6}} => [1,2,2,1] => [2,2,2] => 6
{{1,6},{2,4},{3},{5}} => [2,2,1,1] => [3,2,1] => 8
{{1},{2,4,6},{3},{5}} => [1,3,1,1] => [3,1,2] => 7
{{1},{2,4},{3,6},{5}} => [1,2,2,1] => [2,2,2] => 6
{{1},{2,4},{3},{5,6}} => [1,2,1,2] => [1,3,2] => 5
{{1},{2,4},{3},{5},{6}} => [1,2,1,1,1] => [4,2] => 4
{{1,5,6},{2},{3,4}} => [3,1,2] => [1,3,1,1] => 10
{{1,5},{2,6},{3,4}} => [2,2,2] => [1,2,2,1] => 9
{{1,5},{2},{3,4,6}} => [2,1,3] => [1,1,3,1] => 8
{{1,5},{2},{3,4},{6}} => [2,1,2,1] => [2,3,1] => 7
{{1,6},{2,5},{3,4}} => [2,2,2] => [1,2,2,1] => 9
{{1},{2,5,6},{3,4}} => [1,3,2] => [1,2,1,2] => 8
{{1},{2,5},{3,4,6}} => [1,2,3] => [1,1,2,2] => 7
{{1},{2,5},{3,4},{6}} => [1,2,2,1] => [2,2,2] => 6
{{1,6},{2},{3,4,5}} => [2,1,3] => [1,1,3,1] => 8
{{1},{2,6},{3,4,5}} => [1,2,3] => [1,1,2,2] => 7
{{1},{2},{3,4,5,6}} => [1,1,4] => [1,1,1,3] => 6
{{1},{2},{3,4,5},{6}} => [1,1,3,1] => [2,1,3] => 5
{{1,6},{2},{3,4},{5}} => [2,1,2,1] => [2,3,1] => 7
{{1},{2,6},{3,4},{5}} => [1,2,2,1] => [2,2,2] => 6
{{1},{2},{3,4,6},{5}} => [1,1,3,1] => [2,1,3] => 5
{{1},{2},{3,4},{5,6}} => [1,1,2,2] => [1,2,3] => 4
{{1},{2},{3,4},{5},{6}} => [1,1,2,1,1] => [3,3] => 3
{{1,5,6},{2},{3},{4}} => [3,1,1,1] => [4,1,1] => 9
{{1,5},{2,6},{3},{4}} => [2,2,1,1] => [3,2,1] => 8
{{1,5},{2},{3,6},{4}} => [2,1,2,1] => [2,3,1] => 7
{{1,5},{2},{3},{4,6}} => [2,1,1,2] => [1,4,1] => 6
{{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => [5,1] => 5
{{1,6},{2,5},{3},{4}} => [2,2,1,1] => [3,2,1] => 8
{{1},{2,5,6},{3},{4}} => [1,3,1,1] => [3,1,2] => 7
{{1},{2,5},{3,6},{4}} => [1,2,2,1] => [2,2,2] => 6
{{1},{2,5},{3},{4,6}} => [1,2,1,2] => [1,3,2] => 5
{{1},{2,5},{3},{4},{6}} => [1,2,1,1,1] => [4,2] => 4
{{1,6},{2},{3,5},{4}} => [2,1,2,1] => [2,3,1] => 7
{{1},{2,6},{3,5},{4}} => [1,2,2,1] => [2,2,2] => 6
{{1},{2},{3,5,6},{4}} => [1,1,3,1] => [2,1,3] => 5
{{1},{2},{3,5},{4,6}} => [1,1,2,2] => [1,2,3] => 4
{{1},{2},{3,5},{4},{6}} => [1,1,2,1,1] => [3,3] => 3
{{1,6},{2},{3},{4,5}} => [2,1,1,2] => [1,4,1] => 6
{{1},{2,6},{3},{4,5}} => [1,2,1,2] => [1,3,2] => 5
{{1},{2},{3,6},{4,5}} => [1,1,2,2] => [1,2,3] => 4
{{1},{2},{3},{4,5,6}} => [1,1,1,3] => [1,1,4] => 3
{{1},{2},{3},{4,5},{6}} => [1,1,1,2,1] => [2,4] => 2
{{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => [5,1] => 5
{{1},{2,6},{3},{4},{5}} => [1,2,1,1,1] => [4,2] => 4
{{1},{2},{3,6},{4},{5}} => [1,1,2,1,1] => [3,3] => 3
{{1},{2},{3},{4,6},{5}} => [1,1,1,2,1] => [2,4] => 2
{{1},{2},{3},{4},{5,6}} => [1,1,1,1,2] => [1,5] => 1
{{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => [6] => 0
{{1,2,3,4,5,6,7}} => [7] => [1,1,1,1,1,1,1] => 21
{{1,2,3,4,5,6},{7}} => [6,1] => [2,1,1,1,1,1] => 20
{{1,2,3,4,5,7},{6}} => [6,1] => [2,1,1,1,1,1] => 20
{{1,2,3,4,5},{6,7}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,2,3,4,5},{6},{7}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,2,3,4,6,7},{5}} => [6,1] => [2,1,1,1,1,1] => 20
{{1,2,3,4,6},{5,7}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,2,3,4,6},{5},{7}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,2,3,4,7},{5,6}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,2,3,4},{5,6,7}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,2,3,4},{5,6},{7}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,3,4,7},{5},{6}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,2,3,4},{5,7},{6}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,3,4},{5},{6,7}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,2,3,4},{5},{6},{7}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,2,3,5,6,7},{4}} => [6,1] => [2,1,1,1,1,1] => 20
{{1,2,3,5,6},{4,7}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,2,3,5,6},{4},{7}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,2,3,5,7},{4,6}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,2,3,5},{4,6,7}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,2,3,5},{4,6},{7}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,3,5,7},{4},{6}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,2,3,5},{4,7},{6}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,3,5},{4},{6,7}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,2,3,5},{4},{6},{7}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,2,3,6,7},{4,5}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,2,3,6},{4,5,7}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,2,3,6},{4,5},{7}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,3,7},{4,5,6}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,2,3},{4,5,6,7}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,2,3},{4,5,6},{7}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2,3,7},{4,5},{6}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,3},{4,5,7},{6}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2,3},{4,5},{6,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2,3},{4,5},{6},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2,3,6,7},{4},{5}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,2,3,6},{4,7},{5}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,3,6},{4},{5,7}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,2,3,7},{4,6},{5}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,3},{4,6,7},{5}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2,3},{4,6},{5,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2,3},{4,6},{5},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2,3,7},{4},{5,6}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,2,3},{4,7},{5,6}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2,3},{4},{5,6,7}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,2,3},{4},{5,6},{7}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,2,3},{4,7},{5},{6}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2,3},{4},{5,7},{6}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,2,3},{4},{5},{6,7}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,2,3},{4},{5},{6},{7}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,2,4,5,6,7},{3}} => [6,1] => [2,1,1,1,1,1] => 20
{{1,2,4,5,6},{3,7}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,2,4,5,6},{3},{7}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,2,4,5,7},{3,6}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,2,4,5},{3,6,7}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,2,4,5},{3,6},{7}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,4,5,7},{3},{6}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,2,4,5},{3,7},{6}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,4,5},{3},{6,7}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,2,4,5},{3},{6},{7}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,2,4,6,7},{3,5}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,2,4,6},{3,5,7}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,2,4,6},{3,5},{7}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,4,7},{3,5,6}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,2,4},{3,5,6,7}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,2,4},{3,5,6},{7}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2,4,7},{3,5},{6}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,4},{3,5,7},{6}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2,4},{3,5},{6,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2,4},{3,5},{6},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2,4,6,7},{3},{5}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,2,4,6},{3,7},{5}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,4,6},{3},{5,7}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,2,4,7},{3,6},{5}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,4},{3,6,7},{5}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2,4},{3,6},{5,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2,4},{3,6},{5},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2,4,7},{3},{5,6}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,2,4},{3,7},{5,6}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2,4},{3},{5,6,7}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,2,4},{3},{5,6},{7}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,2,4},{3,7},{5},{6}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2,4},{3},{5,7},{6}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,2,4},{3},{5},{6,7}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,2,4},{3},{5},{6},{7}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,2,5,6,7},{3,4}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,2,5,6},{3,4,7}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,2,5,6},{3,4},{7}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,5,7},{3,4,6}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,2,5},{3,4,6,7}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,2,5},{3,4,6},{7}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2,5,7},{3,4},{6}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,5},{3,4,7},{6}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2,5},{3,4},{6,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2,5},{3,4},{6},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2,6,7},{3,4,5}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,2,6},{3,4,5,7}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,2,6},{3,4,5},{7}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2,7},{3,4,5,6}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,2},{3,4,5,6,7}} => [2,5] => [1,1,1,1,2,1] => 16
{{1,2},{3,4,5,6},{7}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,2,7},{3,4,5},{6}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2},{3,4,5,7},{6}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,2},{3,4,5},{6,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,2},{3,4,5},{6},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,2,6,7},{3,4},{5}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,6},{3,4,7},{5}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2,6},{3,4},{5,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2,6},{3,4},{5},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2,7},{3,4,6},{5}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2},{3,4,6,7},{5}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,2},{3,4,6},{5,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,2},{3,4,6},{5},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,2,7},{3,4},{5,6}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2},{3,4,7},{5,6}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,2},{3,4},{5,6,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,2},{3,4},{5,6},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2},{3,4,7},{5},{6}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,2},{3,4},{5,7},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,2},{3,4},{5},{6,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,2},{3,4},{5},{6},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,2,5,6,7},{3},{4}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,2,5,6},{3,7},{4}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,5,6},{3},{4,7}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,2,5,7},{3,6},{4}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,5},{3,6,7},{4}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2,5},{3,6},{4,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2,5},{3,6},{4},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2,5,7},{3},{4,6}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,2,5},{3,7},{4,6}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2,5},{3},{4,6,7}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,2,5},{3},{4,6},{7}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2,5},{3},{4,7},{6}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,2,5},{3},{4},{6,7}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,2,6,7},{3,5},{4}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,2,6},{3,5,7},{4}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2,6},{3,5},{4,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2,6},{3,5},{4},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2,7},{3,5,6},{4}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,2},{3,5,6,7},{4}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,2},{3,5,6},{4,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,2},{3,5,6},{4},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,2,7},{3,5},{4,6}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2},{3,5,7},{4,6}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,2},{3,5},{4,6,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,2},{3,5},{4,6},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2},{3,5,7},{4},{6}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,2},{3,5},{4,7},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,2},{3,5},{4},{6,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,2},{3,5},{4},{6},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,2,6,7},{3},{4,5}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,2,6},{3,7},{4,5}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2,6},{3},{4,5,7}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,2,6},{3},{4,5},{7}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,2,7},{3,6},{4,5}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,2},{3,6,7},{4,5}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,2},{3,6},{4,5,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,2},{3,6},{4,5},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,2,7},{3},{4,5,6}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,2},{3,7},{4,5,6}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,2},{3},{4,5,6,7}} => [2,1,4] => [1,1,1,3,1] => 12
{{1,2},{3},{4,5,6},{7}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,2,7},{3},{4,5},{6}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,2},{3,7},{4,5},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,2},{3},{4,5,7},{6}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,2},{3},{4,5},{6,7}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,2},{3},{4,5},{6},{7}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,2,6},{3},{4},{5,7}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,2},{3,6,7},{4},{5}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,2},{3,6},{4,7},{5}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,2},{3,6},{4},{5,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,2},{3,6},{4},{5},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,2},{3,7},{4,6},{5}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,2},{3},{4,6,7},{5}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,2},{3},{4,6},{5,7}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,2},{3},{4,6},{5},{7}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,2,7},{3},{4},{5,6}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,2},{3,7},{4},{5,6}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,2},{3},{4,7},{5,6}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,2},{3},{4},{5,6,7}} => [2,1,1,3] => [1,1,4,1] => 9
{{1,2},{3},{4},{5,6},{7}} => [2,1,1,2,1] => [2,4,1] => 8
{{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,2},{3},{4,7},{5},{6}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,2},{3},{4},{5,7},{6}} => [2,1,1,2,1] => [2,4,1] => 8
{{1,2},{3},{4},{5},{6,7}} => [2,1,1,1,2] => [1,5,1] => 7
{{1,2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [6,1] => 6
{{1,3,4,5,6,7},{2}} => [6,1] => [2,1,1,1,1,1] => 20
{{1,3,4,5,6},{2,7}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,3,4,5,6},{2},{7}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,3,4,5,7},{2,6}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,3,4,5},{2,6,7}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,3,4,5},{2,6},{7}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,3,4,5,7},{2},{6}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,3,4,5},{2,7},{6}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,3,4,5},{2},{6,7}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,3,4,5},{2},{6},{7}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,3,4,6,7},{2,5}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,3,4,6},{2,5,7}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,3,4,6},{2,5},{7}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,3,4,7},{2,5,6}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,3,4},{2,5,6,7}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,3,4},{2,5,6},{7}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,3,4,7},{2,5},{6}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,3,4},{2,5,7},{6}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,3,4},{2,5},{6,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,3,4},{2,5},{6},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,3,4,6,7},{2},{5}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,3,4,6},{2,7},{5}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,3,4,6},{2},{5,7}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,3,4,7},{2,6},{5}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,3,4},{2,6,7},{5}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,3,4},{2,6},{5,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,3,4},{2,6},{5},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,3,4,7},{2},{5,6}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,3,4},{2,7},{5,6}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,3,4},{2},{5,6,7}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,3,4},{2},{5,6},{7}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,3,4},{2,7},{5},{6}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,3,4},{2},{5,7},{6}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,3,4},{2},{5},{6,7}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,3,4},{2},{5},{6},{7}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,3,5,6,7},{2,4}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,3,5,6},{2,4,7}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,3,5,6},{2,4},{7}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,3,5,7},{2,4,6}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,3,5},{2,4,6,7}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,3,5},{2,4,6},{7}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,3,5,7},{2,4},{6}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,3,5},{2,4,7},{6}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,3,5},{2,4},{6,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,3,5},{2,4},{6},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,3,6,7},{2,4,5}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,3,6},{2,4,5,7}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,3,6},{2,4,5},{7}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,3,7},{2,4,5,6}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,3},{2,4,5,6,7}} => [2,5] => [1,1,1,1,2,1] => 16
{{1,3},{2,4,5,6},{7}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,3,7},{2,4,5},{6}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,3},{2,4,5,7},{6}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,3},{2,4,5},{6,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,3},{2,4,5},{6},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,3,6,7},{2,4},{5}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,3,6},{2,4,7},{5}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,3,6},{2,4},{5,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,3,6},{2,4},{5},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,3,7},{2,4,6},{5}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,3},{2,4,6,7},{5}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,3},{2,4,6},{5,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,3},{2,4,6},{5},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,3,7},{2,4},{5,6}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,3},{2,4,7},{5,6}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,3},{2,4},{5,6,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,3},{2,4},{5,6},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,3,7},{2,4},{5},{6}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,3},{2,4,7},{5},{6}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,3},{2,4},{5,7},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,3},{2,4},{5},{6,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,3},{2,4},{5},{6},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,3,5,6,7},{2},{4}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,3,5,6},{2,7},{4}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,3,5,6},{2},{4,7}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,3,5,7},{2,6},{4}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,3,5},{2,6,7},{4}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,3,5},{2,6},{4,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,3,5},{2,6},{4},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,3,5,7},{2},{4,6}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,3,5},{2,7},{4,6}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,3,5},{2},{4,6,7}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,3,5},{2},{4,6},{7}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,3,5},{2},{4,7},{6}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,3,5},{2},{4},{6,7}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,3,6,7},{2,5},{4}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,3,6},{2,5,7},{4}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,3,6},{2,5},{4,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,3,6},{2,5},{4},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,3,7},{2,5,6},{4}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,3},{2,5,6,7},{4}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,3},{2,5,6},{4,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,3},{2,5,6},{4},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,3,7},{2,5},{4,6}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,3},{2,5,7},{4,6}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,3},{2,5},{4,6,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,3},{2,5},{4,6},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,3},{2,5,7},{4},{6}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,3},{2,5},{4,7},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,3},{2,5},{4},{6,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,3},{2,5},{4},{6},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,3,6,7},{2},{4,5}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,3,6},{2,7},{4,5}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,3,6},{2},{4,5,7}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,3,6},{2},{4,5},{7}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,3,7},{2,6},{4,5}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,3},{2,6,7},{4,5}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,3},{2,6},{4,5,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,3},{2,6},{4,5},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,3,7},{2},{4,5,6}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,3},{2,7},{4,5,6}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,3},{2},{4,5,6,7}} => [2,1,4] => [1,1,1,3,1] => 12
{{1,3},{2},{4,5,6},{7}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,3,7},{2},{4,5},{6}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,3},{2,7},{4,5},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,3},{2},{4,5,7},{6}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,3},{2},{4,5},{6,7}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,3},{2},{4,5},{6},{7}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,3,6},{2},{4},{5,7}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,3},{2,6,7},{4},{5}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,3},{2,6},{4},{5,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,3},{2},{4,6,7},{5}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,3},{2},{4,6},{5,7}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,3},{2},{4,6},{5},{7}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,3,7},{2},{4},{5,6}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,3},{2,7},{4},{5,6}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,3},{2},{4,7},{5,6}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,3},{2},{4},{5,6,7}} => [2,1,1,3] => [1,1,4,1] => 9
{{1,3},{2},{4},{5,6},{7}} => [2,1,1,2,1] => [2,4,1] => 8
{{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,3},{2},{4,7},{5},{6}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,3},{2},{4},{5,7},{6}} => [2,1,1,2,1] => [2,4,1] => 8
{{1,3},{2},{4},{5},{6,7}} => [2,1,1,1,2] => [1,5,1] => 7
{{1,3},{2},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [6,1] => 6
{{1,4,5,6,7},{2,3}} => [5,2] => [1,2,1,1,1,1] => 19
{{1,4,5,6},{2,3,7}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,4,5,6},{2,3},{7}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,4,5,7},{2,3,6}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,4,5},{2,3,6,7}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,4,5},{2,3,6},{7}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,4,5,7},{2,3},{6}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,4,5},{2,3,7},{6}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,4,5},{2,3},{6,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,4,5},{2,3},{6},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,4,6,7},{2,3,5}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,4,6},{2,3,5,7}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,4,6},{2,3,5},{7}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,4,7},{2,3,5,6}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,4},{2,3,5,6,7}} => [2,5] => [1,1,1,1,2,1] => 16
{{1,4},{2,3,5,6},{7}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,4,7},{2,3,5},{6}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,4},{2,3,5,7},{6}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,4},{2,3,5},{6,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,4},{2,3,5},{6},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,4,6,7},{2,3},{5}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,4,6},{2,3,7},{5}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,4,6},{2,3},{5,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,4,6},{2,3},{5},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,4,7},{2,3,6},{5}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,4},{2,3,6,7},{5}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,4},{2,3,6},{5,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,4},{2,3,6},{5},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,4,7},{2,3},{5,6}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,4},{2,3,7},{5,6}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,4},{2,3},{5,6,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,4},{2,3},{5,6},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,4},{2,3,7},{5},{6}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,4},{2,3},{5,7},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,4},{2,3},{5},{6,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,4},{2,3},{5},{6},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,5,6,7},{2,3,4}} => [4,3] => [1,1,2,1,1,1] => 18
{{1,5,6},{2,3,4,7}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,5,6},{2,3,4},{7}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,5,7},{2,3,4,6}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,5},{2,3,4,6,7}} => [2,5] => [1,1,1,1,2,1] => 16
{{1,5},{2,3,4,6},{7}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,5,7},{2,3,4},{6}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,5},{2,3,4,7},{6}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,5},{2,3,4},{6,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,5},{2,3,4},{6},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,6,7},{2,3,4,5}} => [3,4] => [1,1,1,2,1,1] => 17
{{1,6},{2,3,4,5,7}} => [2,5] => [1,1,1,1,2,1] => 16
{{1,6},{2,3,4,5},{7}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,7},{2,3,4,5,6}} => [2,5] => [1,1,1,1,2,1] => 16
{{1},{2,3,4,5,6,7}} => [1,6] => [1,1,1,1,1,2] => 15
{{1},{2,3,4,5,6},{7}} => [1,5,1] => [2,1,1,1,2] => 14
{{1,7},{2,3,4,5},{6}} => [2,4,1] => [2,1,1,2,1] => 15
{{1},{2,3,4,5,7},{6}} => [1,5,1] => [2,1,1,1,2] => 14
{{1},{2,3,4,5},{6,7}} => [1,4,2] => [1,2,1,1,2] => 13
{{1},{2,3,4,5},{6},{7}} => [1,4,1,1] => [3,1,1,2] => 12
{{1,6,7},{2,3,4},{5}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,6},{2,3,4,7},{5}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,6},{2,3,4},{5,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,6},{2,3,4},{5},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,7},{2,3,4,6},{5}} => [2,4,1] => [2,1,1,2,1] => 15
{{1},{2,3,4,6,7},{5}} => [1,5,1] => [2,1,1,1,2] => 14
{{1},{2,3,4,6},{5,7}} => [1,4,2] => [1,2,1,1,2] => 13
{{1},{2,3,4,6},{5},{7}} => [1,4,1,1] => [3,1,1,2] => 12
{{1,7},{2,3,4},{5,6}} => [2,3,2] => [1,2,1,2,1] => 14
{{1},{2,3,4,7},{5,6}} => [1,4,2] => [1,2,1,1,2] => 13
{{1},{2,3,4},{5,6,7}} => [1,3,3] => [1,1,2,1,2] => 12
{{1},{2,3,4},{5,6},{7}} => [1,3,2,1] => [2,2,1,2] => 11
{{1,7},{2,3,4},{5},{6}} => [2,3,1,1] => [3,1,2,1] => 13
{{1},{2,3,4,7},{5},{6}} => [1,4,1,1] => [3,1,1,2] => 12
{{1},{2,3,4},{5,7},{6}} => [1,3,2,1] => [2,2,1,2] => 11
{{1},{2,3,4},{5},{6,7}} => [1,3,1,2] => [1,3,1,2] => 10
{{1},{2,3,4},{5},{6},{7}} => [1,3,1,1,1] => [4,1,2] => 9
{{1,5,6,7},{2,3},{4}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,5,6},{2,3,7},{4}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,5,6},{2,3},{4,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,5,6},{2,3},{4},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,5,7},{2,3,6},{4}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,5},{2,3,6,7},{4}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,5},{2,3,6},{4,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,5},{2,3,6},{4},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,5,7},{2,3},{4,6}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,5},{2,3,7},{4,6}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,5},{2,3},{4,6,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,5},{2,3},{4,6},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,5},{2,3},{4,7},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,5},{2,3},{4},{6,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,5},{2,3},{4},{6},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,6,7},{2,3,5},{4}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,6},{2,3,5,7},{4}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,6},{2,3,5},{4,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,6},{2,3,5},{4},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,7},{2,3,5,6},{4}} => [2,4,1] => [2,1,1,2,1] => 15
