Identifier
-
Mp00128:
Set partitions
—to composition⟶
Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤ
Values
{{1}} => [1] => [1] => ([],1) => 1
{{1,2}} => [2] => [1] => ([],1) => 1
{{1,2,3}} => [3] => [1] => ([],1) => 1
{{1,2},{3}} => [2,1] => [1,1] => ([(0,1)],2) => 2
{{1,3},{2}} => [2,1] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3}} => [1,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4}} => [4] => [1] => ([],1) => 1
{{1,2,3},{4}} => [3,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,4},{3}} => [3,1] => [1,1] => ([(0,1)],2) => 2
{{1,3,4},{2}} => [3,1] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3,4}} => [1,3] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3},{4}} => [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4},{3}} => [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2},{3,4}} => [1,1,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,3,4,5}} => [5] => [1] => ([],1) => 1
{{1,2,3,4},{5}} => [4,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5},{4}} => [4,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3},{4,5}} => [3,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,5},{3}} => [4,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,4},{3,5}} => [3,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,5},{3,4}} => [3,2] => [1,1] => ([(0,1)],2) => 2
{{1,2},{3,4,5}} => [2,3] => [1,1] => ([(0,1)],2) => 2
{{1,2},{3,4},{5}} => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3,5},{4}} => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3},{4,5}} => [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5},{2}} => [4,1] => [1,1] => ([(0,1)],2) => 2
{{1,3,4},{2,5}} => [3,2] => [1,1] => ([(0,1)],2) => 2
{{1,3,5},{2,4}} => [3,2] => [1,1] => ([(0,1)],2) => 2
{{1,3},{2,4,5}} => [2,3] => [1,1] => ([(0,1)],2) => 2
{{1,3},{2,4},{5}} => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3},{2,5},{4}} => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3},{2},{4,5}} => [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5},{2,3}} => [3,2] => [1,1] => ([(0,1)],2) => 2
{{1,4},{2,3,5}} => [2,3] => [1,1] => ([(0,1)],2) => 2
{{1,4},{2,3},{5}} => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5},{2,3,4}} => [2,3] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3,4,5}} => [1,4] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3,4},{5}} => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,3},{4}} => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1},{2,3,5},{4}} => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,5},{3}} => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4},{2},{3,5}} => [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,4},{3}} => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1},{2,4,5},{3}} => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2},{3,4}} => [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2},{3,4,5}} => [1,1,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,3,4,5,6}} => [6] => [1] => ([],1) => 1
{{1,2,3,4,5},{6}} => [5,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,6},{5}} => [5,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4},{5,6}} => [4,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5,6},{4}} => [5,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5},{4,6}} => [4,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,6},{4,5}} => [4,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3},{4,5},{6}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3},{4,6},{5}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3},{4},{5,6}} => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,5,6},{3}} => [5,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,5},{3,6}} => [4,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,6},{3,5}} => [4,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,4},{3,5},{6}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4},{3,6},{5}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4},{3},{5,6}} => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5,6},{3,4}} => [4,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,5},{3,4},{6}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4,5,6}} => [2,4] => [1,1] => ([(0,1)],2) => 2
{{1,2},{3,4,5},{6}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3,4},{5}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4,6},{5}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5},{3,6},{4}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5},{3},{4,6}} => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3,5},{4}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,5,6},{4}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3},{4,5}} => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3},{4,5,6}} => [2,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3},{4,5},{6}} => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3},{4,6},{5}} => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4,5,6},{2}} => [5,1] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,5},{2,6}} => [4,2] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,6},{2,5}} => [4,2] => [1,1] => ([(0,1)],2) => 2
{{1,3,4},{2,5},{6}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4},{2,6},{5}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4},{2},{5,6}} => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5,6},{2,4}} => [4,2] => [1,1] => ([(0,1)],2) => 2
{{1,3,5},{2,4},{6}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,4,5,6}} => [2,4] => [1,1] => ([(0,1)],2) => 2
{{1,3},{2,4,5},{6}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6},{2,4},{5}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,4,6},{5}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5},{2,6},{4}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5},{2},{4,6}} => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6},{2,5},{4}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,5,6},{4}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6},{2},{4,5}} => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2},{4,5,6}} => [2,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2},{4,5},{6}} => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,6},{5}} => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5,6},{2,3}} => [4,2] => [1,1] => ([(0,1)],2) => 2
{{1,4,5},{2,3},{6}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,3,5,6}} => [2,4] => [1,1] => ([(0,1)],2) => 2
{{1,4},{2,3,5},{6}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,6},{2,3},{5}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
>>> Load all 1852 entries. <<<{{1,4},{2,3,6},{5}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,3,4,6}} => [2,4] => [1,1] => ([(0,1)],2) => 2