{{1},{2,3,5,6,7},{4}} => [1,5,1] => [2,1,1,1,2] => 14
{{1},{2,3,5,6},{4,7}} => [1,4,2] => [1,2,1,1,2] => 13
{{1},{2,3,5,6},{4},{7}} => [1,4,1,1] => [3,1,1,2] => 12
{{1,7},{2,3,5},{4,6}} => [2,3,2] => [1,2,1,2,1] => 14
{{1},{2,3,5,7},{4,6}} => [1,4,2] => [1,2,1,1,2] => 13
{{1},{2,3,5},{4,6,7}} => [1,3,3] => [1,1,2,1,2] => 12
{{1},{2,3,5},{4,6},{7}} => [1,3,2,1] => [2,2,1,2] => 11
{{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => [3,1,2,1] => 13
{{1},{2,3,5,7},{4},{6}} => [1,4,1,1] => [3,1,1,2] => 12
{{1},{2,3,5},{4,7},{6}} => [1,3,2,1] => [2,2,1,2] => 11
{{1},{2,3,5},{4},{6,7}} => [1,3,1,2] => [1,3,1,2] => 10
{{1},{2,3,5},{4},{6},{7}} => [1,3,1,1,1] => [4,1,2] => 9
{{1,6,7},{2,3},{4,5}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,6},{2,3,7},{4,5}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,6},{2,3},{4,5,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,6},{2,3},{4,5},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,7},{2,3,6},{4,5}} => [2,3,2] => [1,2,1,2,1] => 14
{{1},{2,3,6,7},{4,5}} => [1,4,2] => [1,2,1,1,2] => 13
{{1},{2,3,6},{4,5,7}} => [1,3,3] => [1,1,2,1,2] => 12
{{1},{2,3,6},{4,5},{7}} => [1,3,2,1] => [2,2,1,2] => 11
{{1,7},{2,3},{4,5,6}} => [2,2,3] => [1,1,2,2,1] => 13
{{1},{2,3,7},{4,5,6}} => [1,3,3] => [1,1,2,1,2] => 12
{{1},{2,3},{4,5,6,7}} => [1,2,4] => [1,1,1,2,2] => 11
{{1},{2,3},{4,5,6},{7}} => [1,2,3,1] => [2,1,2,2] => 10
{{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1},{2,3,7},{4,5},{6}} => [1,3,2,1] => [2,2,1,2] => 11
{{1},{2,3},{4,5,7},{6}} => [1,2,3,1] => [2,1,2,2] => 10
{{1},{2,3},{4,5},{6,7}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2,3},{4,5},{6},{7}} => [1,2,2,1,1] => [3,2,2] => 8
{{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,6},{2,3},{4},{5,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => [3,1,2,1] => 13
{{1},{2,3,6,7},{4},{5}} => [1,4,1,1] => [3,1,1,2] => 12
{{1},{2,3,6},{4,7},{5}} => [1,3,2,1] => [2,2,1,2] => 11
{{1},{2,3,6},{4},{5,7}} => [1,3,1,2] => [1,3,1,2] => 10
{{1},{2,3,6},{4},{5},{7}} => [1,3,1,1,1] => [4,1,2] => 9
{{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => [2,2,2,1] => 12
{{1},{2,3,7},{4,6},{5}} => [1,3,2,1] => [2,2,1,2] => 11
{{1},{2,3},{4,6,7},{5}} => [1,2,3,1] => [2,1,2,2] => 10
{{1},{2,3},{4,6},{5,7}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2,3},{4,6},{5},{7}} => [1,2,2,1,1] => [3,2,2] => 8
{{1,7},{2,3},{4},{5,6}} => [2,2,1,2] => [1,3,2,1] => 11
{{1},{2,3,7},{4},{5,6}} => [1,3,1,2] => [1,3,1,2] => 10
{{1},{2,3},{4,7},{5,6}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2,3},{4},{5,6,7}} => [1,2,1,3] => [1,1,3,2] => 8
{{1},{2,3},{4},{5,6},{7}} => [1,2,1,2,1] => [2,3,2] => 7
{{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => [4,2,1] => 10
{{1},{2,3,7},{4},{5},{6}} => [1,3,1,1,1] => [4,1,2] => 9
{{1},{2,3},{4,7},{5},{6}} => [1,2,2,1,1] => [3,2,2] => 8
{{1},{2,3},{4},{5,7},{6}} => [1,2,1,2,1] => [2,3,2] => 7
{{1},{2,3},{4},{5},{6,7}} => [1,2,1,1,2] => [1,4,2] => 6
{{1},{2,3},{4},{5},{6},{7}} => [1,2,1,1,1,1] => [5,2] => 5
{{1,4,5,6,7},{2},{3}} => [5,1,1] => [3,1,1,1,1] => 18
{{1,4,5,6},{2,7},{3}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,4,5,6},{2},{3,7}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,4,5,7},{2,6},{3}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,4,5},{2,6,7},{3}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,4,5},{2,6},{3,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,4,5},{2,6},{3},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,4,5,7},{2},{3,6}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,4,5},{2,7},{3,6}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,4,5},{2},{3,6,7}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,4,5},{2},{3,6},{7}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,4,5},{2},{3,7},{6}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,4,5},{2},{3},{6,7}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,4,6,7},{2,5},{3}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,4,6},{2,5,7},{3}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,4,6},{2,5},{3,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,4,6},{2,5},{3},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,4,7},{2,5,6},{3}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,4},{2,5,6,7},{3}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,4},{2,5,6},{3,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,4},{2,5,6},{3},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,4,7},{2,5},{3,6}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,4},{2,5,7},{3,6}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,4},{2,5},{3,6,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,4},{2,5},{3,6},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,4},{2,5},{3},{6,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,4,6,7},{2},{3,5}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,4,6},{2,7},{3,5}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,4,6},{2},{3,5,7}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,4,6},{2},{3,5},{7}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,4,7},{2,6},{3,5}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,4},{2,6,7},{3,5}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,4},{2,6},{3,5,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,4},{2,6},{3,5},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,4,7},{2},{3,5,6}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,4},{2,7},{3,5,6}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,4},{2},{3,5,6,7}} => [2,1,4] => [1,1,1,3,1] => 12
{{1,4},{2},{3,5,6},{7}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,4,7},{2},{3,5},{6}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,4},{2},{3,5,7},{6}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,4},{2},{3,5},{6,7}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,4},{2},{3,5},{6},{7}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,4,6},{2},{3},{5,7}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,4},{2},{3,6,7},{5}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,4},{2},{3,6},{5,7}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,4},{2},{3,6},{5},{7}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,4},{2},{3,7},{5,6}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,4},{2},{3},{5,6,7}} => [2,1,1,3] => [1,1,4,1] => 9
{{1,4},{2},{3},{5,6},{7}} => [2,1,1,2,1] => [2,4,1] => 8
{{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,4},{2},{3},{5,7},{6}} => [2,1,1,2,1] => [2,4,1] => 8
{{1,4},{2},{3},{5},{6,7}} => [2,1,1,1,2] => [1,5,1] => 7
{{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [6,1] => 6
{{1,5,6,7},{2,4},{3}} => [4,2,1] => [2,2,1,1,1] => 17
{{1,5,6},{2,4,7},{3}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,5,6},{2,4},{3,7}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,5,7},{2,4,6},{3}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,5},{2,4,6,7},{3}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,5},{2,4,6},{3,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,5},{2,4,6},{3},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,5,7},{2,4},{3,6}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,5},{2,4,7},{3,6}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,5},{2,4},{3,6,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,5},{2,4},{3,6},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,5},{2,4},{3},{6,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,6,7},{2,4,5},{3}} => [3,3,1] => [2,1,2,1,1] => 16
{{1,6},{2,4,5,7},{3}} => [2,4,1] => [2,1,1,2,1] => 15
{{1,6},{2,4,5},{3,7}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,6},{2,4,5},{3},{7}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,7},{2,4,5,6},{3}} => [2,4,1] => [2,1,1,2,1] => 15
{{1},{2,4,5,6,7},{3}} => [1,5,1] => [2,1,1,1,2] => 14
{{1},{2,4,5,6},{3,7}} => [1,4,2] => [1,2,1,1,2] => 13
{{1},{2,4,5,6},{3},{7}} => [1,4,1,1] => [3,1,1,2] => 12
{{1,7},{2,4,5},{3,6}} => [2,3,2] => [1,2,1,2,1] => 14
{{1},{2,4,5,7},{3,6}} => [1,4,2] => [1,2,1,1,2] => 13
{{1},{2,4,5},{3,6,7}} => [1,3,3] => [1,1,2,1,2] => 12
{{1},{2,4,5},{3,6},{7}} => [1,3,2,1] => [2,2,1,2] => 11
{{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => [3,1,2,1] => 13
{{1},{2,4,5,7},{3},{6}} => [1,4,1,1] => [3,1,1,2] => 12
{{1},{2,4,5},{3,7},{6}} => [1,3,2,1] => [2,2,1,2] => 11
{{1},{2,4,5},{3},{6,7}} => [1,3,1,2] => [1,3,1,2] => 10
{{1},{2,4,5},{3},{6},{7}} => [1,3,1,1,1] => [4,1,2] => 9
{{1,6,7},{2,4},{3,5}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,6},{2,4,7},{3,5}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,6},{2,4},{3,5,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,6},{2,4},{3,5},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,7},{2,4,6},{3,5}} => [2,3,2] => [1,2,1,2,1] => 14
{{1},{2,4,6,7},{3,5}} => [1,4,2] => [1,2,1,1,2] => 13
{{1},{2,4,6},{3,5,7}} => [1,3,3] => [1,1,2,1,2] => 12
{{1},{2,4,6},{3,5},{7}} => [1,3,2,1] => [2,2,1,2] => 11
{{1,7},{2,4},{3,5,6}} => [2,2,3] => [1,1,2,2,1] => 13
{{1},{2,4,7},{3,5,6}} => [1,3,3] => [1,1,2,1,2] => 12
{{1},{2,4},{3,5,6,7}} => [1,2,4] => [1,1,1,2,2] => 11
{{1},{2,4},{3,5,6},{7}} => [1,2,3,1] => [2,1,2,2] => 10
{{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1},{2,4,7},{3,5},{6}} => [1,3,2,1] => [2,2,1,2] => 11
{{1},{2,4},{3,5,7},{6}} => [1,2,3,1] => [2,1,2,2] => 10
{{1},{2,4},{3,5},{6,7}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2,4},{3,5},{6},{7}} => [1,2,2,1,1] => [3,2,2] => 8
{{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => [3,1,2,1] => 13
{{1},{2,4,6,7},{3},{5}} => [1,4,1,1] => [3,1,1,2] => 12
{{1},{2,4,6},{3,7},{5}} => [1,3,2,1] => [2,2,1,2] => 11
{{1},{2,4,6},{3},{5,7}} => [1,3,1,2] => [1,3,1,2] => 10
{{1},{2,4,6},{3},{5},{7}} => [1,3,1,1,1] => [4,1,2] => 9
{{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => [2,2,2,1] => 12
{{1},{2,4,7},{3,6},{5}} => [1,3,2,1] => [2,2,1,2] => 11
{{1},{2,4},{3,6,7},{5}} => [1,2,3,1] => [2,1,2,2] => 10
{{1},{2,4},{3,6},{5,7}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2,4},{3,6},{5},{7}} => [1,2,2,1,1] => [3,2,2] => 8
{{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => [1,3,2,1] => 11
{{1},{2,4,7},{3},{5,6}} => [1,3,1,2] => [1,3,1,2] => 10
{{1},{2,4},{3,7},{5,6}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2,4},{3},{5,6,7}} => [1,2,1,3] => [1,1,3,2] => 8
{{1},{2,4},{3},{5,6},{7}} => [1,2,1,2,1] => [2,3,2] => 7
{{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => [4,2,1] => 10
{{1},{2,4,7},{3},{5},{6}} => [1,3,1,1,1] => [4,1,2] => 9
{{1},{2,4},{3,7},{5},{6}} => [1,2,2,1,1] => [3,2,2] => 8
{{1},{2,4},{3},{5,7},{6}} => [1,2,1,2,1] => [2,3,2] => 7
{{1},{2,4},{3},{5},{6,7}} => [1,2,1,1,2] => [1,4,2] => 6
{{1},{2,4},{3},{5},{6},{7}} => [1,2,1,1,1,1] => [5,2] => 5
{{1,5,6,7},{2},{3,4}} => [4,1,2] => [1,3,1,1,1] => 16
{{1,5,6},{2,7},{3,4}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,5,6},{2},{3,4,7}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,5,6},{2},{3,4},{7}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,5,7},{2,6},{3,4}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,5},{2,6,7},{3,4}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,5},{2,6},{3,4,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,5},{2,6},{3,4},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,5,7},{2},{3,4,6}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,5},{2,7},{3,4,6}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,5},{2},{3,4,6,7}} => [2,1,4] => [1,1,1,3,1] => 12
{{1,5},{2},{3,4,6},{7}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,5,7},{2},{3,4},{6}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,5},{2},{3,4,7},{6}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,5},{2},{3,4},{6,7}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,5},{2},{3,4},{6},{7}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,6,7},{2,5},{3,4}} => [3,2,2] => [1,2,2,1,1] => 15
{{1,6},{2,5,7},{3,4}} => [2,3,2] => [1,2,1,2,1] => 14
{{1,6},{2,5},{3,4,7}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,7},{2,5,6},{3,4}} => [2,3,2] => [1,2,1,2,1] => 14
{{1},{2,5,6,7},{3,4}} => [1,4,2] => [1,2,1,1,2] => 13
{{1},{2,5,6},{3,4,7}} => [1,3,3] => [1,1,2,1,2] => 12
{{1},{2,5,6},{3,4},{7}} => [1,3,2,1] => [2,2,1,2] => 11
{{1,7},{2,5},{3,4,6}} => [2,2,3] => [1,1,2,2,1] => 13
{{1},{2,5,7},{3,4,6}} => [1,3,3] => [1,1,2,1,2] => 12
{{1},{2,5},{3,4,6,7}} => [1,2,4] => [1,1,1,2,2] => 11
{{1},{2,5},{3,4,6},{7}} => [1,2,3,1] => [2,1,2,2] => 10
{{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => [2,2,2,1] => 12
{{1},{2,5,7},{3,4},{6}} => [1,3,2,1] => [2,2,1,2] => 11
{{1},{2,5},{3,4,7},{6}} => [1,2,3,1] => [2,1,2,2] => 10
{{1},{2,5},{3,4},{6,7}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2,5},{3,4},{6},{7}} => [1,2,2,1,1] => [3,2,2] => 8
{{1,6,7},{2},{3,4,5}} => [3,1,3] => [1,1,3,1,1] => 14
{{1,6},{2,7},{3,4,5}} => [2,2,3] => [1,1,2,2,1] => 13
{{1,6},{2},{3,4,5,7}} => [2,1,4] => [1,1,1,3,1] => 12
{{1,6},{2},{3,4,5},{7}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,7},{2,6},{3,4,5}} => [2,2,3] => [1,1,2,2,1] => 13
{{1},{2,6,7},{3,4,5}} => [1,3,3] => [1,1,2,1,2] => 12
{{1},{2,6},{3,4,5,7}} => [1,2,4] => [1,1,1,2,2] => 11
{{1},{2,6},{3,4,5},{7}} => [1,2,3,1] => [2,1,2,2] => 10
{{1,7},{2},{3,4,5,6}} => [2,1,4] => [1,1,1,3,1] => 12
{{1},{2,7},{3,4,5,6}} => [1,2,4] => [1,1,1,2,2] => 11
{{1},{2},{3,4,5,6,7}} => [1,1,5] => [1,1,1,1,3] => 10
{{1},{2},{3,4,5,6},{7}} => [1,1,4,1] => [2,1,1,3] => 9
{{1,7},{2},{3,4,5},{6}} => [2,1,3,1] => [2,1,3,1] => 11
{{1},{2,7},{3,4,5},{6}} => [1,2,3,1] => [2,1,2,2] => 10
{{1},{2},{3,4,5,7},{6}} => [1,1,4,1] => [2,1,1,3] => 9
{{1},{2},{3,4,5},{6,7}} => [1,1,3,2] => [1,2,1,3] => 8
{{1},{2},{3,4,5},{6},{7}} => [1,1,3,1,1] => [3,1,3] => 7
{{1,6,7},{2},{3,4},{5}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,6},{2},{3,4},{5,7}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,6},{2},{3,4},{5},{7}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => [2,2,2,1] => 12
{{1},{2,6,7},{3,4},{5}} => [1,3,2,1] => [2,2,1,2] => 11
{{1},{2,6},{3,4,7},{5}} => [1,2,3,1] => [2,1,2,2] => 10
{{1},{2,6},{3,4},{5,7}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2,6},{3,4},{5},{7}} => [1,2,2,1,1] => [3,2,2] => 8
{{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => [2,1,3,1] => 11
{{1},{2,7},{3,4,6},{5}} => [1,2,3,1] => [2,1,2,2] => 10
{{1},{2},{3,4,6,7},{5}} => [1,1,4,1] => [2,1,1,3] => 9
{{1},{2},{3,4,6},{5,7}} => [1,1,3,2] => [1,2,1,3] => 8
{{1},{2},{3,4,6},{5},{7}} => [1,1,3,1,1] => [3,1,3] => 7
{{1,7},{2},{3,4},{5,6}} => [2,1,2,2] => [1,2,3,1] => 10
{{1},{2,7},{3,4},{5,6}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2},{3,4,7},{5,6}} => [1,1,3,2] => [1,2,1,3] => 8
{{1},{2},{3,4},{5,6,7}} => [1,1,2,3] => [1,1,2,3] => 7
{{1},{2},{3,4},{5,6},{7}} => [1,1,2,2,1] => [2,2,3] => 6
{{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => [3,3,1] => 9
{{1},{2,7},{3,4},{5},{6}} => [1,2,2,1,1] => [3,2,2] => 8
{{1},{2},{3,4,7},{5},{6}} => [1,1,3,1,1] => [3,1,3] => 7
{{1},{2},{3,4},{5,7},{6}} => [1,1,2,2,1] => [2,2,3] => 6
{{1},{2},{3,4},{5},{6,7}} => [1,1,2,1,2] => [1,3,3] => 5
{{1},{2},{3,4},{5},{6},{7}} => [1,1,2,1,1,1] => [4,3] => 4
{{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => [4,1,1,1] => 15
{{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,5,6},{2},{3},{4,7}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,5,7},{2},{3},{4,6}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => [1,1,4,1] => 9
{{1,5},{2},{3},{4,6},{7}} => [2,1,1,2,1] => [2,4,1] => 8
{{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => [2,4,1] => 8
{{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => [1,5,1] => 7
{{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [6,1] => 6
{{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => [3,2,1,1] => 14
{{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => [3,1,2,1] => 13
{{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => [3,1,2,1] => 13
{{1},{2,5,6,7},{3},{4}} => [1,4,1,1] => [3,1,1,2] => 12
{{1},{2,5,6},{3,7},{4}} => [1,3,2,1] => [2,2,1,2] => 11
{{1},{2,5,6},{3},{4,7}} => [1,3,1,2] => [1,3,1,2] => 10
{{1},{2,5,6},{3},{4},{7}} => [1,3,1,1,1] => [4,1,2] => 9
{{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => [2,2,2,1] => 12
{{1},{2,5,7},{3,6},{4}} => [1,3,2,1] => [2,2,1,2] => 11
{{1},{2,5},{3,6,7},{4}} => [1,2,3,1] => [2,1,2,2] => 10
{{1},{2,5},{3,6},{4,7}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2,5},{3,6},{4},{7}} => [1,2,2,1,1] => [3,2,2] => 8
{{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => [1,3,2,1] => 11
{{1},{2,5,7},{3},{4,6}} => [1,3,1,2] => [1,3,1,2] => 10
{{1},{2,5},{3,7},{4,6}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2,5},{3},{4,6,7}} => [1,2,1,3] => [1,1,3,2] => 8
{{1},{2,5},{3},{4,6},{7}} => [1,2,1,2,1] => [2,3,2] => 7
{{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => [4,2,1] => 10
{{1},{2,5,7},{3},{4},{6}} => [1,3,1,1,1] => [4,1,2] => 9
{{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => [3,2,2] => 8
{{1},{2,5},{3},{4,7},{6}} => [1,2,1,2,1] => [2,3,2] => 7
{{1},{2,5},{3},{4},{6,7}} => [1,2,1,1,2] => [1,4,2] => 6
{{1},{2,5},{3},{4},{6},{7}} => [1,2,1,1,1,1] => [5,2] => 5
{{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => [2,3,1,1] => 13
{{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => [2,2,2,1] => 12
{{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => [2,1,3,1] => 11
{{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => [2,2,2,1] => 12
{{1},{2,6,7},{3,5},{4}} => [1,3,2,1] => [2,2,1,2] => 11
{{1},{2,6},{3,5,7},{4}} => [1,2,3,1] => [2,1,2,2] => 10
{{1},{2,6},{3,5},{4,7}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2,6},{3,5},{4},{7}} => [1,2,2,1,1] => [3,2,2] => 8
{{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => [2,1,3,1] => 11
{{1},{2,7},{3,5,6},{4}} => [1,2,3,1] => [2,1,2,2] => 10
{{1},{2},{3,5,6,7},{4}} => [1,1,4,1] => [2,1,1,3] => 9
{{1},{2},{3,5,6},{4,7}} => [1,1,3,2] => [1,2,1,3] => 8
{{1},{2},{3,5,6},{4},{7}} => [1,1,3,1,1] => [3,1,3] => 7
{{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => [1,2,3,1] => 10
{{1},{2,7},{3,5},{4,6}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2},{3,5,7},{4,6}} => [1,1,3,2] => [1,2,1,3] => 8
{{1},{2},{3,5},{4,6,7}} => [1,1,2,3] => [1,1,2,3] => 7
{{1},{2},{3,5},{4,6},{7}} => [1,1,2,2,1] => [2,2,3] => 6
{{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => [3,3,1] => 9
{{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => [3,2,2] => 8
{{1},{2},{3,5,7},{4},{6}} => [1,1,3,1,1] => [3,1,3] => 7
{{1},{2},{3,5},{4,7},{6}} => [1,1,2,2,1] => [2,2,3] => 6
{{1},{2},{3,5},{4},{6,7}} => [1,1,2,1,2] => [1,3,3] => 5
{{1},{2},{3,5},{4},{6},{7}} => [1,1,2,1,1,1] => [4,3] => 4
{{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => [1,4,1,1] => 12
{{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => [1,3,2,1] => 11
{{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => [1,2,3,1] => 10
{{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => [1,1,4,1] => 9
{{1,6},{2},{3},{4,5},{7}} => [2,1,1,2,1] => [2,4,1] => 8
{{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => [1,3,2,1] => 11
{{1},{2,6,7},{3},{4,5}} => [1,3,1,2] => [1,3,1,2] => 10
{{1},{2,6},{3,7},{4,5}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2,6},{3},{4,5,7}} => [1,2,1,3] => [1,1,3,2] => 8
{{1},{2,6},{3},{4,5},{7}} => [1,2,1,2,1] => [2,3,2] => 7
{{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => [1,2,3,1] => 10
{{1},{2,7},{3,6},{4,5}} => [1,2,2,2] => [1,2,2,2] => 9
{{1},{2},{3,6,7},{4,5}} => [1,1,3,2] => [1,2,1,3] => 8
{{1},{2},{3,6},{4,5,7}} => [1,1,2,3] => [1,1,2,3] => 7
{{1},{2},{3,6},{4,5},{7}} => [1,1,2,2,1] => [2,2,3] => 6
{{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => [1,1,4,1] => 9
{{1},{2,7},{3},{4,5,6}} => [1,2,1,3] => [1,1,3,2] => 8
{{1},{2},{3,7},{4,5,6}} => [1,1,2,3] => [1,1,2,3] => 7
{{1},{2},{3},{4,5,6,7}} => [1,1,1,4] => [1,1,1,4] => 6
{{1},{2},{3},{4,5,6},{7}} => [1,1,1,3,1] => [2,1,4] => 5
{{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => [2,4,1] => 8
{{1},{2,7},{3},{4,5},{6}} => [1,2,1,2,1] => [2,3,2] => 7
{{1},{2},{3,7},{4,5},{6}} => [1,1,2,2,1] => [2,2,3] => 6
{{1},{2},{3},{4,5,7},{6}} => [1,1,1,3,1] => [2,1,4] => 5
{{1},{2},{3},{4,5},{6,7}} => [1,1,1,2,2] => [1,2,4] => 4
{{1},{2},{3},{4,5},{6},{7}} => [1,1,1,2,1,1] => [3,4] => 3
{{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => [5,1,1] => 11
{{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => [4,2,1] => 10
{{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => [3,3,1] => 9
{{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => [2,4,1] => 8
{{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => [1,5,1] => 7
{{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [6,1] => 6
{{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => [4,2,1] => 10
{{1},{2,6,7},{3},{4},{5}} => [1,3,1,1,1] => [4,1,2] => 9
{{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => [3,2,2] => 8
{{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => [2,3,2] => 7
{{1},{2,6},{3},{4},{5,7}} => [1,2,1,1,2] => [1,4,2] => 6
{{1},{2,6},{3},{4},{5},{7}} => [1,2,1,1,1,1] => [5,2] => 5
{{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => [3,3,1] => 9
{{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => [3,2,2] => 8
{{1},{2},{3,6,7},{4},{5}} => [1,1,3,1,1] => [3,1,3] => 7
{{1},{2},{3,6},{4,7},{5}} => [1,1,2,2,1] => [2,2,3] => 6
{{1},{2},{3,6},{4},{5,7}} => [1,1,2,1,2] => [1,3,3] => 5
{{1},{2},{3,6},{4},{5},{7}} => [1,1,2,1,1,1] => [4,3] => 4
{{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => [2,4,1] => 8
{{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => [2,3,2] => 7
{{1},{2},{3,7},{4,6},{5}} => [1,1,2,2,1] => [2,2,3] => 6
{{1},{2},{3},{4,6,7},{5}} => [1,1,1,3,1] => [2,1,4] => 5
{{1},{2},{3},{4,6},{5,7}} => [1,1,1,2,2] => [1,2,4] => 4
{{1},{2},{3},{4,6},{5},{7}} => [1,1,1,2,1,1] => [3,4] => 3
{{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => [1,5,1] => 7
{{1},{2,7},{3},{4},{5,6}} => [1,2,1,1,2] => [1,4,2] => 6
{{1},{2},{3,7},{4},{5,6}} => [1,1,2,1,2] => [1,3,3] => 5
{{1},{2},{3},{4,7},{5,6}} => [1,1,1,2,2] => [1,2,4] => 4
{{1},{2},{3},{4},{5,6,7}} => [1,1,1,1,3] => [1,1,5] => 3
{{1},{2},{3},{4},{5,6},{7}} => [1,1,1,1,2,1] => [2,5] => 2
{{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [6,1] => 6
{{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => [5,2] => 5
{{1},{2},{3,7},{4},{5},{6}} => [1,1,2,1,1,1] => [4,3] => 4
{{1},{2},{3},{4,7},{5},{6}} => [1,1,1,2,1,1] => [3,4] => 3
{{1},{2},{3},{4},{5,7},{6}} => [1,1,1,1,2,1] => [2,5] => 2
{{1},{2},{3},{4},{5},{6,7}} => [1,1,1,1,1,2] => [1,6] => 1
{{1},{2},{3},{4},{5},{6},{7}} => [1,1,1,1,1,1,1] => [7] => 0
{{1,2},{3,4},{5,6},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,4},{5,6},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,3},{5,6},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,3},{4,6},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,3},{4,5},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,3},{4,5},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,4},{3,5},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,4},{3,5},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,4},{3,5},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,4},{3,6},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,5},{3,6},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,5},{4,6},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,2},{3,5},{4,6},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,2},{3,6},{4,5},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,6},{4,5},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,6},{3,5},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,6},{3,4},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,5},{3,4},{7,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,5},{3,4},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,6},{3,4},{5,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,6},{3,4},{5,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,7},{3,4},{5,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,7},{3,4},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,7},{3,5},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,7},{4,5},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,2},{3,7},{4,5},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,2},{3,8},{4,5},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,8},{4,5},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,8},{3,5},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,8},{3,4},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,8},{3,4},{5,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,8},{3,4},{5,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,7},{3,5},{4,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,8},{3,5},{4,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,8},{3,6},{4,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,8},{3,6},{5,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,8},{4,6},{5,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,2},{3,8},{4,6},{5,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,2},{3,7},{4,6},{5,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,7},{4,6},{5,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,7},{3,6},{5,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,7},{3,6},{4,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,7},{3,5},{4,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,6},{3,5},{4,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,6},{3,5},{4,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,5},{3,6},{4,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,5},{3,6},{4,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,5},{3,7},{4,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,2},{3,6},{4,7},{5,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,2},{3,5},{4,7},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,5},{4,7},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,4},{3,7},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,4},{3,7},{5,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,4},{3,6},{5,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,4},{3,6},{5,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,3},{4,6},{5,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,3},{4,6},{5,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,3},{4,7},{5,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,3},{4,7},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,3},{5,7},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,4},{5,7},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,2},{3,4},{5,7},{6,8}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,2},{3,4},{5,8},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,4},{5,8},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,3},{5,8},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,3},{4,8},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,3},{4,8},{5,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,3},{4,8},{5,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,4},{3,8},{5,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,4},{3,8},{5,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,4},{3,8},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,5},{3,8},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,5},{4,8},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,2},{3,5},{4,8},{6,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,2},{3,6},{4,8},{5,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,6},{4,8},{5,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,6},{3,8},{5,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,6},{3,8},{4,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,5},{3,8},{4,7}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,5},{3,8},{4,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,5},{3,7},{4,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,6},{3,7},{4,5}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,6},{3,8},{4,5}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,7},{3,8},{4,5}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,7},{3,8},{4,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,7},{3,8},{5,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,7},{4,8},{5,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,2},{3,7},{4,8},{5,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,2},{3,8},{4,7},{5,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,3},{2,8},{4,7},{5,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,6},{2,8},{3,7},{4,5}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,7},{2,8},{3,6},{4,5}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => [1,2,2,2,1] => 16
{{1},{2},{3},{4},{5},{6},{7},{8}} => [1,1,1,1,1,1,1,1] => [8] => 0
{{1},{2},{3},{4},{5},{6},{7,8}} => [1,1,1,1,1,1,2] => [1,7] => 1
{{1},{2},{3},{4},{5},{6,8},{7}} => [1,1,1,1,1,2,1] => [2,6] => 2
{{1},{2},{3},{4},{5},{6,7,8}} => [1,1,1,1,1,3] => [1,1,6] => 3
{{1},{2},{3},{4},{5,6},{7},{8}} => [1,1,1,1,2,1,1] => [3,5] => 3
{{1},{2},{3},{4},{5,6},{7,8}} => [1,1,1,1,2,2] => [1,2,5] => 4
{{1},{2},{3},{4},{5,7},{6},{8}} => [1,1,1,1,2,1,1] => [3,5] => 3
{{1},{2},{3},{4},{5,8},{6},{7}} => [1,1,1,1,2,1,1] => [3,5] => 3
{{1},{2},{3},{4},{5,7,8},{6}} => [1,1,1,1,3,1] => [2,1,5] => 5
{{1},{2},{3},{4},{5,6,7},{8}} => [1,1,1,1,3,1] => [2,1,5] => 5
{{1},{2},{3},{4},{5,8},{6,7}} => [1,1,1,1,2,2] => [1,2,5] => 4
{{1},{2},{3},{4},{5,6,8},{7}} => [1,1,1,1,3,1] => [2,1,5] => 5
{{1},{2},{3},{4},{5,6,7,8}} => [1,1,1,1,4] => [1,1,1,5] => 6
{{1},{2},{3},{4,5},{6},{7,8}} => [1,1,1,2,1,2] => [1,3,4] => 5
{{1},{2},{3},{4,8},{5},{6},{7}} => [1,1,1,2,1,1,1] => [4,4] => 4
{{1},{2},{3},{4,6,7,8},{5}} => [1,1,1,4,1] => [2,1,1,4] => 9
{{1},{2},{3},{4,8},{5,6},{7}} => [1,1,1,2,2,1] => [2,2,4] => 6
{{1},{2},{3},{4,7,8},{5,6}} => [1,1,1,3,2] => [1,2,1,4] => 8
{{1},{2},{3},{4,8},{5,7},{6}} => [1,1,1,2,2,1] => [2,2,4] => 6
{{1},{2},{3},{4,8},{5,6,7}} => [1,1,1,2,3] => [1,1,2,4] => 7
{{1},{2},{3},{4,5,6,7,8}} => [1,1,1,5] => [1,1,1,1,4] => 10
{{1},{2},{3,4},{5},{6},{7,8}} => [1,1,2,1,1,2] => [1,4,3] => 6
{{1},{2},{3,4},{5},{6,8},{7}} => [1,1,2,1,2,1] => [2,3,3] => 7
{{1},{2},{3,4},{5,6},{7},{8}} => [1,1,2,2,1,1] => [3,2,3] => 8
{{1},{2},{3,4},{5,8},{6},{7}} => [1,1,2,2,1,1] => [3,2,3] => 8
{{1},{2},{3,4},{5,8},{6,7}} => [1,1,2,2,2] => [1,2,2,3] => 9
{{1},{2},{3,4},{5,6,7,8}} => [1,1,2,4] => [1,1,1,2,3] => 11
{{1},{2},{3,5},{4},{6,7,8}} => [1,1,2,1,3] => [1,1,3,3] => 8
{{1},{2},{3,8},{4},{5},{6},{7}} => [1,1,2,1,1,1,1] => [5,3] => 5
{{1},{2},{3,7,8},{4},{5},{6}} => [1,1,3,1,1,1] => [4,1,3] => 9
{{1},{2},{3,7,8},{4},{5,6}} => [1,1,3,1,2] => [1,3,1,3] => 10
{{1},{2},{3,5,7,8},{4},{6}} => [1,1,4,1,1] => [3,1,1,3] => 12
{{1},{2},{3,8},{4},{5,6,7}} => [1,1,2,1,3] => [1,1,3,3] => 8
{{1},{2},{3,5,8},{4},{6,7}} => [1,1,3,1,2] => [1,3,1,3] => 10
{{1},{2},{3,5,6,7,8},{4}} => [1,1,5,1] => [2,1,1,1,3] => 14
{{1},{2},{3,4,5},{6},{7},{8}} => [1,1,3,1,1,1] => [4,1,3] => 9
{{1},{2},{3,4,5},{6,7,8}} => [1,1,3,3] => [1,1,2,1,3] => 12
{{1},{2},{3,8},{4,5},{6},{7}} => [1,1,2,2,1,1] => [3,2,3] => 8
{{1},{2},{3,6,7,8},{4,5}} => [1,1,4,2] => [1,2,1,1,3] => 13
{{1},{2},{3,8},{4,6},{5},{7}} => [1,1,2,2,1,1] => [3,2,3] => 8
{{1},{2},{3,7,8},{4,6},{5}} => [1,1,3,2,1] => [2,2,1,3] => 11
{{1},{2},{3,8},{4,7},{5},{6}} => [1,1,2,2,1,1] => [3,2,3] => 8
{{1},{2},{3,8},{4,6,7},{5}} => [1,1,2,3,1] => [2,1,2,3] => 10
{{1},{2},{3,4,5,6},{7,8}} => [1,1,4,2] => [1,2,1,1,3] => 13
{{1},{2},{3,8},{4,5,6},{7}} => [1,1,2,3,1] => [2,1,2,3] => 10
{{1},{2},{3,7,8},{4,5,6}} => [1,1,3,3] => [1,1,2,1,3] => 12
{{1},{2},{3,8},{4,7},{5,6}} => [1,1,2,2,2] => [1,2,2,3] => 9
{{1},{2},{3,4,7,8},{5,6}} => [1,1,4,2] => [1,2,1,1,3] => 13
{{1},{2},{3,4,5,8},{6},{7}} => [1,1,4,1,1] => [3,1,1,3] => 12
{{1},{2},{3,4,5,6,7},{8}} => [1,1,5,1] => [2,1,1,1,3] => 14
{{1},{2},{3,8},{4,5,6,7}} => [1,1,2,4] => [1,1,1,2,3] => 11
{{1},{2},{3,4,8},{5,6,7}} => [1,1,3,3] => [1,1,2,1,3] => 12
{{1},{2},{3,4,5,8},{6,7}} => [1,1,4,2] => [1,2,1,1,3] => 13
{{1},{2},{3,4,5,6,8},{7}} => [1,1,5,1] => [2,1,1,1,3] => 14
{{1},{2},{3,4,5,6,7,8}} => [1,1,6] => [1,1,1,1,1,3] => 15
{{1},{2,3},{4},{5},{6},{7,8}} => [1,2,1,1,1,2] => [1,5,2] => 7
{{1},{2,3},{4},{5},{6,7},{8}} => [1,2,1,1,2,1] => [2,4,2] => 8
{{1},{2,3},{4},{5},{6,8},{7}} => [1,2,1,1,2,1] => [2,4,2] => 8
{{1},{2,3},{4},{5,8},{6,7}} => [1,2,1,2,2] => [1,2,3,2] => 10
{{1},{2,3},{4},{5,6,7,8}} => [1,2,1,4] => [1,1,1,3,2] => 12
{{1},{2,3},{4,5},{6,7},{8}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,3},{4,5},{6,8},{7}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,3},{4,5},{6,7,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1},{2,3},{4,6,7},{5},{8}} => [1,2,3,1,1] => [3,1,2,2] => 13
{{1},{2,3},{4,6,8},{5},{7}} => [1,2,3,1,1] => [3,1,2,2] => 13
{{1},{2,3},{4,6,7,8},{5}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1},{2,3},{4,5,6},{7,8}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,3},{4,7},{5,6},{8}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,3},{4,8},{5,6},{7}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,3},{4,7,8},{5,6}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,3},{4,8},{5,7},{6}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,3},{4,5,8},{6},{7}} => [1,2,3,1,1] => [3,1,2,2] => 13
{{1},{2,3},{4,8},{5,6,7}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1},{2,3},{4,5,8},{6,7}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,3},{4,5,6,8},{7}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1},{2,3},{4,5,6,7,8}} => [1,2,5] => [1,1,1,1,2,2] => 16
{{1},{2,4},{3},{5},{6},{7,8}} => [1,2,1,1,1,2] => [1,5,2] => 7
{{1},{2,4},{3},{5},{6,8},{7}} => [1,2,1,1,2,1] => [2,4,2] => 8
{{1},{2,4},{3},{5},{6,7,8}} => [1,2,1,1,3] => [1,1,4,2] => 9
{{1},{2,4},{3},{5,6},{7,8}} => [1,2,1,2,2] => [1,2,3,2] => 10
{{1},{2,4},{3},{5,7},{6},{8}} => [1,2,1,2,1,1] => [3,3,2] => 9
{{1},{2,4},{3},{5,7,8},{6}} => [1,2,1,3,1] => [2,1,3,2] => 11
{{1},{2,4},{3},{5,8},{6,7}} => [1,2,1,2,2] => [1,2,3,2] => 10
{{1},{2,4},{3},{5,6,7,8}} => [1,2,1,4] => [1,1,1,3,2] => 12
{{1},{2,5},{3},{4},{6,8},{7}} => [1,2,1,1,2,1] => [2,4,2] => 8
{{1},{2,8},{3},{4},{5},{6},{7}} => [1,2,1,1,1,1,1] => [6,2] => 6
{{1},{2,7,8},{3},{4},{5},{6}} => [1,3,1,1,1,1] => [5,1,2] => 11
{{1},{2,5,8},{3},{4},{6},{7}} => [1,3,1,1,1,1] => [5,1,2] => 11
{{1},{2,8},{3},{4},{5,6,7}} => [1,2,1,1,3] => [1,1,4,2] => 9
{{1},{2,5,6,8},{3},{4},{7}} => [1,4,1,1,1] => [4,1,1,2] => 15
{{1},{2,5,6,7,8},{3},{4}} => [1,5,1,1] => [3,1,1,1,2] => 18
{{1},{2,4,5},{3},{6,7},{8}} => [1,3,1,2,1] => [2,3,1,2] => 13
{{1},{2,4,5},{3},{6,8},{7}} => [1,3,1,2,1] => [2,3,1,2] => 13
{{1},{2,4,5},{3},{6,7,8}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1},{2,6},{3},{4,5},{7,8}} => [1,2,1,2,2] => [1,2,3,2] => 10
{{1},{2,6,8},{3},{4,5},{7}} => [1,3,1,2,1] => [2,3,1,2] => 13
{{1},{2,6,7,8},{3},{4,5}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1},{2,4,6},{3},{5},{7,8}} => [1,3,1,1,2] => [1,4,1,2] => 12
{{1},{2,4,6,7},{3},{5},{8}} => [1,4,1,1,1] => [4,1,1,2] => 15
{{1},{2,8},{3},{4,6,7},{5}} => [1,2,1,3,1] => [2,1,3,2] => 11
{{1},{2,4,8},{3},{5},{6,7}} => [1,3,1,1,2] => [1,4,1,2] => 12
{{1},{2,4,6,8},{3},{5},{7}} => [1,4,1,1,1] => [4,1,1,2] => 15
{{1},{2,4,6,7,8},{3},{5}} => [1,5,1,1] => [3,1,1,1,2] => 18
{{1},{2,7,8},{3},{4,5,6}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1},{2,4,7},{3},{5,6},{8}} => [1,3,1,2,1] => [2,3,1,2] => 13
{{1},{2,8},{3},{4,7},{5,6}} => [1,2,1,2,2] => [1,2,3,2] => 10
{{1},{2,4,8},{3},{5,6},{7}} => [1,3,1,2,1] => [2,3,1,2] => 13
{{1},{2,4,7,8},{3},{5,6}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1},{2,4,8},{3},{5,7},{6}} => [1,3,1,2,1] => [2,3,1,2] => 13
{{1},{2,4,5,7,8},{3},{6}} => [1,5,1,1] => [3,1,1,1,2] => 18
{{1},{2,4,8},{3},{5,6,7}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1},{2,4,5,8},{3},{6,7}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1},{2,4,5,6,8},{3},{7}} => [1,5,1,1] => [3,1,1,1,2] => 18
{{1},{2,4,5,6,7,8},{3}} => [1,6,1] => [2,1,1,1,1,2] => 20
{{1},{2,3,4},{5},{6},{7},{8}} => [1,3,1,1,1,1] => [5,1,2] => 11
{{1},{2,3,4},{5},{6,8},{7}} => [1,3,1,2,1] => [2,3,1,2] => 13
{{1},{2,3,4},{5},{6,7,8}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1},{2,3,4},{5,6},{7,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,3,4},{5,6,7},{8}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,3,4},{5,8},{6,7}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,3,4},{5,6,8},{7}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,5},{3,4},{6,7},{8}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,5},{3,4},{6,8},{7}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,5},{3,4},{6,7,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1},{2,8},{3,4},{5},{6},{7}} => [1,2,2,1,1,1] => [4,2,2] => 10
{{1},{2,6,7},{3,4},{5},{8}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1},{2,6,8},{3,4},{5},{7}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1},{2,7},{3,4},{5,6},{8}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,8},{3,4},{5,6},{7}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,7,8},{3,4},{5,6}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,8},{3,4},{5,7},{6}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,8},{3,4},{5,6,7}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1},{2,5,8},{3,4},{6,7}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,5,6,7,8},{3,4}} => [1,5,2] => [1,2,1,1,1,2] => 19
{{1},{2,3,5},{4},{6},{7},{8}} => [1,3,1,1,1,1] => [5,1,2] => 11
{{1},{2,3,5},{4},{6,7,8}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1},{2,6},{3,5},{4},{7,8}} => [1,2,2,1,2] => [1,3,2,2] => 11
{{1},{2,7},{3,5},{4},{6},{8}} => [1,2,2,1,1,1] => [4,2,2] => 10
{{1},{2,8},{3,5},{4},{6},{7}} => [1,2,2,1,1,1] => [4,2,2] => 10
{{1},{2,6,7},{3,5},{4},{8}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1},{2,8},{3,5},{4},{6,7}} => [1,2,2,1,2] => [1,3,2,2] => 11
{{1},{2,6,8},{3,5},{4},{7}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1},{2,6,7,8},{3,5},{4}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,3,6},{4},{5},{7},{8}} => [1,3,1,1,1,1] => [5,1,2] => 11
{{1},{2,3,7},{4},{5},{6},{8}} => [1,3,1,1,1,1] => [5,1,2] => 11
{{1},{2,8},{3,7},{4},{5},{6}} => [1,2,2,1,1,1] => [4,2,2] => 10
{{1},{2,3,8},{4},{5},{6},{7}} => [1,3,1,1,1,1] => [5,1,2] => 11
{{1},{2,3,7,8},{4},{5},{6}} => [1,4,1,1,1] => [4,1,1,2] => 15
{{1},{2,3,6,7},{4},{5},{8}} => [1,4,1,1,1] => [4,1,1,2] => 15
{{1},{2,3,6,8},{4},{5},{7}} => [1,4,1,1,1] => [4,1,1,2] => 15
{{1},{2,3,6,7,8},{4},{5}} => [1,5,1,1] => [3,1,1,1,2] => 18
{{1},{2,7},{3,5,6},{4},{8}} => [1,2,3,1,1] => [3,1,2,2] => 13
{{1},{2,8},{3,5,6},{4},{7}} => [1,2,3,1,1] => [3,1,2,2] => 13
{{1},{2,7,8},{3,5,6},{4}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,3,7},{4},{5,6},{8}} => [1,3,1,2,1] => [2,3,1,2] => 13
{{1},{2,8},{3,7},{4},{5,6}} => [1,2,2,1,2] => [1,3,2,2] => 11
{{1},{2,3,5,7},{4},{6},{8}} => [1,4,1,1,1] => [4,1,1,2] => 15
{{1},{2,8},{3,5,7},{4},{6}} => [1,2,3,1,1] => [3,1,2,2] => 13
{{1},{2,3,5,8},{4},{6},{7}} => [1,4,1,1,1] => [4,1,1,2] => 15
{{1},{2,3,5,7,8},{4},{6}} => [1,5,1,1] => [3,1,1,1,2] => 18
{{1},{2,3,5,6,7},{4},{8}} => [1,5,1,1] => [3,1,1,1,2] => 18
{{1},{2,8},{3,5,6,7},{4}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1},{2,3,8},{4},{5,6,7}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1},{2,3,5,8},{4},{6,7}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1},{2,3,5,6,8},{4},{7}} => [1,5,1,1] => [3,1,1,1,2] => 18
{{1},{2,3,5,6,7,8},{4}} => [1,6,1] => [2,1,1,1,1,2] => 20
{{1},{2,8},{3,4,5},{6},{7}} => [1,2,3,1,1] => [3,1,2,2] => 13
{{1},{2,8},{3,4,5},{6,7}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,6,8},{3,4,5},{7}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,6,7,8},{3,4,5}} => [1,4,3] => [1,1,2,1,1,2] => 18
{{1},{2,3,6},{4,5},{7,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,7},{3,6},{4,5},{8}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,8},{3,6},{4,5},{7}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,7,8},{3,6},{4,5}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,8},{3,7},{4,5},{6}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,3,8},{4,5},{6},{7}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1},{2,3,6,7},{4,5},{8}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,8},{3,6,7},{4,5}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,3,8},{4,5},{6,7}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,3,6,8},{4,5},{7}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,3,4,6},{5},{7,8}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1},{2,8},{3,4,6},{5},{7}} => [1,2,3,1,1] => [3,1,2,2] => 13
{{1},{2,7,8},{3,4,6},{5}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,8},{3,7},{4,6},{5}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,3,8},{4,6},{5},{7}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1},{2,3,7,8},{4,6},{5}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,8},{3,4,7},{5},{6}} => [1,2,3,1,1] => [3,1,2,2] => 13
{{1},{2,3,4,8},{5},{6},{7}} => [1,4,1,1,1] => [4,1,1,2] => 15
{{1},{2,3,4,7,8},{5},{6}} => [1,5,1,1] => [3,1,1,1,2] => 18
{{1},{2,8},{3,4,6,7},{5}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1},{2,3,8},{4,6,7},{5}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,3,4,6,8},{5},{7}} => [1,5,1,1] => [3,1,1,1,2] => 18
{{1},{2,3,4,6,7,8},{5}} => [1,6,1] => [2,1,1,1,1,2] => 20
{{1},{2,3,4,5,6},{7},{8}} => [1,5,1,1] => [3,1,1,1,2] => 18
{{1},{2,3,4,5,6},{7,8}} => [1,5,2] => [1,2,1,1,1,2] => 19
{{1},{2,8},{3,4,5,6},{7}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1},{2,8},{3,7},{4,5,6}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1},{2,3,8},{4,5,6},{7}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,8},{3,4,7},{5,6}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,3,8},{4,7},{5,6}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,3,4,8},{5,6},{7}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,3,4,5,7},{6},{8}} => [1,5,1,1] => [3,1,1,1,2] => 18
{{1},{2,8},{3,4,5,7},{6}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1},{2,3,8},{4,5,7},{6}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,3,4,8},{5,7},{6}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,3,4,5,8},{6},{7}} => [1,5,1,1] => [3,1,1,1,2] => 18
{{1},{2,3,4,5,7,8},{6}} => [1,6,1] => [2,1,1,1,1,2] => 20
{{1},{2,3,4,5,6,7},{8}} => [1,6,1] => [2,1,1,1,1,2] => 20
{{1},{2,8},{3,4,5,6,7}} => [1,2,5] => [1,1,1,1,2,2] => 16
{{1},{2,3,4,8},{5,6,7}} => [1,4,3] => [1,1,2,1,1,2] => 18
{{1},{2,3,4,5,8},{6,7}} => [1,5,2] => [1,2,1,1,1,2] => 19
{{1},{2,3,4,5,6,8},{7}} => [1,6,1] => [2,1,1,1,1,2] => 20
{{1},{2,3,4,5,6,7,8}} => [1,7] => [1,1,1,1,1,1,2] => 21
{{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [7,1] => 7
{{1,2},{3},{4},{5},{6},{7,8}} => [2,1,1,1,1,2] => [1,6,1] => 8
{{1,2},{3},{4},{5},{6,7},{8}} => [2,1,1,1,2,1] => [2,5,1] => 9
{{1,2},{3},{4},{5},{6,8},{7}} => [2,1,1,1,2,1] => [2,5,1] => 9
{{1,2},{3},{4},{5},{6,7,8}} => [2,1,1,1,3] => [1,1,5,1] => 10
{{1,2},{3},{4},{5,6},{7},{8}} => [2,1,1,2,1,1] => [3,4,1] => 10
{{1,2},{3},{4},{5,8},{6},{7}} => [2,1,1,2,1,1] => [3,4,1] => 10
{{1,2},{3},{4},{5,8},{6,7}} => [2,1,1,2,2] => [1,2,4,1] => 11
{{1,2},{3},{4},{5,6,7,8}} => [2,1,1,4] => [1,1,1,4,1] => 13
{{1,2},{3},{4,5},{6},{7},{8}} => [2,1,2,1,1,1] => [4,3,1] => 11
{{1,2},{3},{4,5},{6,7,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,2},{3},{4,8},{5},{6},{7}} => [2,1,2,1,1,1] => [4,3,1] => 11
{{1,2},{3},{4,6,7,8},{5}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,2},{3},{4,5,6},{7,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,2},{3},{4,5,8},{6},{7}} => [2,1,3,1,1] => [3,1,3,1] => 14
{{1,2},{3},{4,5,8},{6,7}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,2},{3},{4,5,6,8},{7}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,2},{3},{4,5,6,7,8}} => [2,1,5] => [1,1,1,1,3,1] => 17
{{1,2},{3,4},{5},{6},{7},{8}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,2},{3,4},{5},{6,7,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,2},{3,4},{5,7,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,2},{3,4},{5,6,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,2},{3,4},{5,6,7,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,2},{3,5},{4},{6},{7},{8}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,2},{3,5},{4},{6,7,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,2},{3,6},{4},{5},{7},{8}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,2},{3,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,2},{3,6,7,8},{4},{5}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2},{3,5,6},{4},{7,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,2},{3,7,8},{4},{5,6}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,2},{3,5,7,8},{4},{6}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2},{3,8},{4},{5,6,7}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,2},{3,5,8},{4},{6,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,2},{3,5,6,8},{4},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2},{3,5,6,7,8},{4}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,2},{3,4,5},{6},{7},{8}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,2},{3,8},{4,5},{6},{7}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,2},{3,7,8},{4,5},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2},{3,6,8},{4,5},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2},{3,6,7,8},{4,5}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,2},{3,4,6},{5},{7,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,2},{3,7,8},{4,6},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2},{3,4,8},{5},{6},{7}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,2},{3,4,7,8},{5},{6}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2},{3,8},{4,6,7},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,2},{3,4,8},{5},{6,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,2},{3,4,6,8},{5},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2},{3,4,6,7,8},{5}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,2},{3,4,5,6},{7,8}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,2},{3,8},{4,5,6},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,2},{3,4,8},{5,6},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2},{3,4,5,7},{6},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2},{3,8},{4,5,7},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,2},{3,4,8},{5,7},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2},{3,4,5,8},{6},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2},{3,4,5,7,8},{6}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,2},{3,4,5,6,7},{8}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,2},{3,8},{4,5,6,7}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,2},{3,4,8},{5,6,7}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,2},{3,4,5,8},{6,7}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,2},{3,4,5,6,8},{7}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,2},{3,4,5,6,7,8}} => [2,6] => [1,1,1,1,1,2,1] => 22
{{1,3},{2},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [7,1] => 7
{{1,3},{2},{4},{5},{6},{7,8}} => [2,1,1,1,1,2] => [1,6,1] => 8
{{1,3},{2},{4},{5},{6,8},{7}} => [2,1,1,1,2,1] => [2,5,1] => 9
{{1,3},{2},{4},{5},{6,7,8}} => [2,1,1,1,3] => [1,1,5,1] => 10
{{1,3},{2},{4},{5,7,8},{6}} => [2,1,1,3,1] => [2,1,4,1] => 12
{{1,3},{2},{4},{5,8},{6,7}} => [2,1,1,2,2] => [1,2,4,1] => 11
{{1,3},{2},{4},{5,6,7,8}} => [2,1,1,4] => [1,1,1,4,1] => 13
{{1,3},{2},{4,5},{6,7},{8}} => [2,1,2,2,1] => [2,2,3,1] => 13
{{1,3},{2},{4,5},{6,8},{7}} => [2,1,2,2,1] => [2,2,3,1] => 13
{{1,3},{2},{4,5},{6,7,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,3},{2},{4,6},{5},{7,8}} => [2,1,2,1,2] => [1,3,3,1] => 12
{{1,3},{2},{4,6,7},{5},{8}} => [2,1,3,1,1] => [3,1,3,1] => 14
{{1,3},{2},{4,8},{5},{6,7}} => [2,1,2,1,2] => [1,3,3,1] => 12
{{1,3},{2},{4,6,8},{5},{7}} => [2,1,3,1,1] => [3,1,3,1] => 14
{{1,3},{2},{4,6,7,8},{5}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,3},{2},{4,5,6},{7,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,3},{2},{4,7},{5,6},{8}} => [2,1,2,2,1] => [2,2,3,1] => 13
{{1,3},{2},{4,8},{5,6},{7}} => [2,1,2,2,1] => [2,2,3,1] => 13
{{1,3},{2},{4,7,8},{5,6}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,3},{2},{4,8},{5,7},{6}} => [2,1,2,2,1] => [2,2,3,1] => 13
{{1,3},{2},{4,5,7,8},{6}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,3},{2},{4,8},{5,6,7}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,3},{2},{4,5,8},{6,7}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,3},{2},{4,5,6,8},{7}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,3},{2},{4,5,6,7,8}} => [2,1,5] => [1,1,1,1,3,1] => 17
{{1,4},{2},{3},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [7,1] => 7
{{1,4},{2},{3},{5},{6,8},{7}} => [2,1,1,1,2,1] => [2,5,1] => 9
{{1,4},{2},{3},{5},{6,7,8}} => [2,1,1,1,3] => [1,1,5,1] => 10
{{1,4},{2},{3},{5,6},{7,8}} => [2,1,1,2,2] => [1,2,4,1] => 11
{{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => [3,4,1] => 10
{{1,4},{2},{3},{5,8},{6,7}} => [2,1,1,2,2] => [1,2,4,1] => 11
{{1,4},{2},{3},{5,6,7,8}} => [2,1,1,4] => [1,1,1,4,1] => 13
{{1,5},{2},{3},{4},{6},{7},{8}} => [2,1,1,1,1,1,1] => [7,1] => 7
{{1,5},{2},{3},{4},{6},{7,8}} => [2,1,1,1,1,2] => [1,6,1] => 8
{{1,5},{2},{3},{4},{6,7,8}} => [2,1,1,1,3] => [1,1,5,1] => 10
{{1,6},{2},{3},{4},{5},{7},{8}} => [2,1,1,1,1,1,1] => [7,1] => 7
{{1,6},{2},{3},{4},{5},{7,8}} => [2,1,1,1,1,2] => [1,6,1] => 8
{{1,7},{2},{3},{4},{5},{6},{8}} => [2,1,1,1,1,1,1] => [7,1] => 7
{{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => [7,1] => 7
{{1,7,8},{2},{3},{4},{5},{6}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,6,7},{2},{3},{4},{5},{8}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,8},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,2] => [1,6,1] => 8
{{1,6,8},{2},{3},{4},{5},{7}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,6,7,8},{2},{3},{4},{5}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,5,6},{2},{3},{4},{7},{8}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,7},{2},{3},{4},{5,6},{8}} => [2,1,1,1,2,1] => [2,5,1] => 9
{{1,8},{2},{3},{4},{5,6},{7}} => [2,1,1,1,2,1] => [2,5,1] => 9
{{1,5,7},{2},{3},{4},{6},{8}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,8},{2},{3},{4},{5,7},{6}} => [2,1,1,1,2,1] => [2,5,1] => 9
{{1,5,8},{2},{3},{4},{6},{7}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,5,7,8},{2},{3},{4},{6}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,5,6,7},{2},{3},{4},{8}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,8},{2},{3},{4},{5,6,7}} => [2,1,1,1,3] => [1,1,5,1] => 10
{{1,5,6,8},{2},{3},{4},{7}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,5,6,7,8},{2},{3},{4}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,4,5},{2},{3},{6},{7},{8}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,4,5},{2},{3},{6,8},{7}} => [3,1,1,2,1] => [2,4,1,1] => 15
{{1,4,5},{2},{3},{6,7,8}} => [3,1,1,3] => [1,1,4,1,1] => 16
{{1,6},{2},{3},{4,5},{7},{8}} => [2,1,1,2,1,1] => [3,4,1] => 10
{{1,8},{2},{3},{4,5},{6},{7}} => [2,1,1,2,1,1] => [3,4,1] => 10
{{1,6,7},{2},{3},{4,5},{8}} => [3,1,1,2,1] => [2,4,1,1] => 15
{{1,6,7,8},{2},{3},{4,5}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,4,6},{2},{3},{5},{7},{8}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,7},{2},{3},{4,6},{5},{8}} => [2,1,1,2,1,1] => [3,4,1] => 10
{{1,4,6,8},{2},{3},{5},{7}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,4,5,6},{2},{3},{7},{8}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,4,5,6},{2},{3},{7,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,7},{2},{3},{4,5,6},{8}} => [2,1,1,3,1] => [2,1,4,1] => 12
{{1,4,8},{2},{3},{5,6},{7}} => [3,1,1,2,1] => [2,4,1,1] => 15
{{1,4,7,8},{2},{3},{5,6}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,4,5,8},{2},{3},{6},{7}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,4,5,6,7},{2},{3},{8}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,4,8},{2},{3},{5,6,7}} => [3,1,1,3] => [1,1,4,1,1] => 16
{{1,4,5,8},{2},{3},{6,7}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,4,5,6,8},{2},{3},{7}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,4,5,6,7,8},{2},{3}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,3,4},{2},{5},{6},{7},{8}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,3,4},{2},{5},{6},{7,8}} => [3,1,1,1,2] => [1,5,1,1] => 14
{{1,3,4},{2},{5},{6,8},{7}} => [3,1,1,2,1] => [2,4,1,1] => 15
{{1,3,4},{2},{5},{6,7,8}} => [3,1,1,3] => [1,1,4,1,1] => 16
{{1,3,4},{2},{5,6},{7,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3,4},{2},{5,7,8},{6}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3,4},{2},{5,8},{6,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3,4},{2},{5,6,8},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3,4},{2},{5,6,7,8}} => [3,1,4] => [1,1,1,3,1,1] => 19
{{1,5},{2},{3,4},{6},{7},{8}} => [2,1,2,1,1,1] => [4,3,1] => 11
{{1,5},{2},{3,4},{6},{7,8}} => [2,1,2,1,2] => [1,3,3,1] => 12
{{1,5},{2},{3,4},{6,8},{7}} => [2,1,2,2,1] => [2,2,3,1] => 13
{{1,5},{2},{3,4},{6,7,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,8},{2},{3,4},{5},{6},{7}} => [2,1,2,1,1,1] => [4,3,1] => 11
{{1,6,7,8},{2},{3,4},{5}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,5,6},{2},{3,4},{7,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,7,8},{2},{3,4},{5,6}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,5,7},{2},{3,4},{6},{8}} => [3,1,2,1,1] => [3,3,1,1] => 16
{{1,5,7,8},{2},{3,4},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,5,6,7},{2},{3,4},{8}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,8},{2},{3,4},{5,6,7}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,5,8},{2},{3,4},{6,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,5,6,8},{2},{3,4},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,5},{2},{4},{6},{7},{8}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,3,5},{2},{4},{6},{7,8}} => [3,1,1,1,2] => [1,5,1,1] => 14
{{1,3,5},{2},{4},{6,7},{8}} => [3,1,1,2,1] => [2,4,1,1] => 15
{{1,3,5},{2},{4},{6,8},{7}} => [3,1,1,2,1] => [2,4,1,1] => 15
{{1,3,5},{2},{4},{6,7,8}} => [3,1,1,3] => [1,1,4,1,1] => 16
{{1,6},{2},{3,5},{4},{7},{8}} => [2,1,2,1,1,1] => [4,3,1] => 11
{{1,6},{2},{3,5},{4},{7,8}} => [2,1,2,1,2] => [1,3,3,1] => 12
{{1,8},{2},{3,5},{4},{6},{7}} => [2,1,2,1,1,1] => [4,3,1] => 11
{{1,6,8},{2},{3,5},{4},{7}} => [3,1,2,1,1] => [3,3,1,1] => 16
{{1,6,7,8},{2},{3,5},{4}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,6},{2},{4},{5},{7},{8}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,3,7},{2},{4},{5},{6},{8}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,3,8},{2},{4},{5},{6},{7}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,3,7,8},{2},{4},{5},{6}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,3,5,6},{2},{4},{7,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,7},{2},{3,5,6},{4},{8}} => [2,1,3,1,1] => [3,1,3,1] => 14
{{1,7,8},{2},{3,5,6},{4}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3,7},{2},{4},{5,6},{8}} => [3,1,1,2,1] => [2,4,1,1] => 15
{{1,3,7,8},{2},{4},{5,6}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,3,5,7},{2},{4},{6},{8}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,3,5,7,8},{2},{4},{6}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,3,8},{2},{4},{5,6,7}} => [3,1,1,3] => [1,1,4,1,1] => 16
{{1,3,5,8},{2},{4},{6,7}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,3,5,6,8},{2},{4},{7}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,3,5,6,7,8},{2},{4}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,3,4,5},{2},{6},{7},{8}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,3,4,5},{2},{6},{7,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,3,4,5},{2},{6,7},{8}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,4,5},{2},{6,8},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,4,5},{2},{6,7,8}} => [4,1,3] => [1,1,3,1,1,1] => 21
{{1,6},{2},{3,4,5},{7},{8}} => [2,1,3,1,1] => [3,1,3,1] => 14
{{1,6},{2},{3,4,5},{7,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,8},{2},{3,4,5},{6},{7}} => [2,1,3,1,1] => [3,1,3,1] => 14
{{1,7,8},{2},{3,4,5},{6}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,8},{2},{3,4,5},{6,7}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,6,8},{2},{3,4,5},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3,6},{2},{4,5},{7,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,7},{2},{3,6},{4,5},{8}} => [2,1,2,2,1] => [2,2,3,1] => 13
{{1,7,8},{2},{3,6},{4,5}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3,7},{2},{4,5},{6},{8}} => [3,1,2,1,1] => [3,3,1,1] => 16
{{1,3,7,8},{2},{4,5},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,8},{2},{3,6,7},{4,5}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,3,8},{2},{4,5},{6,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3,6,8},{2},{4,5},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,4,6},{2},{5},{7,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,7,8},{2},{3,4,6},{5}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3,7},{2},{4,6},{5},{8}} => [3,1,2,1,1] => [3,3,1,1] => 16
{{1,3,7,8},{2},{4,6},{5}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,4,8},{2},{5},{6},{7}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,3,4,7,8},{2},{5},{6}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,8},{2},{3,4,6,7},{5}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,3,8},{2},{4,6,7},{5}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3,4,6,8},{2},{5},{7}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,3,4,6,7,8},{2},{5}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,3,4,5,6},{2},{7},{8}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,3,4,5,6},{2},{7,8}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,8},{2},{3,4,5,6},{7}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,7,8},{2},{3,4,5,6}} => [3,1,4] => [1,1,1,3,1,1] => 19
{{1,3,7},{2},{4,5,6},{8}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3,8},{2},{4,5,6},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,8},{2},{3,4,7},{5,6}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,3,8},{2},{4,7},{5,6}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3,4,8},{2},{5,6},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,8},{2},{3,4,5,7},{6}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,3,8},{2},{4,5,7},{6}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3,4,8},{2},{5,7},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,4,5,8},{2},{6},{7}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,3,4,5,7,8},{2},{6}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,3,4,5,6,7},{2},{8}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,8},{2},{3,4,5,6,7}} => [2,1,5] => [1,1,1,1,3,1] => 17
{{1,3,4,5,8},{2},{6,7}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,3,4,5,6,8},{2},{7}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,3,4,5,6,7,8},{2}} => [7,1] => [2,1,1,1,1,1,1] => 27
{{1,2,3},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,2,3},{4},{5},{6},{7,8}} => [3,1,1,1,2] => [1,5,1,1] => 14
{{1,2,3},{4},{5},{6,8},{7}} => [3,1,1,2,1] => [2,4,1,1] => 15
{{1,2,3},{4},{5},{6,7,8}} => [3,1,1,3] => [1,1,4,1,1] => 16
{{1,2,3},{4},{5,6},{7,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,2,3},{4},{5,8},{6,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,2,3},{4},{5,6,8},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,2,3},{4,6},{5},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,3},{4,6,7},{5},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,3},{4,8},{5},{6,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,3},{4,6,8},{5},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,3},{4,8},{5,7},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,3},{4,5,8},{6},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,3},{4,5,7,8},{6}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,2,3},{4,5,6,7},{8}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,2,3},{4,8},{5,6,7}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,2,3},{4,5,8},{6,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,3},{4,5,6,8},{7}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,2,3},{4,5,6,7,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,4},{2,3},{5},{6},{7},{8}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,4},{2,3},{5},{6},{7,8}} => [2,2,1,1,2] => [1,4,2,1] => 13