{{1,5},{2,3,4},{6}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,3,4,5}} => [2,4] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3,4,5,6}} => [1,5] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3,4,5},{6}} => [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,3,4},{5}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,6},{5}} => [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4},{5,6}} => [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6},{2,3},{4}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,3,6},{4}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,3,5},{4}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,5,6},{4}} => [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,5},{4,6}} => [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,6},{4,5}} => [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3},{4,5,6}} => [1,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3},{4},{5,6}} => [1,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5},{2,6},{3}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5},{2},{3,6}} => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,6},{2,5},{3}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,5,6},{3}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,6},{2},{3,5}} => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2},{3,5,6}} => [2,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2},{3,5},{6}} => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,6},{5}} => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6},{2,4},{3}} => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,4,6},{3}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,4,5},{3}} => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,5,6},{3}} => [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,5},{3,6}} => [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,6},{3,5}} => [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4},{3,5,6}} => [1,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4},{3},{5,6}} => [1,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6},{2},{3,4}} => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2},{3,4,6}} => [2,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2},{3,4},{6}} => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,6},{3,4}} => [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,5},{3,4,6}} => [1,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2},{3,4,5}} => [2,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,6},{3,4,5}} => [1,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2},{3,4,5,6}} => [1,1,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,6},{2},{3,4},{5}} => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,6},{4}} => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3},{4,6}} => [1,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,5},{4}} => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6},{3},{4,5}} => [1,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3,4,5,6,7}} => [7] => [1] => ([],1) => 1
{{1,2,3,4,5,6},{7}} => [6,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,7},{6}} => [6,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5},{6,7}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,6,7},{5}} => [6,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,6},{5,7}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,7},{5,6}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4},{5,6,7}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4},{5,6},{7}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4},{5,7},{6}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4},{5},{6,7}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,5,6,7},{4}} => [6,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5,6},{4,7}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5,7},{4,6}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5},{4,6,7}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5},{4,6},{7}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,5},{4,7},{6}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,5},{4},{6,7}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,6,7},{4,5}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,6},{4,5,7}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,6},{4,5},{7}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,7},{4,5,6}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3},{4,5,6,7}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,2,3},{4,5,6},{7}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,3,7},{4,5},{6}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3},{4,5,7},{6}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,3,6},{4,7},{5}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,6},{4},{5,7}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,7},{4,6},{5}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3},{4,6,7},{5}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,3,7},{4},{5,6}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3},{4},{5,6,7}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3},{4},{5,6},{7}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3},{4},{5,7},{6}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4,5,6,7},{3}} => [6,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,5,6},{3,7}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,5,7},{3,6}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,5},{3,6,7}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,5},{3,6},{7}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,5},{3,7},{6}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,5},{3},{6,7}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,6,7},{3,5}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,6},{3,5,7}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,6},{3,5},{7}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,7},{3,5,6}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,4},{3,5,6,7}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,2,4},{3,5,6},{7}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,4,7},{3,5},{6}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4},{3,5,7},{6}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,4,6},{3,7},{5}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,6},{3},{5,7}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,7},{3,6},{5}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4},{3,6,7},{5}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,4,7},{3},{5,6}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4},{3},{5,6,7}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4},{3},{5,6},{7}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4},{3},{5,7},{6}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5,6,7},{3,4}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,5,6},{3,4,7}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,5,6},{3,4},{7}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5,7},{3,4,6}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,5},{3,4,6,7}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,2,5},{3,4,6},{7}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,5,7},{3,4},{6}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5},{3,4,7},{6}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,6,7},{3,4,5}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,6},{3,4,5,7}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,2,6},{3,4,5},{7}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,7},{3,4,5,6}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,2},{3,4,5,6,7}} => [2,5] => [1,1] => ([(0,1)],2) => 2