{{1,4},{2,3},{5},{6,7},{8}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1,4},{2,3},{5},{6,8},{7}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1,4},{2,3},{5},{6,7,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,4},{2,3},{5,6},{7},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,4},{2,3},{5,7},{6},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,4},{2,3},{5,8},{6},{7}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,4},{2,3},{5,7,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4},{2,3},{5,6,7},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4},{2,3},{5,6,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4},{2,3},{5,6,7,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,5},{2,3},{4},{6},{7},{8}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,5},{2,3},{4},{6,7},{8}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1,5},{2,3},{4},{6,8},{7}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1,6},{2,3},{4},{5},{7},{8}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,6},{2,3},{4},{5},{7,8}} => [2,2,1,1,2] => [1,4,2,1] => 13
{{1,7},{2,3},{4},{5},{6},{8}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,8},{2,3},{4},{5},{6},{7}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,6,8},{2,3},{4},{5},{7}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,5,6},{2,3},{4},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,7},{2,3},{4},{5,6},{8}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1,7,8},{2,3},{4},{5,6}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5,7},{2,3},{4},{6},{8}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,5,7,8},{2,3},{4},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,5,6,7},{2,3},{4},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,8},{2,3},{4},{5,6,7}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,5,8},{2,3},{4},{6,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5,6,8},{2,3},{4},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,5,6,7,8},{2,3},{4}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,4,5},{2,3},{6},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,4,5},{2,3},{6,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,5},{2,3},{6,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,7},{2,3},{4,5},{6},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,8},{2,3},{4,5},{6},{7}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,7,8},{2,3},{4,5},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6,7},{2,3},{4,5},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6,8},{2,3},{4,5},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6,7,8},{2,3},{4,5}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,4,6},{2,3},{5},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,7},{2,3},{4,6},{5},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,7,8},{2,3},{4,6},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,8},{2,3},{5},{6},{7}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,4,7,8},{2,3},{5},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,6,7},{2,3},{5},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,8},{2,3},{4,6,7},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4,8},{2,3},{5},{6,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,4,6,8},{2,3},{5},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,6,7,8},{2,3},{5}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,4,5,6},{2,3},{7,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,7},{2,3},{4,5,6},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4,7},{2,3},{5,6},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,8},{2,3},{5,6},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,5,7},{2,3},{6},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,8},{2,3},{4,5,7},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4,8},{2,3},{5,7},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,5,8},{2,3},{6},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,5,7,8},{2,3},{6}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,4,5,6,7},{2,3},{8}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,4,8},{2,3},{5,6,7}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,4,5,8},{2,3},{6,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,4,5,6,8},{2,3},{7}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,4,5,6,7,8},{2,3}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,4},{3},{5},{6},{7},{8}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,2,4},{3},{5,6},{7,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,2,4},{3},{5,7,8},{6}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,2,4},{3},{5,6,7},{8}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,2,4},{3},{5,8},{6,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,2,4},{3},{5,6,8},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,2,4},{3},{5,6,7,8}} => [3,1,4] => [1,1,1,3,1,1] => 19
{{1,5},{2,4},{3},{6},{7},{8}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,5},{2,4},{3},{6},{7,8}} => [2,2,1,1,2] => [1,4,2,1] => 13
{{1,5},{2,4},{3},{6,7},{8}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1,5},{2,4},{3},{6,8},{7}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1,5},{2,4},{3},{6,7,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,7},{2,4},{3},{5},{6},{8}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,8},{2,4},{3},{5},{6,7}} => [2,2,1,1,2] => [1,4,2,1] => 13
{{1,6,7,8},{2,4},{3},{5}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,5,6},{2,4},{3},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,7},{2,4},{3},{5,6},{8}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1,7,8},{2,4},{3},{5,6}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5,7},{2,4},{3},{6},{8}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,8},{2,4},{3},{5,7},{6}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1,5,7,8},{2,4},{3},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,5,6,7},{2,4},{3},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,8},{2,4},{3},{5,6,7}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,5,8},{2,4},{3},{6,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5,6,8},{2,4},{3},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,5,6,7,8},{2,4},{3}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,5},{3},{4},{6},{7},{8}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,2,5},{3},{4},{6},{7,8}} => [3,1,1,1,2] => [1,5,1,1] => 14
{{1,6},{2,5},{3},{4},{7},{8}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,6},{2,5},{3},{4},{7,8}} => [2,2,1,1,2] => [1,4,2,1] => 13
{{1,7},{2,5},{3},{4},{6},{8}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,8},{2,5},{3},{4},{6},{7}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,7,8},{2,5},{3},{4},{6}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,6,7,8},{2,5},{3},{4}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,6},{3},{4},{5},{7},{8}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,2,6},{3},{4},{5},{7,8}} => [3,1,1,1,2] => [1,5,1,1] => 14
{{1,7,8},{2,6},{3},{4},{5}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,2,7},{3},{4},{5},{6},{8}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => [6,1,1] => 13
{{1,2,7,8},{3},{4},{5},{6}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,2,6,7,8},{3},{4},{5}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,2,5,6},{3},{4},{7,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,7,8},{2,5,6},{3},{4}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,7,8},{3},{4},{5,6}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,2,5,7,8},{3},{4},{6}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,2,5,6,7},{3},{4},{8}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,8},{2,5,6,7},{3},{4}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2,5,8},{3},{4},{6,7}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,2,5,6,8},{3},{4},{7}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,2,5,6,7,8},{3},{4}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,6},{2,4,5},{3},{7,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,7},{2,4,5},{3},{6},{8}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,7,8},{2,4,5},{3},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,6,7},{2,4,5},{3},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,8},{2,4,5},{3},{6,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,6,8},{2,4,5},{3},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,6},{3},{4,5},{7,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,7},{2,6},{3},{4,5},{8}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1,7,8},{2,6},{3},{4,5}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,7,8},{3},{4,5},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,8},{2,6,7},{3},{4,5}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,2,8},{3},{4,5},{6,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,2,6,8},{3},{4,5},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,2,4,6},{3},{5},{7,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,7},{2,4,6},{3},{5},{8}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,7,8},{2,4,6},{3},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,7,8},{3},{4,6},{5}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,8},{2,4,7},{3},{5},{6}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,2,4,8},{3},{5},{6},{7}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,2,4,7,8},{3},{5},{6}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,8},{2,4,6,7},{3},{5}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2,8},{3},{4,6,7},{5}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,2,4,8},{3},{5},{6,7}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,2,4,6,8},{3},{5},{7}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,2,4,6,7,8},{3},{5}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,2,4,5,6},{3},{7,8}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,7},{2,4,5,6},{3},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,8},{2,4,5,6},{3},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,7,8},{2,4,5,6},{3}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,8},{2,7},{3},{4,5,6}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,2,8},{3},{4,5,6},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,2,7,8},{3},{4,5,6}} => [4,1,3] => [1,1,3,1,1,1] => 21
{{1,2,4,7},{3},{5,6},{8}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,8},{2,4,7},{3},{5,6}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,2,8},{3},{4,7},{5,6}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,2,4,8},{3},{5,6},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,2,4,7,8},{3},{5,6}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,8},{2,4,5,7},{3},{6}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2,8},{3},{4,5,7},{6}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,2,4,8},{3},{5,7},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,2,4,5,7,8},{3},{6}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,2,4,5,6,7},{3},{8}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,8},{2,4,5,6,7},{3}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,2,8},{3},{4,5,6,7}} => [3,1,4] => [1,1,1,3,1,1] => 19
{{1,2,4,5,8},{3},{6,7}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,2,4,5,6,8},{3},{7}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,2,4,5,6,7,8},{3}} => [7,1] => [2,1,1,1,1,1,1] => 27
{{1,2,3,4},{5},{6},{7},{8}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,2,3,4},{5},{6,7},{8}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,2,3,4},{5},{6,8},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,2,3,4},{5,6},{7,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,3,4},{5,7,8},{6}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,3,4},{5,6,7},{8}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,3,4},{5,8},{6,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,3,4},{5,6,8},{7}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,3,4},{5,6,7,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,5},{2,3,4},{6},{7},{8}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,5},{2,3,4},{6,8},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5},{2,3,4},{6,7,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,6},{2,3,4},{5},{7},{8}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,6},{2,3,4},{5},{7,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,7},{2,3,4},{5},{6},{8}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,8},{2,3,4},{5},{6},{7}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,8},{2,3,4},{5},{6,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,6,8},{2,3,4},{5},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,5,6},{2,3,4},{7},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,7},{2,3,4},{5,6},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,8},{2,3,4},{5,6},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5,7},{2,3,4},{6},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,8},{2,3,4},{5,7},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5,8},{2,3,4},{6},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,5,6,7},{2,3,4},{8}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,5,8},{2,3,4},{6,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,5,6,8},{2,3,4},{7}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,5,6,7,8},{2,3,4}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,5},{3,4},{6},{7},{8}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,2,5},{3,4},{6},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,5},{3,4},{6,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,5},{3,4},{6,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,5},{3,4},{6,7,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,7},{2,5},{3,4},{6},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,7,8},{2,5},{3,4},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6,7},{2,5},{3,4},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6,8},{2,5},{3,4},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6,7,8},{2,5},{3,4}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,6},{3,4},{5},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,7},{2,6},{3,4},{5},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,8},{2,6},{3,4},{5},{7}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,7,8},{2,6},{3,4},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,8},{2,7},{3,4},{5},{6}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,2,8},{3,4},{5},{6},{7}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,2,7,8},{3,4},{5},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,8},{2,6,7},{3,4},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2,8},{3,4},{5},{6,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,6,8},{3,4},{5},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,5,6},{3,4},{7},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,8},{2,5,6},{3,4},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7,8},{2,5,6},{3,4}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,7},{3,4},{5,6},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,8},{3,4},{5,6},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,5,7},{3,4},{6},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,8},{2,5,7},{3,4},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2,8},{3,4},{5,7},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,5,8},{3,4},{6},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,5,6,8},{3,4},{7}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,5,6,7,8},{3,4}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,3,5},{4},{6},{7,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,2,3,5},{4},{6,8},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,2,3,5},{4},{6,7,8}} => [4,1,3] => [1,1,3,1,1,1] => 21
{{1,6},{2,3,5},{4},{7,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,8},{2,3,5},{4},{6},{7}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,7,8},{2,3,5},{4},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,6,7},{2,3,5},{4},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,8},{2,3,5},{4},{6,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,6,8},{2,3,5},{4},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,6,7,8},{2,3,5},{4}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,6},{3,5},{4},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,7},{2,6},{3,5},{4},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,7,8},{2,6},{3,5},{4}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,7,8},{3,5},{4},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,8},{2,6,7},{3,5},{4}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2,8},{3,5},{4},{6,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,6,8},{3,5},{4},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,6,7,8},{3,5},{4}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,3,6},{4},{5},{7,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,8},{2,3,6},{4},{5},{7}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,7,8},{2,3,6},{4},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,7,8},{3,6},{4},{5}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,8},{2,3,7},{4},{5},{6}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,2,3,8},{4},{5},{6},{7}} => [4,1,1,1,1] => [5,1,1,1] => 18
{{1,2,3,7,8},{4},{5},{6}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,8},{2,3,6,7},{4},{5}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2,8},{3,6,7},{4},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,3,8},{4},{5},{6,7}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,2,3,6,8},{4},{5},{7}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,2,3,6,7,8},{4},{5}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,2,3,5,6},{4},{7},{8}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,2,3,5,6},{4},{7,8}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,7},{2,3,5,6},{4},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,8},{2,3,5,6},{4},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2,7},{3,5,6},{4},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,8},{2,7},{3,5,6},{4}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,2,8},{3,5,6},{4},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,3,7},{4},{5,6},{8}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,8},{2,3,7},{4},{5,6}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,2,8},{3,7},{4},{5,6}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,3,8},{4},{5,6},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,2,3,7,8},{4},{5,6}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,2,3,5,7},{4},{6},{8}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,8},{2,3,5,7},{4},{6}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2,8},{3,5,7},{4},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,3,8},{4},{5,7},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,2,3,5,8},{4},{6},{7}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,2,3,5,7,8},{4},{6}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,2,3,5,6,7},{4},{8}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,8},{2,3,5,6,7},{4}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,2,3,8},{4},{5,6,7}} => [4,1,3] => [1,1,3,1,1,1] => 21
{{1,2,3,5,6,8},{4},{7}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,2,3,5,6,7,8},{4}} => [7,1] => [2,1,1,1,1,1,1] => 27
{{1,2,3,4,5},{6},{7},{8}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,2,3,4,5},{6,7},{8}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,3,4,5},{6,8},{7}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,3,4,5},{6,7,8}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,6},{2,3,4,5},{7},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,7},{2,3,4,5},{6},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,6,8},{2,3,4,5},{7}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,6,7,8},{2,3,4,5}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,2,6},{3,4,5},{7},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,6},{3,4,5},{7,8}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,7},{2,6},{3,4,5},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,8},{2,6},{3,4,5},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,7,8},{2,6},{3,4,5}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,8},{2,7},{3,4,5},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,2,8},{3,4,5},{6,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,6,7,8},{3,4,5}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,3,6},{4,5},{7},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,3,6},{4,5},{7,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,8},{2,3,6},{4,5},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7,8},{2,3,6},{4,5}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,7},{3,6},{4,5},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,8},{3,6},{4,5},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,3,7},{4,5},{6},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,8},{2,3,7},{4,5},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2,8},{3,7},{4,5},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,3,8},{4,5},{6},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,3,6,7},{4,5},{8}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,8},{2,3,6,7},{4,5}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,2,3,8},{4,5},{6,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,3,6,8},{4,5},{7}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,3,6,7,8},{4,5}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,3,4,6},{5},{7},{8}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,2,3,4,6},{5},{7,8}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,8},{2,3,4,6},{5},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,7,8},{2,3,4,6},{5}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,2,7},{3,4,6},{5},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,8},{2,7},{3,4,6},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,2,8},{3,4,6},{5},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,7,8},{3,4,6},{5}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,3,7},{4,6},{5},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,8},{2,3,7},{4,6},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2,8},{3,7},{4,6},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,3,8},{4,6},{5},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,3,7,8},{4,6},{5}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,3,4,7},{5},{6},{8}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,8},{2,3,4,7},{5},{6}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2,8},{3,4,7},{5},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,3,8},{4,7},{5},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,3,4,8},{5},{6},{7}} => [5,1,1,1] => [4,1,1,1,1] => 22
{{1,2,3,4,7,8},{5},{6}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,2,3,4,6,7},{5},{8}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,8},{2,3,4,6,7},{5}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,2,8},{3,4,6,7},{5}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,2,3,4,8},{5},{6,7}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,2,3,4,6,8},{5},{7}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,2,3,4,6,7,8},{5}} => [7,1] => [2,1,1,1,1,1,1] => 27
{{1,2,3,4,5,6},{7},{8}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,2,3,4,5,6},{7,8}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,7},{2,3,4,5,6},{8}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,8},{2,3,4,5,6},{7}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,7,8},{2,3,4,5,6}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,2,7},{3,4,5,6},{8}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,2,7,8},{3,4,5,6}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,2,3,7},{4,5,6},{8}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,8},{2,3,7},{4,5,6}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,2,8},{3,7},{4,5,6}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,2,3,8},{4,5,6},{7}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,3,7,8},{4,5,6}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,3,4,7},{5,6},{8}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,8},{2,3,4,7},{5,6}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,2,8},{3,4,7},{5,6}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,3,8},{4,7},{5,6}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,3,4,8},{5,6},{7}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,3,4,7,8},{5,6}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,3,4,5,7},{6},{8}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,8},{2,3,4,5,7},{6}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,2,8},{3,4,5,7},{6}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,2,3,8},{4,5,7},{6}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,3,4,8},{5,7},{6}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,3,4,5,8},{6},{7}} => [6,1,1] => [3,1,1,1,1,1] => 25
{{1,2,3,4,5,7,8},{6}} => [7,1] => [2,1,1,1,1,1,1] => 27
{{1,2,3,4,5,6,7},{8}} => [7,1] => [2,1,1,1,1,1,1] => 27
{{1,8},{2,3,4,5,6,7}} => [2,6] => [1,1,1,1,1,2,1] => 22
{{1,2,8},{3,4,5,6,7}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,2,3,8},{4,5,6,7}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,2,3,4,8},{5,6,7}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,3,4,5,8},{6,7}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,3,4,5,6,8},{7}} => [7,1] => [2,1,1,1,1,1,1] => 27
{{1,2,3,4,5,6,7,8}} => [8] => [1,1,1,1,1,1,1,1] => 28
{{1,3,5,6,7,8},{2,4}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,3,4,6,7,8},{2,5}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,4,6,7,8},{3,5}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,3,4,5,7,8},{2,6}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,4,5,7,8},{3,6}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,3,5,7,8},{4,6}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,3,4,5,6,8},{2,7}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,4,5,6,8},{3,7}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,3,5,6,8},{4,7}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,3,4,6,8},{5,7}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,3,4,5,6,7},{2,8}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,4,5,6,7},{3,8}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,3,5,6,7},{4,8}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,3,4,6,7},{5,8}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,2,3,4,5,7},{6,8}} => [6,2] => [1,2,1,1,1,1,1] => 26
{{1,3,5,7,8},{2,4,6}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,5,7,8},{3,4,6}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,3,4,7,8},{2,5,6}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,4,7,8},{3,5,6}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,3,5,6,8},{2,4,7}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,5,6,8},{3,4,7}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,3,4,6,8},{2,5,7}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,4,6,8},{3,5,7}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,3,6,8},{4,5,7}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,4,5,8},{3,6,7}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,3,5,8},{4,6,7}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,3,5,6,7},{2,4,8}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,5,6,7},{3,4,8}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,3,4,6,7},{2,5,8}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,4,6,7},{3,5,8}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,3,6,7},{4,5,8}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,3,4,5,7},{2,6,8}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,4,5,7},{3,6,8}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,3,5,7},{4,6,8}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,3,4,7},{5,6,8}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,4,5,6},{3,7,8}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,3,5,6},{4,7,8}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,3,4,6},{5,7,8}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,4,6,7,8},{2,5},{3}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,6,7,8},{2,5},{4}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,6,7,8},{2,4},{5}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,5,7,8},{3,6},{4}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,4,7,8},{2,6},{5}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,4,7,8},{3,6},{5}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,4,7,8},{2,5},{6}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,5,6,8},{2,7},{4}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,5,6,8},{3,7},{4}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,4,6,8},{2,7},{5}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,4,6,8},{3,7},{5}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,4,5,8},{2,7},{6}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,5,6,8},{2,4},{7}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,4,6,8},{2,5},{7}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,4,5,8},{3,6},{7}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,4,6,7},{2,8},{5}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,4,6,7},{3,8},{5}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,4,5,7},{2,8},{6}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,4,5,7},{3,8},{6}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,3,5,7},{4,8},{6}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,4,5,6},{2,8},{7}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,3,5,6},{4,8},{7}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,3,4,6},{5,8},{7}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,5,6,7},{2,4},{8}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,4,6,7},{2,5},{8}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,4,6,7},{3,5},{8}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,4,5,7},{3,6},{8}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,3,5,7},{4,6},{8}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,3,5,6},{4,7},{8}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,2,3,4,6},{5,7},{8}} => [5,2,1] => [2,2,1,1,1,1] => 24