{{1,2},{3,4,5,6},{7}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,7},{3,4,5},{6}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3,4,5,7},{6}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4,5},{6,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6,7},{3,4},{5}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3,4,7},{5}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,7},{3,4,6},{5}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3,4,6,7},{5}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4,6},{5,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4,7},{5,6}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4},{5,6,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,5,6},{3,7},{4}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5,6},{3},{4,7}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5,7},{3,6},{4}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5},{3,6,7},{4}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,5,7},{3},{4,6}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5},{3},{4,6,7}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5},{3},{4,6},{7}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5},{3},{4,7},{6}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,6,7},{3,5},{4}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3,5,7},{4}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,7},{3,5,6},{4}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3,5,6,7},{4}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,5,6},{4,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,5,7},{4,6}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,5},{4,6,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,6,7},{3},{4,5}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3},{4,5,7}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3},{4,5},{7}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,6,7},{4,5}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,6},{4,5,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,7},{3},{4,5,6}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,7},{4,5,6}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3},{4,5,6,7}} => [2,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3},{4,5,6},{7}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,7},{3},{4,5},{6}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3},{4,5,7},{6}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3},{4,6,7},{5}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4,5,6,7},{2}} => [6,1] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,5,6},{2,7}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,5,7},{2,6}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,5},{2,6,7}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,5},{2,6},{7}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5},{2,7},{6}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5},{2},{6,7}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,6,7},{2,5}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,6},{2,5,7}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,6},{2,5},{7}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,7},{2,5,6}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,4},{2,5,6,7}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,3,4},{2,5,6},{7}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,4,7},{2,5},{6}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4},{2,5,7},{6}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,4,6},{2,7},{5}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,6},{2},{5,7}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,7},{2,6},{5}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4},{2,6,7},{5}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,4,7},{2},{5,6}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4},{2},{5,6,7}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4},{2},{5,6},{7}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4},{2},{5,7},{6}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,5,6,7},{2,4}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,3,5,6},{2,4,7}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,5,6},{2,4},{7}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5,7},{2,4,6}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,5},{2,4,6,7}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,3,5},{2,4,6},{7}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,5,7},{2,4},{6}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5},{2,4,7},{6}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,6,7},{2,4,5}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,6},{2,4,5,7}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,3,6},{2,4,5},{7}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,7},{2,4,5,6}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,3},{2,4,5,6,7}} => [2,5] => [1,1] => ([(0,1)],2) => 2
{{1,3},{2,4,5,6},{7}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,7},{2,4,5},{6}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3},{2,4,5,7},{6}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,4,5},{6,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6,7},{2,4},{5}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6},{2,4,7},{5}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,7},{2,4,6},{5}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3},{2,4,6,7},{5}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,4,6},{5,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,4,7},{5,6}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,4},{5,6,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,5,6},{2,7},{4}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5,6},{2},{4,7}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5,7},{2,6},{4}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5},{2,6,7},{4}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,5,7},{2},{4,6}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5},{2},{4,6,7}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5},{2},{4,6},{7}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,5},{2},{4,7},{6}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,6,7},{2,5},{4}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6},{2,5,7},{4}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,7},{2,5,6},{4}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3},{2,5,6,7},{4}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,5,6},{4,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,5,7},{4,6}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,5},{4,6,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,6,7},{2},{4,5}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6},{2},{4,5,7}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6},{2},{4,5},{7}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,6,7},{4,5}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,6},{4,5,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,7},{2},{4,5,6}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,7},{4,5,6}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3},{2},{4,5,6,7}} => [2,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2},{4,5,6},{7}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,7},{2},{4,5},{6}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,5,7},{6}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,6,7},{5}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5,6,7},{2,3}} => [5,2] => [1,1] => ([(0,1)],2) => 2
{{1,4,5,6},{2,3,7}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,4,5,6},{2,3},{7}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,7},{2,3,6}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,4,5},{2,3,6,7}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,4,5},{2,3,6},{7}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,5,7},{2,3},{6}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5},{2,3,7},{6}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,6,7},{2,3,5}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,4,6},{2,3,5,7}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,4,6},{2,3,5},{7}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,7},{2,3,5,6}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,4},{2,3,5,6,7}} => [2,5] => [1,1] => ([(0,1)],2) => 2
{{1,4},{2,3,5,6},{7}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,7},{2,3,5},{6}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4},{2,3,5,7},{6}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,3,5},{6,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,6,7},{2,3},{5}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,6},{2,3,7},{5}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,7},{2,3,6},{5}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4},{2,3,6,7},{5}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,3,6},{5,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,3,7},{5,6}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,3},{5,6,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5,6,7},{2,3,4}} => [4,3] => [1,1] => ([(0,1)],2) => 2
{{1,5,6},{2,3,4,7}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,5,6},{2,3,4},{7}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5,7},{2,3,4,6}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,5},{2,3,4,6,7}} => [2,5] => [1,1] => ([(0,1)],2) => 2
{{1,5},{2,3,4,6},{7}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,7},{2,3,4},{6}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5},{2,3,4,7},{6}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,3,4},{6,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6,7},{2,3,4,5}} => [3,4] => [1,1] => ([(0,1)],2) => 2
{{1,6},{2,3,4,5,7}} => [2,5] => [1,1] => ([(0,1)],2) => 2
{{1,6},{2,3,4,5},{7}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7},{2,3,4,5,6}} => [2,5] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3,4,5,6,7}} => [1,6] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3,4,5,6},{7}} => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7},{2,3,4,5},{6}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,5,7},{6}} => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,5},{6,7}} => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6,7},{2,3,4},{5}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,6},{2,3,4,7},{5}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,3,4},{5,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7},{2,3,4,6},{5}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,6,7},{5}} => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,6},{5,7}} => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7},{2,3,4},{5,6}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,7},{5,6}} => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4},{5,6},{7}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,4},{5,7},{6}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,4},{5},{6,7}} => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6,7},{2,3},{4}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6},{2,3,7},{4}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5,7},{2,3,6},{4}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5},{2,3,6,7},{4}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,3,6},{4,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,3,7},{4,6}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,3},{4,6,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,6,7},{2,3,5},{4}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,6},{2,3,5,7},{4}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,3,5},{4,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7},{2,3,5,6},{4}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,5,6,7},{4}} => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,5,6},{4,7}} => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7},{2,3,5},{4,6}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,5,7},{4,6}} => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,5},{4,6},{7}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,5},{4,7},{6}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,5},{4},{6,7}} => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,3,7},{4,5}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,3},{4,5,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,7},{2,3,6},{4,5}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,6,7},{4,5}} => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,6},{4,5},{7}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,3},{4,5,6}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1},{2,3},{4,5,6,7}} => [1,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3},{4,5,6},{7}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,7},{4,5},{6}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3},{4,5,7},{6}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,6},{4,7},{5}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,6},{4},{5,7}} => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,7},{4,6},{5}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3},{4,6,7},{5}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,7},{4},{5,6}} => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3},{4},{5,6,7}} => [1,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3},{4},{5,6},{7}} => [1,2,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,3},{4},{5,7},{6}} => [1,2,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,4,5,6},{2,7},{3}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,6},{2},{3,7}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,7},{2,6},{3}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5},{2,6,7},{3}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,5,7},{2},{3,6}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5},{2},{3,6,7}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5},{2},{3,6},{7}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5},{2},{3,7},{6}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6,7},{2,5},{3}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,6},{2,5,7},{3}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,7},{2,5,6},{3}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4},{2,5,6,7},{3}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,5,6},{3,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,5,7},{3,6}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,5},{3,6,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,6,7},{2},{3,5}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,6},{2},{3,5,7}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,6},{2},{3,5},{7}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,6,7},{3,5}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,6},{3,5,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,7},{2},{3,5,6}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,7},{3,5,6}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4},{2},{3,5,6,7}} => [2,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2},{3,5,6},{7}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,7},{2},{3,5},{6}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,5,7},{6}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,6,7},{5}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6,7},{2,4},{3}} => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6},{2,4,7},{3}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5,7},{2,4,6},{3}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5},{2,4,6,7},{3}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,4,6},{3,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,4,7},{3,6}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,4},{3,6,