{{1,3,5,7},{2,4,6,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,2,5,7},{3,4,6,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,3,4,7},{2,5,6,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,2,4,7},{3,5,6,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,2,3,7},{4,5,6,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,3,5,6},{2,4,7,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,2,5,6},{3,4,7,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,3,4,6},{2,5,7,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,2,4,6},{3,5,7,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,2,3,6},{4,5,7,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,3,4,5},{2,6,7,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,2,4,5},{3,6,7,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,2,3,5},{4,6,7,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,3,6,8},{2,5,7},{4}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,6,8},{3,5,7},{4}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,5,8},{3,6,7},{4}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,5,8},{3,4,7},{6}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,3,4,8},{2,5,7},{6}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,5,8},{3,4,6},{7}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,4,8},{3,5,6},{7}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,6,7},{3,5,8},{4}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,3,6,7},{2,4,8},{5}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,4,5,7},{2,6,8},{3}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,3,5,7},{2,6,8},{4}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,3,4,7},{2,6,8},{5}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,4,7},{3,6,8},{5}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,3,5,7},{2,4,8},{6}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,5,7},{3,4,8},{6}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,4,7},{3,5,8},{6}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,3,4,5},{2,7,8},{6}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,4,5},{3,7,8},{6}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,3,5,6},{2,4,8},{7}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,3,6},{4,5,8},{7}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,4,5},{3,6,8},{7}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,3,5,7},{2,4,6},{8}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,3,4,6},{2,5,7},{8}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,3,5},{4,6,7},{8}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,4,7,8},{2,5},{3,6}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,7,8},{3,5},{4,6}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,6,8},{3,5},{4,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,3,6,8},{2,4},{5,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,4,5,8},{2,6},{3,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,3,5,8},{2,6},{4,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,5,8},{3,6},{4,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,3,4,8},{2,6},{5,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,3,5,8},{2,4},{6,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,4,8},{3,5},{6,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,3,6,7},{2,4},{5,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,6,7},{3,4},{5,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,4,5,7},{2,6},{3,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,3,5,7},{2,6},{4,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,3,4,7},{2,6},{5,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,3,7},{4,6},{5,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,5,7},{3,4},{6,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,3,4,7},{2,5},{6,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,5,6},{3,7},{4,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,3,4,6},{2,7},{5,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,4,6},{3,7},{5,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,3,6},{4,7},{5,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,4,5},{3,7},{6,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,3,5},{4,7},{6,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,3,4},{5,7},{6,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,3,5,6},{2,4},{7,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,3,4,6},{2,5},{7,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,4,6},{3,5},{7,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,4,5},{3,6},{7,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,3,5},{4,6},{7,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,5,7,8},{2,6},{3},{4}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,7,8},{2,6},{3},{5}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,7,8},{2,6},{4},{5}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,7,8},{2,5},{3},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,7,8},{2,5},{4},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,7,8},{2,4},{5},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,5,6,8},{2,7},{3},{4}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,6,8},{2,7},{3},{5}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,6,8},{2,7},{4},{5}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,6,8},{3,7},{4},{5}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,5,8},{2,7},{3},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,5,8},{2,7},{4},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,5,8},{3,7},{4},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,4,8},{2,7},{5},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,4,8},{3,7},{5},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,6,8},{2,5},{3},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,6,8},{2,5},{4},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,6,8},{2,4},{5},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,5,8},{2,6},{3},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,5,8},{2,6},{4},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,5,8},{3,6},{4},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,4,8},{2,6},{5},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,4,8},{3,6},{5},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,4,8},{2,5},{6},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,4,8},{3,5},{6},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,5,6,7},{2,8},{3},{4}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,6,7},{2,8},{3},{5}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,6,7},{2,8},{4},{5}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,6,7},{3,8},{4},{5}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,5,7},{2,8},{3},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,5,7},{2,8},{4},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,5,7},{3,8},{4},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,4,7},{2,8},{5},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,4,7},{3,8},{5},{6}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,5,6},{2,8},{3},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,5,6},{2,8},{4},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,5,6},{3,8},{4},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,4,6},{2,8},{5},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,4,6},{3,8},{5},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,3,6},{4,8},{5},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,4,5},{2,8},{6},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,4,5},{3,8},{6},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,3,5},{4,8},{6},{7}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,6,7},{2,5},{3},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,6,7},{2,5},{4},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,5,7},{2,6},{3},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,5,7},{2,6},{4},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,5,7},{3,6},{4},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,4,7},{2,6},{5},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,4,7},{3,6},{5},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,5,7},{2,4},{6},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,4,7},{2,5},{6},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,4,7},{3,5},{6},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,5,6},{2,7},{3},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,4,6},{2,7},{5},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,4,6},{3,7},{5},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,3,6},{4,7},{5},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,4,5},{2,7},{6},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,4,5},{3,7},{6},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,3,5},{4,7},{6},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,5,6},{2,4},{7},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,4,6},{3,5},{7},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,3,4,5},{2,6},{7},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,4,5},{3,6},{7},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,2,3,5},{4,6},{7},{8}} => [4,2,1,1] => [3,2,1,1,1] => 21
{{1,4,7},{2,5,8},{3,6}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,3,7},{2,4,8},{5,6}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,4,6},{2,5,8},{3,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,3,6},{2,5,8},{4,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,6},{3,4,8},{5,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,4,5},{2,6,8},{3,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,3,5},{2,6,8},{4,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,5},{3,6,8},{4,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,3,4},{2,6,8},{5,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,3,5},{2,4,8},{6,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,5},{3,4,8},{6,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,3,4},{2,5,8},{6,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,4},{3,5,8},{6,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,4,6},{2,5,7},{3,8}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,3,6},{2,5,7},{4,8}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,4},{3,5,7},{6,8}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,5},{3,4,6},{7,8}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,3,4},{2,5,6},{7,8}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,4},{3,5,6},{7,8}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,5,7},{2,6,8},{3},{4}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,7},{2,6,8},{3},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,7},{2,6,8},{4},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,7},{3,6,8},{4},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,7},{2,5,8},{3},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,7},{2,5,8},{4},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,7},{3,5,8},{4},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,7},{2,4,8},{5},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,7},{3,4,8},{5},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,5,6},{2,7,8},{3},{4}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,6},{2,7,8},{3},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,6},{2,7,8},{4},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,6},{3,7,8},{4},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,5},{2,7,8},{3},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,5},{2,7,8},{4},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,5},{3,7,8},{4},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,4},{2,7,8},{5},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,4},{3,7,8},{5},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,6},{2,5,8},{3},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,6},{2,5,8},{4},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,6},{3,5,8},{4},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,6},{2,4,8},{5},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,6},{3,4,8},{5},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,5},{2,6,8},{3},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,5},{2,6,8},{4},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,5},{3,6,8},{4},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,4},{2,6,8},{5},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,4},{3,6,8},{5},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,5},{2,4,8},{6},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,5},{3,4,8},{6},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,4},{2,5,8},{6},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,4},{3,5,8},{6},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,6},{2,5,7},{3},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,6},{2,5,7},{4},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,6},{3,5,7},{4},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,6},{2,4,7},{5},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,5},{2,6,7},{4},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,5},{3,6,7},{4},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,4},{2,6,7},{5},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,5},{2,4,7},{6},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,5},{3,4,7},{6},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,4},{2,5,7},{6},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,4},{3,5,7},{6},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,5},{2,4,6},{7},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,5},{3,4,6},{7},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,5,8},{2,6},{3,7},{4}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,8},{2,6},{3,7},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,8},{2,6},{4,7},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,8},{3,6},{4,7},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,8},{2,5},{3,7},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,8},{2,5},{4,7},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,8},{3,5},{4,7},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,8},{2,4},{5,7},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,8},{2,5},{3,6},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,8},{2,5},{4,6},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,8},{3,5},{4,6},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,8},{2,4},{5,6},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,5,7},{2,6},{3,8},{4}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,7},{2,6},{3,8},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,7},{2,6},{4,8},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,7},{3,6},{4,8},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,7},{2,5},{3,8},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,7},{2,5},{4,8},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,7},{3,5},{4,8},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,7},{2,4},{5,8},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,7},{3,4},{5,8},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,5,6},{2,7},{3,8},{4}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,6},{2,7},{3,8},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,6},{2,7},{4,8},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,6},{3,7},{4,8},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,5},{2,7},{3,8},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,5},{2,7},{4,8},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,5},{3,7},{4,8},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,4},{2,7},{5,8},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,4},{3,7},{5,8},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,3},{4,7},{5,8},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,6},{2,5},{3,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,6},{2,5},{4,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,6},{3,5},{4,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,6},{2,4},{5,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,6},{3,4},{5,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,5},{2,6},{3,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,5},{2,6},{4,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,5},{3,6},{4,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,4},{2,6},{5,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,4},{3,6},{5,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,3},{4,6},{5,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,5},{2,4},{6,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,4},{2,5},{6,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,7},{2,5},{3,6},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,7},{2,5},{4,6},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,7},{3,5},{4,6},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,7},{2,4},{5,6},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,6},{3,5},{4,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,6},{2,4},{5,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,6},{3,4},{5,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,5},{2,6},{3,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,5},{2,6},{4,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,5},{3,6},{4,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,4},{2,6},{5,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,4},{3,6},{5,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,3},{4,6},{5,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,4},{2,5},{6,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,8},{2,4},{5},{6},{7}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,6,7},{2,8},{3},{4},{5}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,3,4},{2,8},{5},{6},{7}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,4,7},{2,6},{3},{5},{8}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,4,7},{2,5},{3},{6},{8}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,3,7},{2,4},{5},{6},{8}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,4,6},{2,7},{3},{5},{8}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,3,5},{2,4},{6},{7},{8}} => [3,2,1,1,1] => [4,2,1,1] => 17
{{1,5},{2,6},{3,7},{4},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,3},{2,6},{4,7},{5},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,3},{2,5},{4,7},{6},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,4},{2,5},{3,6},{7},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,3},{2,5},{4,6},{7},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,4},{2,8},{3},{5},{6},{7}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,3},{2,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,5},{2,6},{3},{4},{7},{8}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,4},{2,5},{3},{6},{7},{8}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,3},{2,4},{5},{6},{7},{8}} => [2,2,1,1,1,1] => [5,2,1] => 12
{{1,3,5,8},{2},{4,6},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,5,7},{2},{4},{6,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,5,7},{2,4},{3},{6,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5},{2,4,8},{3},{6,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,5,8},{2,4},{3,6},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6,8},{2,4},{3,5},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1},{2,3,5,8},{4,6},{7}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1,5,8},{2,6},{3,4},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,8},{2,6},{3,5},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4},{2,5,8},{3},{6,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,4,7},{2,5},{3},{6,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,4},{2},{3,6,7},{5,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,4},{2},{3,6},{5,7,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,4},{2},{3,7},{5,6,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,4},{2},{3,5,8},{6,7}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,5},{2},{3,4,8},{6,7}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,2,5},{3},{4,7,8},{6}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,2,5,7},{3},{4,8},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1},{2,3,5,7},{4},{6,8}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1,5,7},{2},{3,4},{6,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,4,7},{2},{3,5},{6,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,4},{2},{3,8},{5,6,7}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,4,6},{2},{3,8},{5,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,4,6},{2},{3,7},{5,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1},{2,6},{3,4,7},{5,8}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,6},{2,3,7},{4},{5,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,2},{3,6,7},{4,8},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2},{3,6},{4,7,8},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6},{2,3},{4},{5,7,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1},{2,6},{3,4},{5,7,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1},{2,7},{3,4},{5,6,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1,7},{2,3},{4},{5,6,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,2},{3,7},{4,6,8},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,2},{3,5,8},{4,7},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7},{2,3,8},{4,5},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1},{2,5},{3,4,8},{6,7}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,4},{3,5,8},{6,7}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,4},{3,7},{5,6,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1},{2,4},{3,6},{5,7,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1},{2,4},{3,6,7},{5,8}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,3},{2,6,7},{4},{5,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,3},{2,6},{4},{5,7,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,3},{2,7},{4},{5,6,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,3},{2,7,8},{4,5},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3,8},{2,4,7},{5},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,8},{2,3,7},{5},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,7},{2,3,8},{5},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,7},{2,8},{4,5},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3},{2,8},{4},{5,6,7}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,3,6},{2,8},{4},{5,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,3,6},{2,7},{4},{5,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1},{2,4,6},{3,7},{5,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,4,6},{3,8},{5,7}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,4},{3,8},{5,6,7}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1},{2,4,7},{3,5},{6,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,5,7},{3,4},{6,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,8},{3,4,6},{5,7}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,8},{2,3,6},{4},{5,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,2,6},{3,8},{4,7},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,7},{2,3,6},{4},{5,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1},{2,7},{3,4,6},{5,8}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,2},{3,6,8},{4,7},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2},{3,5,7},{4,8},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2},{3,7},{4,5,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4,8},{2,7},{3},{5,6}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,3,7},{2,8},{4},{5,6}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,3,7},{2,8},{4,6},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,7},{2},{4,5,8},{6}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,7},{2,3},{4,5,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,7},{2,3,8},{4,6},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7},{2,3,8},{4},{5,6}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,7,8},{2,5},{3,6},{4}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,7},{2,4,6,8},{3},{5}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,7},{2,4,5},{3,8},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4,6},{2,5},{3},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5,7,8},{2},{3,6},{4}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,5,8},{2,7},{3,6},{4}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,8},{2,5,7},{3,6},{4}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5,8},{2,6,7},{3},{4}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,5,7},{2},{3,8},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,5},{2,6},{4},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,3,6},{2,8},{4,7},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,6,8},{2},{3,7},{5}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,8},{2,4,6},{3,7},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4,8},{2,5},{3},{6,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,3,5},{2,8},{4},{6,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5},{2,3,8},{4},{6,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,8},{2,6},{3,4,7},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6,8},{2},{3,4,7},{5}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,6,8},{2,4},{3,7},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6},{2,3,8},{4,7},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,6},{2,3,7,8},{4},{5}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,5},{2,3,7},{4,8},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5},{2,3,6},{4},{7,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,5,7},{2,4},{3,8},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6,7},{2,4,8},{3},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,6,8},{2,5,7},{3},{4}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,6,8},{2,7},{3,5},{4}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6,8},{2,7},{3},{4,5}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,6,7},{2,8},{3,4},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,5,7},{2},{3,4,8},{6}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,7},{2,5},{3,4,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,7},{2,6,8},{3,4},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4,8},{2,3,6},{5},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,5},{2,4,8},{3,7},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5},{2,4,7},{3,8},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5},{2,4,8},{3,6},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,6},{2,4,8},{3,5},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,6},{2,5},{3,4,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6},{2,3,5},{4,8},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5},{2,3,6},{4,8},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5},{2,6},{3,4,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4,8},{2,7},{3,6},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,7},{2,8},{3,6},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,6},{2,8},{3,7},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,7},{2,8},{3,5},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,5},{2,8},{3,4,7},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,5},{2,3,8},{4,7},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2,5},{3,8},{4,7},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,5},{2,7},{3,4,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4,8},{2,7},{3,5},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,7},{2,6},{3,4,8},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,7},{2,3,6},{4,8},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,8},{2,3,6},{4,7},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,8},{2,3,5},{4,7},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,8},{2,5},{3,4,7},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,8},{2,4,7},{3,5},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,8},{2,4,7},{3,6},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7},{2,4,8},{3,6},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3,5},{2,8},{4,7},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,8},{2,7},{4,6},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6},{2,4,8},{3,7},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,6},{2,4,7},{3,8},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7},{2,4,6},{3,8},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7},{2,4,8},{3,5},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7},{2,3,5},{4,8},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2,7},{3,8},{4,6},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,7},{2,8},{3,4,6},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6},{2,8},{3,4,7},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6},{2,3,7},{4,8},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,6},{2,7},{3,4,8},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,3,5},{2},{4,6,8},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3},{2,4,6,8},{5},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1},{2,4,6,8},{3},{5,7}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1,3},{2},{4,6,8},{5,7}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,3,6},{2},{4,8},{5,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3,6},{2},{4,7},{5,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3,5},{2},{4,7},{6,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3,5,7},{2},{4,6},{8}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,7},{2},{4,6,8},{5}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3,7},{2},{4,6},{5,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3,5,7},{2},{4,8},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3},{2,4,8},{5,7},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1},{2,4,8},{3,5,7},{6}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,4},{2,8},{3,5,7},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4},{2,5,7},{3,8},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,5,7},{4,8},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,7},{4,6,8},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,3,7},{2,4,6},{5},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,7},{2,4,6},{3},{5,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,5,7},{2,4,8},{3},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1},{2,8},{3,5,7},{4,6}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,7},{2,4,6},{3,5},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4,7},{2,6},{3,5},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1},{2,5,8},{3,7},{4,6}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,5,8},{3,6},{4,7}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,4,8},{3,6},{5,7}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,4,6,8},{3,5},{7}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1,4},{2,6,8},{3,5},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4},{2,5},{3,6,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,3},{2,5},{4,6,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,5},{2,4,6,8},{3},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,5},{2,4},{3,6,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1},{2,6,8},{3,5,7},{4}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,6},{2,8},{3,5,7},{4}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6},{2,4,8},{3},{5,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,6},{2,4,7},{3},{5,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,5},{2,4,7},{3},{6,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,5,7},{2,4,6},{3},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,5,7},{2,4},{3,6},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1},{2,6,8},{3,5},{4,7}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,4,6,8},{3,7},{5}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1,6},{2,7},{3,5,8},{4}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,3,5},{2,7},{4},{6,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,7},{2,6,8},{3,5},{4}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7},{2,6},{3,5,8},{4}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,2},{3,4,6},{5,8},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2},{3,6},{4,5,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,2},{3,5,6},{4,8},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2,5,6},{3},{4,8},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,2,6},{3},{4,5,8},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,6},{2,3},{4,5,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,5,6},{2,3},{4,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,5,6},{2,3,8},{4},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,5,6},{2,8},{3,4},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,5},{2,8},{3,4,6},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,5},{2,3,8},{4,6},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,6},{2,3,5,8},{4},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2,5},{3,8},{4,6},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,4},{3,6},{5},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,4,6},{3},{5,8},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,2,4},{3,8},{5,7},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,4},{3,8},{5},{6,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,4},{2,3,8},{5},{6,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,3,4},{2,8},{5},{6,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,3,4},{2,8},{5,7},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4},{2,3,8},{5,7},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4,6},{2,3},{5,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4},{2,3,6},{5},{7,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,4},{2,3,6,8},{5},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,4},{2,3,6},{5,8},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,8},{2,4,5},{3,7},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3,8},{2,6},{4,5},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,4},{2,6},{5},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,6},{2,5,8},{3,4},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,6},{2,4,5},{3,8},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4,5},{2,8},{3,6},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,8},{2,5,6},{4},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3,8},{2,5},{4},{6,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5},{2,4},{3,7,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,5,6},{2,4},{3,8},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4},{2,8},{3,5,6},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4},{2,7,8},{3,5},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4,7},{2,8},{3},{5,6}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5,7},{2,8},{3,4},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,5,7},{2,3,8},{4},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,5},{3,7},{4},{6,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5},{2,3,7},{4},{6,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,4,5},{2,7},{3},{6,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,4},{2,7},{3},{5,6,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,4},{2,6,7},{3},{5,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,4},{2,6},{3},{5,7,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,6},{2,5,7,8},{3},{4}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,6,7},{2,5,8},{3},{4}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,7},{2,5,6,8},{3},{4}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,7},{2,6,8},{3},{4,5}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,7},{2,3,6,8},{4},{5}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2,8},{3,6},{4},{5,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,8},{2,6},{3},{4,5,7}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,8},{2,5,6},{3},{4,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,8},{2,5},{3},{4,6,7}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,7,8},{2,5},{3},{4,6}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,8},{2,4},{3,6,7},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,7,8},{2,4},{3,6},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4},{2,3,7},{5,8},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,7},{4,5,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,3},{2,6,7},{4,8},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,6},{4,7,8},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6},{2,4,7,8},{3},{5}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,7},{2,4,8},{3},{5,6}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,7},{2,4,5,8},{3},{6}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,7},{2,5,8},{3,4},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7},{2,3,5,8},{4},{6}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2,7},{3},{4,6},{5,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,7},{2},{3,4,6},{5,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,7},{2},{3,6},{4,5,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,7},{2},{3,5,6},{4,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,6,7},{2},{3,5},{4,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,6},{2},{3,5},{4,7,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,5},{2},{3,7,8},{4,6}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,5},{2},{3,8},{4,6,7}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,5,6},{2},{3,8},{4,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,6},{2},{3,8},{4,5,7}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,6},{2},{3,4,8},{5,7}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,2,6},{3},{4,8},{5,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,2,6,8},{3},{4,7},{5}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,6,8},{2,3},{4,7},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6,8},{2},{3,7},{4,5}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,5,6,8},{2},{3,7},{4}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,5,8},{2},{3,6,7},{4}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1},{2},{3},{4},{5},{6},{7},{8,9}} => [1,1,1,1,1,1,1,2] => [1,8] => 1
{{1,9},{2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1,1] => [8,1] => 8
{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => [1,1,1,1,1,1,1,1,2] => [1,9] => 1
{{1},{2},{3},{4},{5,10},{6},{7},{8},{9}} => [1,1,1,1,2,1,1,1,1] => [5,5] => 5
{{1,9},{2,3},{4},{5},{6},{7},{8}} => [2,2,1,1,1,1,1] => [6,2,1] => 14
{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
{{1},{2,3,4,5,6,7,8,10},{9}} => [1,8,1] => [2,1,1,1,1,1,1,2] => 35
{{1,3,6,8},{2},{4},{5,7}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,4,6,8},{2},{3,5},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,5,7},{2,3},{4,8},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,8},{2},{3,6},{5,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3,8},{2},{4,6},{5,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,4,7,8},{2},{3,6},{5}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,4,6,7},{2},{3,5},{8}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,4,8},{2},{3,7},{5,6}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,5,8},{2},{3,7},{4,6}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,5,8},{2},{3,6},{4,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,4,7},{2,3},{5,8},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3},{2,5,8},{4,7},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5},{2,4,7,8},{3},{6}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,3},{2,4,6,7},{5},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,3},{2,4,8},{5,6},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,5,8},{4,6},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,6},{2,3,4},{5,8},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,6},{2,4},{3,5,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4},{2,6},{3,5,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4},{2,5,6},{3,7},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4},{2,6,7},{3,8},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2,5},{3,6},{4},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,4},{3,7},{5,6},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,4},{2,7},{5,6},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6,7},{2,8},{3},{4,5}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5,6},{2,3},{4,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,6},{2,3},{5,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4},{2,3,6},{5,7},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4},{2,3,7},{5},{6,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,2,4},{3,7},{5},{6,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,3,4},{2,7},{5},{6,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,7},{3},{4,5},{6,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,2,6},{3},{4},{5,7,8}} => [3,1,1,3] => [1,1,4,1,1] => 16
{{1,7},{2,3,4},{5},{6,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,7},{2,4},{3,6,8},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4},{2,7},{3,6,8},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4},{2,6},{3,5,7},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6},{2,4},{3,5,7},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6},{2,3,4},{5,7},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,5,7},{4,6},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,4,7},{5,6},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5},{2,7,8},{3},{4,6}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,7},{2,4},{3,5,6},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6},{2,5},{3,7,8},{4}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,5},{2,6},{3,7,8},{4}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4},{2,8},{3,6,7},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4},{2,7},{3,5,6},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,3},{2,4,5,6},{7,8}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,4},{2,3,5,6},{7,8}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,4},{2,3,5,7},{6,8}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,3},{2,4,5,7},{6,8}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,2},{3,4,5,7},{6,8}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,3},{2,4,5,6,7,8}} => [2,6] => [1,1,1,1,1,2,1] => 22
{{1,4},{2,3,5,6,7,8}} => [2,6] => [1,1,1,1,1,2,1] => 22
{{1,5},{2,3,4,6,7,8}} => [2,6] => [1,1,1,1,1,2,1] => 22
{{1,2},{3,4,6,7},{5,8}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,3},{2,4,6,7},{5,8}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,4},{2,3,6,7},{5,8}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,5},{2,3,6,7},{4,8}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,3},{2,4},{5,6,7,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,4},{2,5},{3,6,7,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,3},{2,5},{4,6,7,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,2},{3,5},{4,6,7,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,2},{3,6},{4,5,7,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,3},{2,6},{4,5,7,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,4},{2,6},{3,5,7,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,5},{2,6},{3,4,7,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,2},{3,5,6,8},{4,7}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,3},{2,5,6,8},{4,7}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,4},{2,5,6,8},{3,7}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,5},{2,4,6,8},{3,7}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,4,5,8},{2,3,6,7}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,4},{2},{3,5,6},{7,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,4,5},{2},{3,6},{7,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,5},{2},{3,4,6},{7,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,6},{2},{3,4,7,8},{5}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,5},{2},{3,4,7,8},{6}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,4,5},{2},{3,7,8},{6}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,4,5},{2},{3,8},{6,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,6,7},{2},{3,4,8},{5}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,7},{2},{3,4,8},{5,6}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,4,6,7},{2},{3,8},{5}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,4,6},{2},{3,7,8},{5}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3,6},{2},{4},{5,7,8}} => [3,1,1,3] => [1,1,4,1,1] => 16
{{1,2},{3,6},{4},{5,7,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,4},{2},{3,5,7,8},{6}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,6},{2,4},{3},{5,7,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,6,7},{2,3},{4},{5,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,7},{2,4},{3},{5,6,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,6,7},{2,4},{3},{5,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2},{3,6,7},{4},{5,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,3,6,7},{2},{4},{5,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,3,7},{2},{4},{5,6,8}} => [3,1,1,3] => [1,1,4,1,1] => 16
{{1,2},{3,7},{4},{5,6,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,4,7},{2},{3,8},{5,6}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,7},{2,4,5},{3},{6,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,8},{2,4,5},{3,6},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,8},{2,4},{3,5,6},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,5,8},{2,3},{4,6},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,8},{2,5},{3,4,6},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4,8},{2},{3,5,6},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,4},{2},{3,6,8},{5,7}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,5,7},{2,3},{4},{6,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,4,6},{2},{3},{5,7,8}} => [3,1,1,3] => [1,1,4,1,1] => 16
{{1},{2,5,6},{3,7},{4,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,5,6},{3},{4,7,8}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1},{2,5},{3,7},{4,6,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1},{2},{3,6,7},{4,5,8}} => [1,1,3,3] => [1,1,2,1,3] => 12
{{1},{2,3,6,7},{4},{5,8}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1},{2,3,6},{4,8},{5,7}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2},{3,4,6,8},{5,7}} => [1,1,4,2] => [1,2,1,1,3] => 13
{{1},{2},{3,6},{4,5,7,8}} => [1,1,2,4] => [1,1,1,2,3] => 11
{{1},{2,5},{3},{4,6,7,8}} => [1,2,1,4] => [1,1,1,3,2] => 12
{{1},{2,5},{3,6},{4,7,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1},{2,5},{3,6,7},{4,8}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2},{3,5,6,7},{4,8}} => [1,1,4,2] => [1,2,1,1,3] => 13
{{1},{2},{3,5,6},{4,7,8}} => [1,1,3,3] => [1,1,2,1,3] => 12
{{1},{2},{3,5},{4,6,7,8}} => [1,1,2,4] => [1,1,1,2,3] => 11
{{1},{2,4,8},{3,5},{6,7}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,4},{3,6,8},{5,7}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,4,7},{3,6},{5,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1,3},{2,8},{4,5,7},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,3},{2,4,7,8},{5},{6}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,7},{2,3,4,8},{5},{6}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1},{2,4,7},{3},{5,6,8}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1,7},{2},{3,4,5},{6,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1},{2,3,7},{4,8},{5,6}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2},{3,7},{4,5,6,8}} => [1,1,2,4] => [1,1,1,2,3] => 11
{{1},{2},{3,5,7},{4,6,8}} => [1,1,3,3] => [1,1,2,1,3] => 12
{{1},{2,6},{3,5},{4,7,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1},{2,6},{3,5,7},{4,8}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,5},{2},{3,6,7},{4,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,5},{2},{3,6},{4,7,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,5},{2},{3},{4,6,7,8}} => [2,1,1,4] => [1,1,1,4,1] => 13
{{1},{2,6},{3},{4,5,7,8}} => [1,2,1,4] => [1,1,1,3,2] => 12
{{1,6},{2},{3,4},{5,7,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,2,6},{3},{4,7,8},{5}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,6},{2},{3,4,7},{5,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1},{2,6},{3,7},{4,5,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1,5},{2},{3,7},{4,6,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,5},{2,6},{3},{4,7,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,3,6},{2,5},{4},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5},{2,4,6},{3},{7,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,4,5},{2,6},{3},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5,8},{2,7},{3,4},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,5},{2,8},{3},{6,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,6,7},{2,8},{3,5},{4}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6},{2,8},{3},{4,5,7}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,6},{2,5,8},{3},{4,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,6},{2,4,5,8},{3},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,5},{2,7},{3},{4,6,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,7},{2,5},{3,6,8},{4}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,8},{2,6},{3,5,7},{4}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,5,8},{2,3},{4,7},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,7},{2,3},{4,6,8},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6,7},{2,3},{4,8},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,8},{2,5,6},{3,7},{4}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3,8},{2,6},{4},{5,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,6,7},{2,5},{3,8},{4}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,5},{2,6,7},{3},{4,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,3,8},{2,7},{4,5},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,5,6},{2,4,8},{3},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,5,6},{2,8},{3},{4,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5,7},{2},{3,6,8},{4}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,5},{2},{3,6,8},{4,7}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,6,8},{2,5},{3},{4,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5},{2,6,8},{3},{4,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,5,7},{2,6},{3},{4,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,6},{2,5,7},{3},{4,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,5,7},{2},{3,6},{4,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,5,7},{2},{3,8},{4,6}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,5,6},{2},{3,7},{4,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,5,8},{2,6},{3},{4,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,7},{2,5,8},{3,6},{4}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7},{2,5,8},{3},{4,6}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,7},{2,5,6},{3},{4,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,6,7},{2,5},{3},{4,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,6},{2,5},{3},{4,7,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,5,6},{2,7},{3},{4,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5,8},{2,7},{3},{4,6}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,6},{2,5,8},{3,7},{4}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5,6},{2,8},{3,7},{4}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,5},{2,8},{3,6,7},{4}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,5},{2,7,8},{3,6},{4}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,8},{2,5},{3,6,7},{4}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,8},{2,5,7},{3},{4,6}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,5,7},{2,8},{3,6},{4}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,5},{2,7},{3,6,8},{4}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,7},{2,5},{3},{4,6,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,6,8},{2,5},{3,7},{4}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,5},{2,6,8},{3,7},{4}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,6},{2,5,7},{3,8},{4}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5,7},{2,8},{3},{4,6}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,5},{2,8},{3},{4,6,7}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,6},{2,7,8},{3,5},{4}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7},{2,8},{3,5,6},{4}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,7},{2,5,6},{3,8},{4}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5},{2,6,7},{3,8},{4}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3,8},{2,4,6},{5},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,8},{2,3,5},{4,6},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,8},{2,4,6},{3,5},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7},{2,8},{3,4,5},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,2,7},{3,8},{4,5},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,5},{2},{4,6},{7,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3,6},{2},{4,7,8},{5}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,6},{2},{3,7,8},{4,5}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,6,7},{2},{3,8},{4,5}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3,6,7},{2},{4,8},{5}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,4,8},{2},{3,6,7},{5}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,5,6},{2},{3,4,8},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,6},{2},{3,5,7,8},{4}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,6,7},{2},{3,5,8},{4}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,4},{2,6,8},{3},{5,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,8},{2,4,6},{3},{5,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,7},{2},{3,6,8},{4,5}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,6,8},{2},{3,5,7},{4}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,4},{2},{3,5,7},{6,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,2},{3,5,7},{4},{6,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,5,8},{2},{3,4,7},{6}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,2},{3,4,7},{5},{6,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,2,5},{3},{4,7},{6,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,2,5,8},{3},{4,7},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,2},{3,4,7},{5,8},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2},{3,5},{4,6,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,2,6},{3},{4,7},{5,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3,7},{2,6},{4},{5,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,6},{3,7},{4},{5,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,5},{3},{4,6,8},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,2,5},{3},{4,6},{7,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3},{2,5,6},{4,8},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,8},{4,5,6},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,3,5},{2,8},{4,6},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,6},{3,8},{4,5},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,4,7},{3},{5,8},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,7},{2,5},{4},{6,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,7},{3,4},{5},{6,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,4,7},{3},{5},{6,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,2,4},{3},{5,7},{6,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3},{2,4},{5,6,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,3},{2,4,7},{5},{6,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,4},{2,5,8},{3,7},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7},{2,3,4},{5,8},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,4,7},{5,8},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,4,6},{5},{7,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,3,4},{2,8},{5,6},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6},{2,3,4,8},{5},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,4},{2,5,6},{3,8},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4,6},{2,8},{3,5},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6},{2,8},{3,4,5},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,2,5,7},{3},{4},{6,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,2,5,8},{3},{4,6},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,6},{2,8},{4,5},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,6},{2},{3,5},{7,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,2},{3,5,8},{4,6},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,5,7},{4},{6,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,2,7},{3,5},{4},{6,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,3,7},{2,4},{5},{6,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1},{2,3,4,7},{5},{6,8}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1,4},{2,5,7},{3},{6,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,3},{2,4,6},{5,8},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1},{2,3,4},{5,7},{6,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,4,5},{3,7},{6,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,3,5},{4,7},{6,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,3,5},{4,6},{7,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1,4},{2,5,8},{3,6},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1},{2,4,5},{3,6},{7,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1,4,6,7},{2,3,5,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,6},{2,4},{3,7,8},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6},{2,4},{3,7},{5},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,5,6},{2,3,4,7},{8}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,5,6},{2,3,4,7,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,5,6,7},{2,3,4,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,7},{2,8},{3,4},{5},{6}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,6,7},{2,3,4,8},{5}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,5,6,7},{2,4,8},{3}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,5,7},{2,4,6,8},{3}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,5},{2,3},{4,6,7},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,5},{2,3},{4,6,7,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,5},{2,3},{4,6,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,5,6},{2,3,4,8},{7}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,6},{2,4},{3,8},{5},{7}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,5},{2,3},{4,6},{7},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,5},{2,3},{4,7,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,5},{2,3},{4,8},{6},{7}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,5},{2,3},{4,7},{6},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,6},{2,4},{3,5,7,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,6},{2,5},{3,4,7,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,5,6,8},{2,3,4,7}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,3,7},{2},{4,8},{5,6}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3,6},{2},{4,7},{5},{8}} => [3,1,2,1,1] => [3,3,1,1] => 16
{{1,3},{2},{4,7},{5,8},{6}} => [2,1,2,2,1] => [2,2,3,1] => 13
{{1},{2,4,7},{3},{5,8},{6}} => [1,3,1,2,1] => [2,3,1,2] => 13
{{1},{2,7},{3,4,5,8},{6}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1,6},{2,3,4,7},{5},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,4,8},{2,6,7},{3},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,6},{2,8},{3},{5,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,7},{2,4},{3,5,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,5,8},{2,3,7},{4},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1},{2,5,8},{3,7},{4},{6}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1},{2,7},{3,5,8},{4,6}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,6},{2,4,7},{3,5},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,7},{2,5},{3,4,6},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1},{2,8},{3,6},{4,5,7}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1,6},{2,3,7},{4,5},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1},{2,7},{3,4,8},{5,6}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,5},{2,6,8},{3,4},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4},{2,5,7},{3},{6},{8}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,4},{2,5},{3},{6,8},{7}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1,5},{2,3,6,8},{4},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1},{2,5},{3,6,8},{4},{7}} => [1,2,3,1,1] => [3,1,2,2] => 13
{{1},{2,5,6,7},{3,8},{4}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,8},{3,5},{4,6,7}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1},{2,6,7},{3,4,8},{5}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,5,6},{2,3,7},{4},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1},{2,6},{3,7},{4,8},{5}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,6},{3,7},{4},{5},{8}} => [1,2,2,1,1,1] => [4,2,2] => 10
{{1},{2,5,6},{3,4,7},{8}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,6,7},{2,3,8},{4},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1},{2,4,6},{3,5,7},{8}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,3,5},{4,6,7},{8}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,4,6},{2},{3,5,8},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => [4,3,1] => 11
{{1},{2},{3,5},{4,6},{7},{8}} => [1,1,2,2,1,1] => [3,2,3] => 8
{{1,5},{2},{3},{4,8},{6},{7}} => [2,1,1,2,1,1] => [3,4,1] => 10
{{1},{2,5},{3},{4,7},{6},{8}} => [1,2,1,2,1,1] => [3,3,2] => 9
{{1,7},{2},{3,4},{5,6,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,6,8},{2},{3,4},{5,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,2,7},{3},{4,5,8},{6}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,6,7},{2},{3,4},{5,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,8},{2},{3,4,6},{5,7}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1},{2,4,8},{3,7},{5,6}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1,3,8},{2,7},{4},{5,6}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,3},{2,7,8},{4},{5,6}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1},{2,4},{3,7,8},{5,6}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,3},{2,6,8},{4},{5,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1},{2,6,8},{3,4},{5,7}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1,6,8},{2,3},{4},{5,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1},{2,6,7},{3,4},{5,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1,3},{2,6,8},{4,7},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3,6,8},{2},{4,7},{5}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,4,7},{2,6},{3},{5,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,6,8},{2,4,7},{3},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,5,7},{2},{3},{6,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,3,4},{2},{5,7},{6,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,3},{2,4},{5,7,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4},{2,5,6},{3},{7,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,5},{2,6,7,8},{3},{4}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,5},{2},{3,6,7,8},{4}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,4,5,8},{2},{3,7},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,5},{2,4,6},{3,8},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4,5},{2},{3,7},{6,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1},{2,4,7},{3,8},{5,6}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1,6},{2,3,8},{4},{5,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1},{2,6},{3,4,8},{5,7}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,3},{4,5,7},{6,8}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,3},{4,6,8},{5,7}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,3,5,6},{4,7},{8}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,3,5,7},{4,8},{6}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,3,7},{4,6},{5,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,3,6},{4,7},{5,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1,3},{2,5,8},{4,6,7}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,5},{2},{3,4,6,7},{8}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,5},{2,6,7},{3,4},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,5,7,8},{4,6}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,4,5,7},{2},{3,6},{8}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,4},{2},{3,5,6,8},{7}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,4,8},{2},{3,5,7},{6}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3,8},{2,5,7},{4},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3},{2,5,6,8},{4},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,3,7},{2,6},{4,5},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,5,8},{2,4,7},{3},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,6,8},{2,4},{3},{5,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,4,8},{2,6},{3},{5,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,7},{2},{3,4,6,8},{5}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1},{2,7},{3,4,5},{6,8}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,6},{3,4,5,8},{7}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1,6},{2},{3,4,5,7},{8}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,6},{2,7},{3,4,5},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,7},{2,4},{3,5,6,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,4},{2,7},{3,5,6,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,4,8},{2,6},{3,5,7}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,6,8},{2,4},{3,5,7}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,3,8},{2,5,7},{4,6}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,5},{2,7},{3,4,6},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1},{2,4,8},{3,5,6},{7}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,6},{2,4,5},{3,7},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1},{2,5,7},{3,8},{4},{6}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1},{2,7},{3,5,6},{4,8}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,5,8},{3,6,7},{4}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,4,7},{2,5,6},{3},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1},{2,6,8},{3,4,7},{5}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,5,7},{2,3,6},{4},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3},{2,6},{4,5,8},{7}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4,6},{2,3,8},{5},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4},{2,3,8},{5,6},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2,6},{3,8},{4},{5,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1},{2,6},{3,8},{4},{5,7}} => [1,2,2,1,2] => [1,3,2,2] => 11
{{1},{2,5,6,7},{3,4,8}} => [1,4,3] => [1,1,2,1,1,2] => 18
{{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => [1,4,2,1] => 13
{{1,5,6,7},{2,3,8},{4}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,5,7},{2,3,4,8},{6}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1},{2,3,5},{4,8},{6,7}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1,2,3,5},{4,8},{6,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,3,5},{2},{4,8},{6,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,5,6,7},{2},{3,4,8}} => [4,1,3] => [1,1,3,1,1,1] => 21
{{1,6},{2},{3,8},{4},{5,7}} => [2,1,2,1,2] => [1,3,3,1] => 12
{{1},{2},{3,5},{4,8},{6,7}} => [1,1,2,2,2] => [1,2,2,3] => 9
{{1,2,5},{3},{4,8},{6,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,5},{2},{3},{4,8},{6,7}} => [2,1,1,2,2] => [1,2,4,1] => 11
{{1},{2,5},{3},{4,8},{6,7}} => [1,2,1,2,2] => [1,2,3,2] => 10
{{1,2,4,6},{3,8},{5,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,5,6},{3,8},{4,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,3,4,8},{2,5,6,7}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,5,8},{2,4},{3,7},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4},{2,7},{3,5,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1},{2,7},{3,8},{4,5,6}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1,5},{2,4,6},{3,7},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,6},{2,3,5},{4,7},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4,6},{2,7},{3},{5,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1},{2,5},{3,8},{4,6,7}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1},{2,3,7},{4,8},{5},{6}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1,4,7},{2,3},{5},{6,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1},{2,4},{3,7,8},{5},{6}} => [1,2,3,1,1] => [3,1,2,2] => 13
{{1},{2,5,7},{3,4,8},{6}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,5,6},{2,4},{3,7},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1},{2,4},{3,5},{6,7},{8}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,4,8},{3,5},{6},{7}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1},{2,4,6},{3,5},{7,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,5},{3,6},{4},{7,8}} => [1,2,2,1,2] => [1,3,2,2] => 11
{{1},{2,5,7},{3,6,8},{4}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,5,7},{3,8},{4,6}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1,8},{2,4},{3,5,7},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6,7},{2,4},{3,5},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1},{2,5},{3,6},{4,7},{8}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1},{2,5},{3,6,8},{4,7}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,3,6,7},{4,8},{5}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1,3,5,8},{2},{4,7},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,5,6},{2},{3,7,8},{4}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,4,7},{2},{3,5,8},{6}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,4},{2,6,8},{3,7},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5},{2,3,7,8},{4},{6}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1},{2,3,6,8},{4},{5,7}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1,2},{3},{4,6},{5,7,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1},{2,5,6,8},{3},{4,7}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1},{2},{3,5,6,8},{4,7}} => [1,1,4,2] => [1,2,1,1,3] => 13
{{1},{2,4,5,7},{3,8},{6}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2},{3,4,6,7},{5,8}} => [1,1,4,2] => [1,2,1,1,3] => 13
{{1},{2,6},{3,7,8},{4,5}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,6,7},{3,5},{4,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2},{3,6,8},{4,5,7}} => [1,1,3,3] => [1,1,2,1,3] => 12
{{1},{2,3},{4,7},{5,6,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1,7,8},{2,4},{3,5},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,6,8},{2},{3},{5,7}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1},{2,4,6},{3,7,8},{5}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,3},{2},{4,6},{5,7,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1},{2,4,6,7},{3},{5,8}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1},{2,5},{3,7,8},{4,6}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,4,7},{2},{3,6,8},{5}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3},{2,4,5},{6,8},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,8},{4,6,7},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,3},{2,4,5},{6,7},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4},{2,7,8},{3},{5,6}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,4},{2,3,7,8},{5},{6}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,3,8},{2,4},{5},{6,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,6,8},{2},{3},{4,5,7}} => [3,1,1,3] => [1,1,4,1,1] => 16
{{1,5},{2,3,7},{4,6},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4},{2,3,6,7},{5},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,4,6},{2,3,7},{5},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,6},{2,4,5,7},{3},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,7},{2,4,5},{3,6},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5,6,7},{2},{3},{4,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,5,7},{2,6},{3,4},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1},{2,6,7},{3,5,8},{4}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,3},{2},{4,6,7},{5,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,6},{2,5,8},{3,4,7}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,3,6,7},{2,4,5,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1},{2,8},{3,5,6},{4,7}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,5,6,7},{3},{4,8}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1,6},{2,7,8},{3,4},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5},{2,7},{3,4,6,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,7},{2},{3,8},{4,5,6}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,7},{2,4,5},{3,6,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1},{2,6,8},{3,7},{4,5}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,4,5,8},{3,7},{6}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,4,5},{3,7,8},{6}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,6},{3,8},{4,5,7}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1,4,5,6},{2},{3,8},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,5,6},{2},{4,8},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1},{2,4,6,7},{3,8},{5}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1,5},{2,7,8},{3,4},{6}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3,5},{2},{4,7,8},{6}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3},{2,5},{4,7,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,7},{2,6},{3},{4,5,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,3},{2,7,8},{4,6},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4,5},{2,8},{3,7},{6}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,3,6},{2,4},{5},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,3,6},{2},{4,5,8},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,2},{3,5},{4,7,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1},{2,3,4,7},{5,8},{6}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1,4,8},{2,5,7},{3},{6}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1},{2,3,4,6},{5,8},{7}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,4,5,8},{3,6},{7}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1,6},{2},{3,4,5,8},{7}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1},{2,4},{3,6},{5,8},{7}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1,3},{2},{4,6},{5,8},{7}} => [2,1,2,2,1] => [2,2,3,1] => 13
{{1,3},{2,5},{4},{6,8},{7}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1},{2,4,5,6},{3,8},{7}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,6},{3,5},{4,8},{7}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1,5},{2,4},{3,7},{6},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,5},{2,4,6,7},{3},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1},{2,6},{3,5,7,8},{4}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1},{2,8},{3,5},{4,7},{6}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1,7},{2,4},{3,6},{5},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1},{2,5,7,8},{3,6},{4}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1,5,6},{2,4,7},{3},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3},{2,5,6,7},{4},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,3},{2,6,7,8},{4},{5}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1},{2,4},{3,6,7,8},{5}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1},{2,4},{3,8},{5,7},{6}} => [1,2,2,2,1] => [2,2,2,2] => 12
{{1,3},{2,7},{4,6},{5},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1},{2,4,7},{3,6,8},{5}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,4,7},{2,3,5},{6},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,7},{2,3,6},{5},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,5},{2,3,6,7},{4},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,4},{2,3,7},{5,6},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1},{2,5,8},{3,4,6},{7}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,5,7},{3,4,6},{8}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,3,6},{4,5,7},{8}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,6},{2,3},{4,5,7},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,3,6},{2},{4,5,7},{8}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,4},{2,3,5},{6,7},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,6},{2,5,7},{3,4},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4},{2,3,5},{6,8},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1},{2,3,6},{4,5,8},{7}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,5,8},{3,4,7},{6}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,3,7},{4,6,8},{5}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,3,7},{4,5,8},{6}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,4,8},{2},{3,5},{6,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,6,8},{2},{3,5},{4,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,4},{2,3,5,8},{6},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2,6,8},{3},{4},{5,7}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,2},{3,6,8},{4},{5,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [8,1] => 8
{{1,3},{2},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [8,1] => 8
{{1,4},{2},{3},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [8,1] => 8
{{1,5},{2},{3},{4},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [8,1] => 8
{{1,6},{2},{3},{4},{5},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [8,1] => 8
{{1,7},{2},{3},{4},{5},{6},{8},{9}} => [2,1,1,1,1,1,1,1] => [8,1] => 8
{{1,8},{2},{3},{4},{5},{6},{7},{9}} => [2,1,1,1,1,1,1,1] => [8,1] => 8
{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
{{1,2,3},{4},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
{{1,3,4},{2},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,4},{2},{3},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
{{1,4,5},{2},{3},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,5},{2},{3},{4},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
{{1,5,6},{2},{3},{4},{7},{8},{9}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,6},{2},{3},{4},{5},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
{{1,6,7},{2},{3},{4},{5},{8},{9}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,7},{2},{3},{4},{5},{6},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
{{1,7,8},{2},{3},{4},{5},{6},{9}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,8},{2},{3},{4},{5},{6},{7},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
{{1,8,9},{2},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
{{1,8},{2},{3,6},{4,5,7}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,8},{2},{3,5,6},{4,7}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,5,8},{2},{3,4,6},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3},{2,4,8},{5},{6,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,5},{2,6},{3,4,7},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4,5},{2,3,6},{7},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,5},{2,4},{3,6,7},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,5},{2,3,6},{4,7},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,5},{2,3,4,6},{7},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,5,7},{2,3},{4,6},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4},{2,5,7},{3,6},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,2,5},{3,7},{4,6},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2,4},{3,8},{5,6},{7}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,2},{3,4},{5},{6},{7},{8},{9}} => [2,2,1,1,1,1,1] => [6,2,1] => 14
{{1,2,3,4,5,6,7,8,9,10}} => [10] => [1,1,1,1,1,1,1,1,1,1] => 45
{{1,2,3,4,5,6,7},{8,9},{10}} => [7,2,1] => [2,2,1,1,1,1,1,1] => 41
{{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => [3,1,1,1,1,1,1,1] => [8,1,1] => 17
{{1,4},{2,3},{5},{6},{7},{8},{9}} => [2,2,1,1,1,1,1] => [6,2,1] => 14
{{1,9},{2},{3},{4},{5},{6},{7,8}} => [2,1,1,1,1,1,2] => [1,7,1] => 9
{{1,2,3},{4,7},{5},{6,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,5},{3},{4,6,7},{8}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,2,7},{3},{4,8},{5,6}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,2,5},{3,8},{4},{6,7}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,4},{2,5,7,8},{3},{6}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2,6},{3},{4,5,7},{8}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,2,5,6},{3},{4,7},{8}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1},{2,6},{3,4,7,8},{5}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1,3},{2},{4,7},{5,6,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,4},{2},{3,6,7,8},{5}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1},{2,3,7},{4},{5,6,8}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1},{2,3,6},{4},{5,7,8}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1},{2,3},{4,6,7},{5,8}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1},{2,3},{4,6},{5,7,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1,4},{2,6},{3,7,8},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1},{2,3,5,6},{4,8},{7}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,3,5},{4,7,8},{6}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,5},{3,4,7,8},{6}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1,4,7},{2},{3,6},{5,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1},{2,4,8},{3,6,7},{5}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,3,6},{4,7,8},{5}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,4,5,7},{2,3,6,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,5},{2,3,7},{4,6,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,5},{2,3,6,8},{4,7}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1},{2,5},{3,4,7},{6,8}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,5},{2,6,8},{3,4,7}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,5,7},{2,6},{3,4,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,6},{2,5,7},{3,4,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,5,7},{2,3,6},{4,8}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,5,7},{2,3,8},{4,6}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1},{2,7},{3,6},{4,5,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1,7},{2,4,5,8},{3,6}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,7},{2,5,8},{3,4,6}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,6},{2,5},{3,4,7},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6},{2,4,5,8},{3,7}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,4,5},{2,7},{3,6},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1},{2,4,5,7},{3,6},{8}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1,4,5,7},{2,8},{3,6}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,4,5},{2,7},{3,6,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,7},{2,5},{3,4,6,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1},{2,6},{3,4,5,7},{8}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1},{2,7},{3,6,8},{4,5}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,6},{2,4,5,7},{3,8}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,5,7},{2,8},{3,4,6}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,3,6},{2,7},{4,5},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1},{2,6,8},{3},{4,7},{5}} => [1,3,1,2,1] => [2,3,1,2] => 13
{{1,3},{2},{4,7},{5},{6,8}} => [2,1,2,1,2] => [1,3,3,1] => 12
{{1,3,4,7},{2},{5},{6,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,4},{2},{3,5},{6,8},{7}} => [2,1,2,2,1] => [2,2,3,1] => 13
{{1,5,7},{2},{3,6},{4},{8}} => [3,1,2,1,1] => [3,3,1,1] => 16
{{1},{2,7},{3,5},{4},{6,8}} => [1,2,2,1,2] => [1,3,2,2] => 11
{{1,6},{2,4},{3},{5,7},{8}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1},{2,7},{3,5,6,8},{4}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1},{2,8},{3,6},{4},{5,7}} => [1,2,2,1,2] => [1,3,2,2] => 11
{{1,7},{2,5},{3},{4,6},{8}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1},{2,7},{3,4,6,8},{5}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1,6},{2,3,5,7},{4},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,4,5,8},{2},{3,6},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,4,6},{2},{5,8},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1},{2,6},{3},{4,8},{5,7}} => [1,2,1,2,2] => [1,2,3,2] => 10
{{1,5},{2},{3,7},{4,6},{8}} => [2,1,2,2,1] => [2,2,3,1] => 13
{{1},{2,6},{3,5,8},{4,7}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,5},{2,4,7},{3,6},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1},{2,5},{3,4,6,8},{7}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1,4},{2,3,5,7},{6},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1},{2,5,6,8},{3,7},{4}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,7},{3,5},{4,6,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1,5},{2,3,7},{4},{6},{8}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,5},{2,3,8},{4},{6},{7}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,5,8},{2,3,6},{4},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,6},{2,3,8},{4},{5},{7}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,6},{2,4,8},{3},{5},{7}} => [2,3,1,1,1] => [4,1,2,1] => 16
{{1,6,8},{2,3,7},{4},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,6},{2,3},{4,7},{5},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,6},{2,3},{4,7,8},{5}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,7},{2,3},{4,8},{5},{6}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,7},{2,4},{3,8},{5},{6}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1,5},{2},{3,4,7},{6,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1},{2,4},{3,5,7},{6,8}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,7},{2,5},{3},{4,8},{6}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1,5,8},{2,4,6},{3},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,8},{2,3,5},{6},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1},{2,4},{3,5,7},{6},{8}} => [1,2,3,1,1] => [3,1,2,2] => 13
{{1},{2,4},{3,5,8},{6},{7}} => [1,2,3,1,1] => [3,1,2,2] => 13
{{1},{2,4,7},{3,5,6},{8}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,7},{2,3,5},{4},{6,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1},{2,4,5},{3,8},{6,7}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,3,8},{4,6},{5,7}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,4,5,7},{3},{6,8}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1,3,7},{2},{4,5},{6,8}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1},{2,4,7},{3,5,8},{6}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2},{3,5,7,8},{4,6}} => [1,1,4,2] => [1,2,1,1,3] => 13
{{1},{2},{3,5,8},{4,6,7}} => [1,1,3,3] => [1,1,2,1,3] => 12
{{1},{2,5,7},{3,6},{4,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1,5,7,8},{2},{3},{4,6}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1},{2,5,7,8},{3},{4,6}} => [1,4,1,2] => [1,3,1,1,2] => 16
{{1,9,10},{2},{3},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1,1,1] => [8,1,1] => 17
{{1,5,6,7},{2},{3,8},{4}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,7,8},{2},{3,5},{4,6}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1,5,6,8},{2},{3},{4,7}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1},{2,4,5,6,7,8,9,10},{3}} => [1,8,1] => [2,1,1,1,1,1,1,2] => 35
{{1},{2,3,5},{4,6,7,8}} => [1,3,4] => [1,1,1,2,1,2] => 17
{{1},{2,3,5},{4,6,8},{7}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1,4,5,6,8},{2,3,7}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,4},{2},{3,5,6,7,8}} => [2,1,5] => [1,1,1,1,3,1] => 17
{{1,3},{2,5,6},{4},{7,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,4},{2,5},{3,7,8},{6}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,6},{2},{3,7},{4,5,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,7},{2},{3,5},{4,6,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,3},{2,5,7,8},{4},{6}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,7},{2},{3,5,6,8},{4}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,7},{2},{3,5,8},{4,6}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,6},{2},{3,5,7},{4,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,8},{2},{3,5,7},{4,6}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,4,6},{2,3,5},{7},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,5,8},{2},{3},{4,6,7}} => [3,1,1,3] => [1,1,4,1,1] => 16
{{1,5,6},{2},{3,4,7},{8}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,3,6},{2,4,5},{7},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,7},{2,3,5,6},{8}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,6},{2,3,5,7,8},{4}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,4,6},{2,3,7,8},{5}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,3,5,6,8},{2},{4,7}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,4,5,8},{2,7},{3,6}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1},{2,4,5,7,8},{3,6}} => [1,5,2] => [1,2,1,1,1,2] => 19
{{1},{2,4,6,8},{3,5,7}} => [1,4,3] => [1,1,2,1,1,2] => 18
{{1,4,7},{2,6},{3,5,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,5},{2,4,7},{3,6,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,3,5,7},{2},{4,6,8}} => [4,1,3] => [1,1,3,1,1,1] => 21
{{1,3,6},{2},{4,5,7,8}} => [3,1,4] => [1,1,1,3,1,1] => 19
{{1},{2,5,8},{3,4,6,7}} => [1,3,4] => [1,1,1,2,1,2] => 17
{{1,5,6,8},{2,4,7},{3}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,6},{2,4,5,7,8},{3}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,2,4,6,7},{3},{5,8}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,3,5},{2,4,6,8},{7}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,4},{2,3,5,6,8},{7}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,3,4,6,7},{2},{5,8}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1},{2,3,5,6,8},{4,7}} => [1,5,2] => [1,2,1,1,1,2] => 19
{{1,3,7},{2,4,6,8},{5}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,4},{2,3,5,7,8},{6}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1},{2,3,7},{4,5},{6,8}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1,3},{2},{4,5,7},{6,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,2},{3},{4,5,7},{6,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1},{2},{3,4,6},{5,7,8}} => [1,1,3,3] => [1,1,2,1,3] => 12
{{1},{2},{3,4,7},{5,6,8}} => [1,1,3,3] => [1,1,2,1,3] => 12
{{1,2},{3},{4,6,8},{5,7}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,2},{3},{4,6,7},{5,8}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1,3},{2,4},{5},{6,7,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,4},{2,5},{3},{6,7,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,3},{2,5},{4},{6,7,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,7},{2,8},{3},{4,5,6}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1,4},{2,8},{3},{5,6,7}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1},{2,6,7},{3},{4,5,8}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1,4,8},{2,5,6},{3},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,3},{2,4,5,8},{6},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2,4,6},{3},{5,7},{8}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,4,6},{2},{5,7},{8}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,2,6},{3,7},{4,5},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6,8},{2,7},{3,4},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6,7},{2,4},{3,8},{5}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4},{2},{3,5},{6,7,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,6},{2,7},{3},{4,5,8}} => [2,2,1,3] => [1,1,3,2,1] => 15
{{1},{2,3,4,6},{5,7},{8}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,7,8},{3,5},{4,6}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1,5,6},{2,7},{3,4},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,6},{2,7,8},{3},{4,5}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,8},{2},{3,5},{4,6,7}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,6},{2},{3,5,8},{4,7}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1},{2,6,8},{3},{4,5,7}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1},{2,6,7},{3,8},{4,5}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1},{2,5,6},{3,8},{4,7}} => [1,3,2,2] => [1,2,2,1,2] => 15
{{1,3,8},{2,6,7},{4},{5}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2,7},{3,6},{4},{5,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,8},{3},{4,6},{5,7}} => [3,1,2,2] => [1,2,3,1,1] => 17
{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}} => [1,1,1,1,1,1,1,1,1,2] => [1,10] => 1
{{1,7},{2,3,5},{4,6},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,5,6},{4,7},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3},{2,7},{4,5,6},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1},{2,5,8},{3},{4,6,7}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1,4},{2,6,7},{3,5},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4},{2,7,8},{3,6},{5}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1},{2,4,5},{3,6,7},{8}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,4,5},{3,6,8},{7}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,5,6},{3,7,8},{4}} => [1,3,3,1] => [2,1,2,1,2] => 16
{{1},{2,4},{3,5,6},{7,8}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,4,6},{2,3,8},{5,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,3},{2,6},{4,5,7},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,4},{2},{3,5,6,7},{8}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,3,6},{2,7},{4,5,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,4,6},{2,3,5,7,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,2,4,6},{3},{5,7,8}} => [4,1,3] => [1,1,3,1,1,1] => 21
{{1,5,6},{2,4,7},{3,8}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,3,6,7},{4},{5,8}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1},{2,4,6,7,8},{3,5}} => [1,5,2] => [1,2,1,1,1,2] => 19
{{1,2,6},{3,4,5,7,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,5,8},{2},{3,4,6,7}} => [3,1,4] => [1,1,1,3,1,1] => 19
{{1},{2,3,5,8},{4,7},{6}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1,4,7},{2,3,5,6,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1},{2,3,4,5,6,7,8,9},{10}} => [1,8,1] => [2,1,1,1,1,1,1,2] => 35
{{1,5,7,8},{2,3,4,6}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,3,6,8},{2,4,5,7}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,2,6,8},{3,4,5,7}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,6},{2,3,4,5,7,8}} => [2,6] => [1,1,1,1,1,2,1] => 22
{{1,2,6},{3,4,5,8},{7}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,4,8},{2,3,5,6},{7}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,5},{2,3,4,8},{6,7}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,4,8},{2,3,5},{6,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,4},{3,5,6,7,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,5,8},{2,3,4,6,7}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,3,4},{2,5,6,7,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,4,6,7},{2,3,8},{5}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,3,8},{2,4,6,7},{5}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,3,5},{2,8},{4,6,7}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,4,7,8},{2,3,6},{5}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,6},{2,3,5},{4,7,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,2,6},{3,5},{4,7,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,2,5},{3,6},{4,7,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,5},{2,3,6},{4,7,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,4,7,8},{2,6},{3,5}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,7,8},{2,3,5},{4,6}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,7,8},{2,5},{3,4,6}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,7,8},{2,4,6},{3,5}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,4,8},{2,3,5,7},{6}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,2,5},{3,4,6,7,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,8},{2,3},{4},{5},{6},{7},{9}} => [2,2,1,1,1,1,1] => [6,2,1] => 14
{{1,2},{3},{4},{5},{6},{7},{8,9}} => [2,1,1,1,1,1,2] => [1,7,1] => 9
{{1,7},{2},{3},{4},{5},{6},{8,9}} => [2,1,1,1,1,1,2] => [1,7,1] => 9
{{1,3,4,5,6,7,8},{2,10},{9}} => [7,2,1] => [2,2,1,1,1,1,1,1] => 41
{{1},{2},{3},{4},{5,7},{6,8}} => [1,1,1,1,2,2] => [1,2,5] => 4
{{1},{2},{3},{4,6},{5,8},{7}} => [1,1,1,2,2,1] => [2,2,4] => 6
{{1},{2},{3,5},{4,8},{6},{7}} => [1,1,2,2,1,1] => [3,2,3] => 8
{{1},{2,4},{3,8},{5},{6},{7}} => [1,2,2,1,1,1] => [4,2,2] => 10
{{1},{2},{3},{4,7},{5,8},{6}} => [1,1,1,2,2,1] => [2,2,4] => 6
{{1},{2},{3,6},{4,8},{5},{7}} => [1,1,2,2,1,1] => [3,2,3] => 8
{{1},{2},{3},{4,6,7},{5,8}} => [1,1,1,3,2] => [1,2,1,4] => 8
{{1},{2,5},{3,8},{4},{6},{7}} => [1,2,2,1,1,1] => [4,2,2] => 10
{{1},{2},{3,5,6},{4,8},{7}} => [1,1,3,2,1] => [2,2,1,3] => 11
{{1},{2,4,5},{3,8},{6},{7}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1,3},{2,9},{4},{5},{6},{7},{8}} => [2,2,1,1,1,1,1] => [6,2,1] => 14
{{1,2,5,7},{3},{4,6,8}} => [4,1,3] => [1,1,3,1,1,1] => 21
{{1,7},{2,3,4,5,6,8}} => [2,6] => [1,1,1,1,1,2,1] => 22
{{1,4,6,7,8},{2,3,5}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,2,6,7},{3,4,5,8}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,3,6,7,8},{2,4,5}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,6},{2,5,7,8},{3,4}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,6},{2,3,7},{4,5,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,3,5},{2,6},{4,7,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,4,5,7,8},{2,3,6}} => [5,3] => [1,1,2,1,1,1,1] => 25
{{1,3,7},{2,4,6},{5,8}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,5,7},{2,3,6,8},{4}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,3,7},{2,4,5,8},{6}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,3,7},{2,4,5,6,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,5,8},{2,4,6},{3,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,6},{2,3,4,7,8},{5}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,2,5,8},{3,4,6,7}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1},{2,3,5,7,8},{4,6}} => [1,5,2] => [1,2,1,1,1,2] => 19
{{1},{2,3,5,7},{4,6},{8}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,3,5,7},{4,6,8}} => [1,4,3] => [1,1,2,1,1,2] => 18
{{1},{2,3,4,5,7},{6,8}} => [1,5,2] => [1,2,1,1,1,2] => 19
{{1},{2,3,5,8},{4,6,7}} => [1,4,3] => [1,1,2,1,1,2] => 18
{{1,3},{2,6,8},{4,5},{7}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,4,6,7},{2},{3},{5,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1,4,7,8},{2},{3,5},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1},{2,4,7,8},{3,5},{6}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1},{2,4,7,8},{3,6},{5}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1,4},{2},{3,7,8},{5,6}} => [2,1,3,2] => [1,2,1,3,1] => 15
{{1},{2,3,4,6,8},{5,7}} => [1,5,2] => [1,2,1,1,1,2] => 19
{{1,5,6,8},{2,3,7},{4}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,5,6},{2,3},{4,7,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,2,9},{3},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,3},{2,4,5,6,8},{7}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,6,7},{2,3,4,5,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,7},{2,3,4},{5,6,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,4,5},{2,3,7,8},{6}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,4,6,8},{2,3,5,7}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,4,8},{2,3,6,7},{5}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,3,7},{2,6},{4,5,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,2,6},{3,7},{4,5,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,2},{3,4,6},{5,7,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,2,3},{4,7},{5,6,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,5},{2,6,7,8},{3,4}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,7},{2,6,8},{3,4,5}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,2,6},{3,5,7,8},{4}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1},{2,3,6},{4,5,7,8}} => [1,3,4] => [1,1,1,2,1,2] => 17
{{1,7,8},{2,4},{3,5,6}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}} => [2,1,1,1,1,1,1,1,1,1] => [10,1] => 10
{{1,2},{3,5},{4},{6},{7},{8},{9}} => [2,2,1,1,1,1,1] => [6,2,1] => 14
{{1,9},{2,4},{3},{5},{6},{7},{8}} => [2,2,1,1,1,1,1] => [6,2,1] => 14
{{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1,1] => [10,1] => 10
{{1,3},{2,5,8},{4},{6,7}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,9},{2,8},{3},{4},{5},{6},{7}} => [2,2,1,1,1,1,1] => [6,2,1] => 14
{{1,3,9},{2},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,2,7},{3},{4},{5},{6},{8,9}} => [3,1,1,1,1,2] => [1,6,1,1] => 16
{{1,3,8},{2},{4},{5},{6},{7},{9}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,3,10},{2},{4},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1,1] => [8,1,1] => 17
{{1},{2,4},{3,5,6,7,8}} => [1,2,5] => [1,1,1,1,2,2] => 16
{{1,5,6},{2},{3},{4,7,8}} => [3,1,1,3] => [1,1,4,1,1] => 16
{{1,3,5},{2},{4,6},{7},{8}} => [3,1,2,1,1] => [3,3,1,1] => 16
{{1,3,7},{2},{4},{5},{6,8}} => [3,1,1,1,2] => [1,5,1,1] => 14
{{1,3,6},{2},{4},{5,8},{7}} => [3,1,1,2,1] => [2,4,1,1] => 15
{{1},{2},{3,7},{4,8},{5},{6}} => [1,1,2,2,1,1] => [3,2,3] => 8
{{1,7},{2},{3},{4},{5},{6,8}} => [2,1,1,1,1,2] => [1,6,1] => 8
{{1,6},{2},{3},{4},{5,8},{7}} => [2,1,1,1,2,1] => [2,5,1] => 9
{{1,4},{2,6},{3},{5,8},{7}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1,5},{2,6},{3},{4,8},{7}} => [2,2,1,2,1] => [2,3,2,1] => 14
{{1,5,7},{2},{3},{4},{6,8}} => [3,1,1,1,2] => [1,5,1,1] => 14
{{1,5},{2},{3},{4,6},{7},{8}} => [2,1,1,2,1,1] => [3,4,1] => 10
{{1,4},{2},{3,6},{5},{7},{8}} => [2,1,2,1,1,1] => [4,3,1] => 11
{{1},{2,5},{3,6},{4},{7},{8}} => [1,2,2,1,1,1] => [4,2,2] => 10
{{1,4,6},{2},{3,5,7},{8}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,6},{2},{3},{4,7},{5},{8}} => [2,1,1,2,1,1] => [3,4,1] => 10
{{1,6},{2},{3},{4,7},{5,8}} => [2,1,1,2,2] => [1,2,4,1] => 11
{{1,5},{2},{3},{4,7},{6,8}} => [2,1,1,2,2] => [1,2,4,1] => 11
{{1,5,7},{2},{3},{4,6},{8}} => [3,1,1,2,1] => [2,4,1,1] => 15
{{1,4,7},{2},{3,6},{5},{8}} => [3,1,2,1,1] => [3,3,1,1] => 16
{{1,4},{2},{3,7},{5},{6,8}} => [2,1,2,1,2] => [1,3,3,1] => 12
{{1,5},{2},{3,7},{4,8},{6}} => [2,1,2,2,1] => [2,2,3,1] => 13
{{1,5},{2},{3,7},{4},{6},{8}} => [2,1,2,1,1,1] => [4,3,1] => 11
{{1,7},{2,5},{3,6},{4},{8}} => [2,2,2,1,1] => [3,2,2,1] => 15
{{1},{2,6},{3},{4,8},{5},{7}} => [1,2,1,2,1,1] => [3,3,2] => 9
{{1,5},{2,3,4,8},{6},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,4,5},{2,3,8},{6},{7}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,2},{3,9},{4},{5},{6},{7},{8}} => [2,2,1,1,1,1,1] => [6,2,1] => 14
{{1,3},{2,5},{4,6,7},{8}} => [2,2,3,1] => [2,1,2,2,1] => 17
{{1,3,5},{2,7},{4,6},{8}} => [3,2,2,1] => [2,2,2,1,1] => 19
{{1,4,5,8},{2,3,7},{6}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,8},{2,3,4,6},{5,7}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,7},{2,3},{4,5,6,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,7},{2,3,5,6},{4,8}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,4,7,8},{2,3,5,6}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,5,7,8},{2,4},{3,6}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,5,7,8},{2,3},{4,6}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,5,6,8},{2,3},{4,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,5},{2},{3,4,6,8},{7}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,6},{2},{3},{4,5,7,8}} => [2,1,1,4] => [1,1,1,4,1] => 13
{{1,4},{2,6,7,8},{3},{5}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1},{2,5},{3,6,7,8},{4}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1,3,4,7},{2},{5,8},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,2,6},{3,7},{4,8},{5,10},{9}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,2,6},{3,7},{4,9},{5,10},{8}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,2,6},{3,8},{4,9},{5,10},{7}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,2,7},{3,8},{4,9},{5,10},{6}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,3,6},{2,4,8},{5,10},{7},{9}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,3,6},{2,4,9},{5,10},{7},{8}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,3,7},{2,4,8},{5,10},{6},{9}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,3,7},{2,4,9},{5,10},{6},{8}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,3,8},{2,4,9},{5,10},{6},{7}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,3,6},{2,5,10},{4,8},{7},{9}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,3,6},{2,5,10},{4,9},{7},{8}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,3,7},{2,5,10},{4,8},{6},{9}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,3,7},{2,5,10},{4,9},{6},{8}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,3,8},{2,5,10},{4,9},{6},{7}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,3,7},{2,6},{4,8},{5,10},{9}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,3,7},{2,6},{4,9},{5,10},{8}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,3,8},{2,6},{4,9},{5,10},{7}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,3,8},{2,7},{4,9},{5,10},{6}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,4,8},{2,5,10},{3,6},{7},{9}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,4,9},{2,5,10},{3,6},{7},{8}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,4,8},{2,5,10},{3,7},{6},{9}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,4,9},{2,5,10},{3,7},{6},{8}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,4,9},{2,5,10},{3,8},{6},{7}} => [3,3,2,1,1] => [3,2,1,2,1,1] => 31
{{1,4,8},{2,6},{3,7},{5,10},{9}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,4,9},{2,6},{3,7},{5,10},{8}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,4,9},{2,6},{3,8},{5,10},{7}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,4,9},{2,7},{3,8},{5,10},{6}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,5,10},{2,6},{3,7},{4,8},{9}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,5,10},{2,6},{3,7},{4,9},{8}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,5,10},{2,6},{3,8},{4,9},{7}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,5,10},{2,7},{3,8},{4,9},{6}} => [3,2,2,2,1] => [2,2,2,2,1,1] => 29
{{1,4,6},{2,3,5},{7,8}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,6,8},{2,3,4,5,7}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,2},{3,6,8},{4,5,7}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,6,7},{2,4,5,8},{3}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,2,7},{3,6,8},{4,5}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,3,5,8},{2,7},{4,6}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,4,5,8},{2,3,6},{7}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,7},{2,3,5},{4,6,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,5,7},{2,3,4,6,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,5},{2,4,6,7,8},{3}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,7},{2,4,5,6,8},{3}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,7,9},{2},{3},{4},{5},{6},{8}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,6,9},{2},{3},{4},{5},{7},{8}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,5,9},{2},{3},{4},{6},{7},{8}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,4,8},{2,3,5,6,7}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,3},{2,4,5,6,7},{8}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1},{2,5},{3,4,6,7,8}} => [1,2,5] => [1,1,1,1,2,2] => 16
{{1,4},{2,3,5,6,7},{8}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,2,4},{3,5,6,7},{8}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1},{2,4},{3,5,6,7,8,9,10}} => [1,2,7] => [1,1,1,1,1,1,2,2] => 29
{{1},{2,6},{3,4,5,7,8}} => [1,2,5] => [1,1,1,1,2,2] => 16
{{1},{2,3,4,6},{5,7,8}} => [1,4,3] => [1,1,2,1,1,2] => 18
{{1,5},{2,3,4,6,7},{8}} => [2,5,1] => [2,1,1,1,2,1] => 21
{{1,2,7},{3},{4,6,8},{5}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1,2,4,7,9},{3},{5,10},{6},{8}} => [5,1,2,1,1] => [3,3,1,1,1,1] => 33
{{1,2,5,7,10},{3},{4,8},{6},{9}} => [5,1,2,1,1] => [3,3,1,1,1,1] => 33
{{1,3,5,8,10},{2},{4,6},{7},{9}} => [5,1,2,1,1] => [3,3,1,1,1,1] => 33
{{1,3,5,7,9},{2},{4},{6},{8,10}} => [5,1,1,1,2] => [1,5,1,1,1,1] => 31
{{1},{2,4,6},{3},{5,7,8}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1,2,4,5,7},{3},{6,8}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,4,5},{2},{3,6,7,8}} => [3,1,4] => [1,1,1,3,1,1] => 19
{{1,3,4,6,8},{2},{5,7}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1},{2,5,7},{3},{4,6,8}} => [1,3,1,3] => [1,1,3,1,2] => 14
{{1,2},{3,5,7},{4,6,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,2,3},{4,6},{5,7,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,3,4,5,7},{2},{6,8}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,4,5,7,8},{2},{3,6}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,2,5,6,7},{3},{4,8}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,4,6,8},{2},{3,5,7}} => [4,1,3] => [1,1,3,1,1,1] => 21
{{1,8},{2,9},{3},{4},{5},{6},{7}} => [2,2,1,1,1,1,1] => [6,2,1] => 14
{{1},{2,7},{3,8},{4},{5},{6}} => [1,2,2,1,1,1] => [4,2,2] => 10
{{1,5,6},{2},{3,8},{4},{7}} => [3,1,2,1,1] => [3,3,1,1] => 16
{{1,3},{2},{4},{5},{6},{7},{8,9}} => [2,1,1,1,1,1,2] => [1,7,1] => 9
{{1},{2},{3},{4,6,8},{5,7}} => [1,1,1,3,2] => [1,2,1,4] => 8
{{1},{2},{3,5,8},{4,6},{7}} => [1,1,3,2,1] => [2,2,1,3] => 11
{{1,2,8},{3},{4},{5},{6},{7},{9}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,2,7},{3},{4},{5},{6},{8},{9}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,4,6},{2,3},{5,7,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,3,8},{2,4,5},{6,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,7},{3},{4,5,6,8}} => [3,1,4] => [1,1,1,3,1,1] => 19
{{1},{2,4,8},{3,5,6,7}} => [1,3,4] => [1,1,1,2,1,2] => 17
{{1,4,5,6,7},{2},{3,8}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1},{2,7},{3,6},{4},{5,8}} => [1,2,2,1,2] => [1,3,2,2] => 11
{{1,3,5},{2,4,6,7,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,5},{2},{3,7},{4},{6,8}} => [2,1,2,1,2] => [1,3,3,1] => 12
{{1,5,6,7},{2,4},{3,8}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,5,6},{2,4,8},{3,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,7},{3,8},{4},{5,6}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,2,6,7},{3},{4,8},{5}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,5},{2,3,4,7},{6,8}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,2,4,6,8},{3},{5,7}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,3,8},{2,4,5,6,7}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,3,4,6},{2,8},{5,7}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,3},{2,7},{4,5,6,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1},{2,7},{3},{4,5,6,8}} => [1,2,1,4] => [1,1,1,3,2] => 12
{{1,3,8},{2,6},{4,5,7}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,2,4},{3,6},{5,7,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,2,7},{3,4,6,8},{5}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,3,4,8},{2,7},{5,6}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1},{2,5},{3},{4,7},{6,8}} => [1,2,1,2,2] => [1,2,3,2] => 10
{{1,4,8},{2,3,7},{5,6}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2},{3,4,7},{5,6,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,4,7},{2,3},{5,6,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,3,7},{2,4},{5,6,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,3,7},{2,6,8},{4,5}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,7},{2,3,5,8},{4,6}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,2,6},{3,8},{4,5,7}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,2,8},{3,4,6},{5,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2},{3,5,7,8},{4,6}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,5,7,8},{2,6},{3,4}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,5,8},{2,7},{3,4,6}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,6,8},{2,3},{4,5,7}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,6,8},{2,5,7},{3,4}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,6,8},{2,4,7},{3,5}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2,6,7},{3},{4},{5,8}} => [4,1,1,2] => [1,4,1,1,1] => 19
{{1},{2,4},{3,5},{6,7,8}} => [1,2,2,3] => [1,1,2,2,2] => 13
{{1,4},{2,5,6,8},{3},{7}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,6},{2},{3},{4},{5},{7,8,9}} => [2,1,1,1,1,3] => [1,1,6,1] => 11
{{1,5},{2,3,4,6},{7,8}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,3,4},{2,8},{5,6,7}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,3,6,7},{2,8},{4,5}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,8},{2,3,6},{4,5,7}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,2,7},{3,4,5,6,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,2},{3,5,6},{4,7,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,5,6},{2,7,8},{3,4}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,4,5},{2,7,8},{3,6}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,7},{2,6},{3,4,5,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,2},{3,7},{4,5,6,8}} => [2,2,4] => [1,1,1,2,2,1] => 18
{{1,7},{2,5,6,8},{3,4}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,2,3,7},{4},{5,8},{6}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1,3,4},{2,6},{5,7,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,7},{2},{3,4,5,8},{6}} => [2,1,4,1] => [2,1,1,3,1] => 16
{{1,4},{2,3,5,6},{7},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,3,5},{2,4},{6},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,4},{2,5,6,7},{3},{8}} => [2,4,1,1] => [3,1,1,2,1] => 19
{{1,2,6},{3},{4},{5},{7},{8},{9}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,2,5},{3},{4},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1,2,4},{3},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1] => [7,1,1] => 15
{{1},{2},{3,4,5,7},{6,8}} => [1,1,4,2] => [1,2,1,1,3] => 13
{{1,4,7},{2},{3},{5,6,8}} => [3,1,1,3] => [1,1,4,1,1] => 16
{{1,6},{2,4,7,8},{3,5}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,3,4},{2,5},{6},{7,8}} => [3,2,1,2] => [1,3,2,1,1] => 18
{{1,3},{2,4,5},{6},{7,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,4},{2,3,5},{6},{7,8}} => [2,3,1,2] => [1,3,1,2,1] => 17
{{1,4,5},{2},{3,6,7},{8}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1},{2,5},{3,4,6,7},{8}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1},{2,4,5,6},{3,7},{8}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1,4,5},{2},{3,6,8},{7}} => [3,1,3,1] => [2,1,3,1,1] => 18
{{1},{2,3},{4},{5},{6},{7},{8,9}} => [1,2,1,1,1,1,2] => [1,6,2] => 8
{{1,2},{3},{4},{5},{6},{7},{8},{9,10}} => [2,1,1,1,1,1,1,2] => [1,8,1] => 10
{{1},{2,3,6},{4},{5,8},{7}} => [1,3,1,2,1] => [2,3,1,2] => 13
{{1},{2,3,7},{4},{5,8},{6}} => [1,3,1,2,1] => [2,3,1,2] => 13
{{1},{2,4},{3,7},{5},{6,8}} => [1,2,2,1,2] => [1,3,2,2] => 11
{{1},{2,5},{3},{4,6,8},{7}} => [1,2,1,3,1] => [2,1,3,2] => 11
{{1},{2,5},{3},{4,6,7},{8}} => [1,2,1,3,1] => [2,1,3,2] => 11
{{1,5,8},{2,3,7},{4,6}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,8},{2,5,6},{3,4,7}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,2},{3,4,6,8},{5,7}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,2,3,4,5,6,10},{7,8},{9}} => [7,2,1] => [2,2,1,1,1,1,1,1] => 41
{{1,3},{2,6,7},{4,5},{8}} => [2,3,2,1] => [2,2,1,2,1] => 18
{{1,3,7},{2,4,5},{6},{8}} => [3,3,1,1] => [3,1,2,1,1] => 20
{{1,4,6,7,8},{2},{3,5}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1,4},{2,3,6,8},{5,7}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,4,5},{2,3,6,7,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,6},{2},{3,4,5,7,8}} => [2,1,5] => [1,1,1,1,3,1] => 17
{{1,4,5},{2,3,6},{7,8}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,4,5},{2,3,8},{6,7}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,4,7},{2,3,8},{5,6}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,3,4},{2,7},{5,6,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,3,6,8},{2,7},{4,5}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1,2,8},{3,6},{4,5,7}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,5,6},{2,4},{3,7,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,7,8},{2,4,5},{3,6}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,2},{3,6,7},{4,5,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,6,7},{2,3},{4,5,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,6,7},{2,5,8},{3,4}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,4,8},{2,6,7},{3,5}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,5,6},{2,8},{3,4,7}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,6,7},{2,4,5},{3,8}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1},{2,4,8,10,12},{3},{5,7},{6},{9},{11}} => [1,5,1,2,1,1,1] => [4,3,1,1,1,2] => 38
{{1},{2,4,12},{3},{5,7,9,11},{6},{8},{10}} => [1,3,1,4,1,1,1] => [4,1,1,3,1,2] => 34
{{1},{2,4,12},{3},{5,11},{6,8,10},{7},{9}} => [1,3,1,2,3,1,1] => [3,1,2,3,1,2] => 32
{{1},{2,6,10,12},{3,5},{4},{7,9},{8},{11}} => [1,4,2,1,2,1,1] => [3,3,2,1,1,2] => 36
{{1},{2,6,12},{3,5},{4},{7,11},{8,10},{9}} => [1,3,2,1,2,2,1] => [2,2,3,2,1,2] => 32
{{1},{2,10,12},{3,7,9},{4,6},{5},{8},{11}} => [1,3,3,2,1,1,1] => [4,2,1,2,1,2] => 36
{{1},{2,10,12},{3,9},{4,8},{5,7},{6},{11}} => [1,3,2,2,2,1,1] => [3,2,2,2,1,2] => 34
{{1},{2,12},{3,5,9,11},{4},{6,8},{7},{10}} => [1,2,4,1,2,1,1] => [3,3,1,1,2,2] => 34
{{1},{2,12},{3,11},{4,8,10},{5,7},{6},{9}} => [1,2,2,3,2,1,1] => [3,2,1,2,2,2] => 32
{{1},{2,12},{3,11},{4,10},{5,9},{6,8},{7}} => [1,2,2,2,2,2,1] => [2,2,2,2,2,2] => 30
{{1,3,5},{2},{4},{6,8,10,12},{7},{9},{11}} => [3,1,1,4,1,1,1] => [4,1,1,4,1,1] => 36
{{1,3,5},{2},{4},{6,12},{7,9,11},{8},{10}} => [3,1,1,2,3,1,1] => [3,1,2,4,1,1] => 34
{{1,3,7},{2},{4,6},{5},{8,12},{9,11},{10}} => [3,1,2,1,2,2,1] => [2,2,3,3,1,1] => 34
{{1,3,5,9,11},{2},{4},{6,8},{7},{10},{12}} => [5,1,1,2,1,1,1] => [4,4,1,1,1,1] => 42
{{1,3,11},{2},{4,8,10},{5,7},{6},{9},{12}} => [3,1,3,2,1,1,1] => [4,2,1,3,1,1] => 38
{{1,3,11},{2},{4,10},{5,9},{6,8},{7},{12}} => [3,1,2,2,2,1,1] => [3,2,2,3,1,1] => 36
{{1,7,11},{2,6},{3,5},{4},{8,10},{9},{12}} => [3,2,2,1,2,1,1] => [3,3,2,2,1,1] => 38
{{1,9,11},{2,4,8},{3},{5,7},{6},{10},{12}} => [3,3,1,2,1,1,1] => [4,3,1,2,1,1] => 40
{{1,9},{2},{3},{4},{5},{6,7,8}} => [2,1,1,1,1,3] => [1,1,6,1] => 11
{{1,5},{2},{3},{4},{6},{7},{8,9}} => [2,1,1,1,1,1,2] => [1,7,1] => 9
{{1,2,4},{3,6,7,8},{5}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,4,8},{2},{3,6},{5},{7}} => [3,1,2,1,1] => [3,3,1,1] => 16
{{1,2,4},{3,5,6,8},{7}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,2,3,6},{4},{5,8},{7}} => [4,1,2,1] => [2,3,1,1,1] => 20
{{1},{2,4},{3,5,6,8},{7}} => [1,2,4,1] => [2,1,1,2,2] => 15
{{1},{2,5},{3,4,6},{7,8}} => [1,2,3,2] => [1,2,1,2,2] => 14
{{1,2},{3},{4,7},{5,6,8}} => [2,1,2,3] => [1,1,2,3,1] => 14
{{1,6,7},{2,3,5,8},{4}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,3,5,8},{2,4,6,7}} => [4,4] => [1,1,1,2,1,1,1] => 24
{{1,4},{2,3,6},{5,7,8}} => [2,3,3] => [1,1,2,1,2,1] => 19
{{1,5,7,8},{2,3,6},{4}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,2,3,6},{4},{5,7,8}} => [4,1,3] => [1,1,3,1,1,1] => 21
{{1,5,7,8},{2},{3,4,6}} => [4,1,3] => [1,1,3,1,1,1] => 21
{{1,3,4,6},{2},{5,7,8}} => [4,1,3] => [1,1,3,1,1,1] => 21
{{1,2,4},{3,5,7,8},{6}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1},{2,4,6},{3},{5,7},{8}} => [1,3,1,2,1] => [2,3,1,2] => 13
{{1,4,6},{2,3,5,8},{7}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,6},{2,3,5,8},{4,7}} => [2,4,2] => [1,2,1,1,2,1] => 20
{{1,3,6},{2,4,5,7,8}} => [3,5] => [1,1,1,1,2,1,1] => 23
{{1,3,5},{2,7,8},{4,6}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1,3,4},{2,5,7,8},{6}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,4,5,6},{2},{3,7,8}} => [4,1,3] => [1,1,3,1,1,1] => 21
{{1,2,5,7,8},{3},{4,6}} => [5,1,2] => [1,3,1,1,1,1] => 23
{{1},{2,3,6,8},{4,7},{5}} => [1,4,2,1] => [2,2,1,1,2] => 17
{{1,3,6},{2,4},{5,7,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,4,8},{2,5,7},{3,6}} => [3,3,2] => [1,2,1,2,1,1] => 21
{{1},{2,4,7},{3,5,6,8}} => [1,3,4] => [1,1,1,2,1,2] => 17
{{1},{2,4,5,7},{3,6,8}} => [1,4,3] => [1,1,2,1,1,2] => 18
{{1,2,6,8},{3},{4,5,7}} => [4,1,3] => [1,1,3,1,1,1] => 21
{{1,4,6,8},{2,3,5},{7}} => [4,3,1] => [2,1,2,1,1,1] => 23
{{1,3,6},{2,4,5,7},{8}} => [3,4,1] => [2,1,1,2,1,1] => 22
{{1,4,7},{2,5},{3,6,8}} => [3,2,3] => [1,1,2,2,1,1] => 20
{{1,2,5,7},{3,8},{4,6}} => [4,2,2] => [1,2,2,1,1,1] => 22
{{1},{2,3,4,6,7},{5,8}} => [1,5,2] => [1,2,1,1,1,2] => 19
{{1},{2,3,6},{4,7},{5},{8}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1},{2,4,7},{3,8},{5},{6}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1},{2,5,7},{3},{4,8},{6}} => [1,3,1,2,1] => [2,3,1,2] => 13
{{1},{2,4,7},{3,5},{6},{8}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1},{2,5,8},{3,6},{4},{7}} => [1,3,2,1,1] => [3,2,1,2] => 14
{{1},{2,4,6,7},{3,5},{8}} => [1,4,2,1] => [2,2,1,1,2] => 17
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,1,2,1 1,1,2,4,3,3,1 1,1,2,4,7,7,9,10,6,4,1 1,1,2,4,7,12,14,20,26,29,26,25,20,10,5,1 1,1,2,4,7,12,20,26,38,53,68,82,89,100,101,90,71,55,35,15,6,1
F1=1
F2=1+q
F3=1+q+2 q2+q3
F4=1+q+2 q2+4 q3+3 q4+3 q5+q6
F5=1+q+2 q2+4 q3+7 q4+7 q5+9 q6+10 q7+6 q8+4 q9+q10
F6=1+q+2 q2+4 q3+7 q4+12 q5+14 q6+20 q7+26 q8+29 q9+26 q10+25 q11+20 q12+10 q13+5 q14+q15
F7=1+q+2 q2+4 q3+7 q4+12 q5+20 q6+26 q7+38 q8+53 q9+68 q10+82 q11+89 q12+100 q13+101 q14+90 q15+71 q16+55 q17+35 q18+15 q19+6 q20+q21
Description
The major index of the composition.
The descents of a composition [c1,c2,…,ck] are the partial sums c1,c1+c2,…,c1+⋯+ck−1, excluding the sum of all parts. The major index of a composition is the sum of its descents.
For details about the major index see Permutations/Descents-Major.
The descents of a composition [c1,c2,…,ck] are the partial sums c1,c1+c2,…,c1+⋯+ck−1, excluding the sum of all parts. The major index of a composition is the sum of its descents.
For details about the major index see Permutations/Descents-Major.
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Description
The integer composition of block sizes of a set partition.
For a set partition of {1,2,…,n}, this is the integer composition of n obtained by sorting the blocks by their minimal element and then taking the block sizes.
For a set partition of {1,2,…,n}, this is the integer composition of n obtained by sorting the blocks by their minimal element and then taking the block sizes.
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