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,6,7},{2,4,5},{3}} => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,6},{2,4,5,7},{3}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,4,5},{3,7}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7},{2,4,5,6},{3}} => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,5,6,7},{3}} => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,5,6},{3,7}} => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7},{2,4,5},{3,6}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,5,7},{3,6}} => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,5},{3,6},{7}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,5},{3,7},{6}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,5},{3},{6,7}} => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,4,7},{3,5}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,4},{3,5,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,7},{2,4,6},{3,5}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,6,7},{3,5}} => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,6},{3,5},{7}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,4},{3,5,6}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1},{2,4},{3,5,6,7}} => [1,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4},{3,5,6},{7}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,7},{3,5},{6}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4},{3,5,7},{6}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,6},{3,7},{5}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,6},{3},{5,7}} => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,7},{3,6},{5}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4},{3,6,7},{5}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,7},{3},{5,6}} => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4},{3},{5,6,7}} => [1,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4},{3},{5,6},{7}} => [1,2,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,4},{3},{5,7},{6}} => [1,2,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,5,6,7},{2},{3,4}} => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6},{2},{3,4,7}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6},{2},{3,4},{7}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,6,7},{3,4}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,6},{3,4,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5,7},{2},{3,4,6}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,7},{3,4,6}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5},{2},{3,4,6,7}} => [2,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2},{3,4,6},{7}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,7},{2},{3,4},{6}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,4,7},{6}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,5,7},{3,4}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,5},{3,4,7}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,7},{2,5,6},{3,4}} => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,5,6,7},{3,4}} => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,5,6},{3,4},{7}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,5},{3,4,6}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1},{2,5},{3,4,6,7}} => [1,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,5},{3,4,6},{7}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,7},{3,4},{6}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3,4,7},{6}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,7},{2},{3,4,5}} => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,7},{3,4,5}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,6},{2},{3,4,5,7}} => [2,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2},{3,4,5},{7}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,6},{3,4,5}} => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1},{2,6},{3,4,5,7}} => [1,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,6},{3,4,5},{7}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2},{3,4,5,6}} => [2,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,7},{3,4,5,6}} => [1,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2},{3,4,5,6,7}} => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,7},{2},{3,4,5},{6}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,7},{3,4,5},{6}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,7},{2},{3,4},{5}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6,7},{3,4},{5}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6},{3,4,7},{5}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,7},{3,4,6},{5}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2},{3,4},{5},{6,7}} => [1,1,2,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,6},{3,7},{4}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,6},{3},{4,7}} => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,7},{3,6},{4}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3,6,7},{4}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,7},{3},{4,6}} => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3},{4,6,7}} => [1,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3},{4,6},{7}} => [1,2,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,5},{3},{4,7},{6}} => [1,2,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6,7},{3,5},{4}} => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6},{3,5,7},{4}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,7},{3,5,6},{4}} => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2},{3,5},{4},{6,7}} => [1,1,2,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,6,7},{3},{4,5}} => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6},{3},{4,5,7}} => [1,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6},{3},{4,5},{7}} => [1,2,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,7},{3},{4,5,6}} => [1,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,7},{3},{4,5},{6}} => [1,2,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2},{3,6},{4},{5,7}} => [1,1,2,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2},{3,7},{4},{5,6}} => [1,1,2,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2},{3},{4,5},{6},{7,8}} => [1,1,1,2,1,2] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
{{1},{2},{3,4},{5},{6,8},{7}} => [1,1,2,1,2,1] => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
{{1},{2},{3,5},{4},{6,7,8}} => [1,1,2,1,3] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2},{3,7,8},{4},{5,6}} => [1,1,3,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2},{3,8},{4},{5,6,7}} => [1,1,2,1,3] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2},{3,5,8},{4},{6,7}} => [1,1,3,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2},{3,7,8},{4,6},{5}} => [1,1,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2},{3,8},{4,6,7},{5}} => [1,1,2,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2},{3,8},{4,5,6},{7}} => [1,1,2,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2},{3,4,5,6,7,8}} => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1},{2,3},{4},{5,6,7,8}} => [1,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3},{4,6,7,8},{5}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3},{4,5,6},{7,8}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3},{4,7,8},{5,6}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3},{4,5,8},{6,7}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3},{4,5,6,8},{7}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3},{4,5,6,7,8}} => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4},{3},{5,7,8},{6}} => [1,2,1,3,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,4},{3},{5,6,7,8}} => [1,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,5},{3},{6,7},{8}} => [1,3,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,4,5},{3},{6,8},{7}} => [1,3,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,4,5},{3},{6,7,8}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6,8},{3},{4,5},{7}} => [1,3,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,6,7,8},{3},{4,5}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,8},{3},{4,6,7},{5}} => [1,2,1,3,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,7,8},{3},{4,5,6}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,7},{3},{5,6},{8}} => [1,3,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,4,8},{3},{5,6},{7}} => [1,3,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,4,7,8},{3},{5,6}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,8},{3},{5,7},{6}} => [1,3,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,4,8},{3},{5,6,7}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,5,8},{3},{6,7}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,5,6,7,8},{3}} => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4},{5},{6,8},{7}} => [1,3,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,3,4},{5},{6,7,8}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,6,7,8},{3,4}} => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,5},{4},{6,7,8}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6,7,8},{3,5},{4}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,7},{4},{5,6},{8}} => [1,3,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,8},{3,5,6,7},{4}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,8},{4},{5,6,7}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,5,8},{4},{6,7}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,5,6,7,8},{4}} => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,8},{3,4,5},{6,7}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6,7,8},{3,4,5}} => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,6,7},{4,5},{8}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,8},{3,6,7},{4,5}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,6,8},{4,5},{7}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,4,6},{5},{7,8}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,7,8},{4,6},{5}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,8},{3,4,6,7},{5}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,4,6,7,8},{5}} => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,5,6},{7,8}} => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,8},{3,4,5,6},{7}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,8},{3,4,7},{5,6}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,4,8},{5,6},{7}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,8},{3,4,5,7},{6}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,4,8},{5,7},{6}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,4,5,7,8},{6}} => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,5,6,7},{8}} => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,8},{3,4,5,6,7}} => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,8},{5,6,7}} => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,5,8},{6,7}} => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,5,6,8},{7}} => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,5,6,7,8}} => [1,7] => [1,1] => ([(0,1)],2) => 2
{{1,2},{3},{4,5},{6,7,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3},{4,6,7,8},{5}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3},{4,5,6},{7,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3},{4,5,8},{6,7}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3},{4,5,6,8},{7}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3},{4,5,6,7,8}} => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4},{5,6,7,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3,5,6},{4},{7,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,7,8},{4},{5,6}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,5,8},{4},{6,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,5,6,7,8},{4}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,7,8},{4,5},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,6,8},{4,5},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,6,7,8},{4,5}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4,6},{5},{7,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,7,8},{4,6},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,4,8},{5},{6,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,4,6,7,8},{5}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4,5,6},{7,8}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4,8},{5,6},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,4,8},{5,7},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,4,5,7,8},{6}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4,5,6,7},{8}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,8},{4,5,6,7}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3,4,5,8},{6,7}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4,5,6,8},{7}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4,5,6,7,8}} => [2,6] => [1,1] => ([(0,1)],2) => 2
{{1,3},{2},{4,5},{6,7,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,6},{5},{7,8}} => [2,1,2,1,2] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,3},{2},{4,8},{5},{6,7}} => [2,1,2,1,2] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,3},{2},{4,6,7,8},{5}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,5,6},{7,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,7,8},{5,6}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,5,7,8},{6}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,8},{5,6,7}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,5,8},{6,7}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,5,6,8},{7}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,5,6,7,8}} => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4},{2},{5,7,8},{6}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4},{2},{5,6,8},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4},{2},{5,6,7,8}} => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2},{3,4},{6},{7,8}} => [2,1,2,1,2] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,5},{2},{3,4},{6,7,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,7,8},{2},{3,4},{5}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,7,8},{2},{3,4},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6,7},{2},{3,4},{8}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2},{3,4},{5,6,7}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6,8},{2},{3,4},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,5},{4},{7,8}} => [2,1,2,1,2] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,6,7,8},{2},{3,5},{4}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7,8},{2},{3,5,6},{4}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4,5},{2},{6,7},{8}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4,5},{2},{6,8},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4,5},{2},{6,7,8}} => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2},{3,4,5},{7,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7,8},{2},{3,4,5},{6}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2},{3,4,5},{6,7}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,8},{2},{3,4,5},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,7,8},{2},{4,5},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2},{3,6,7},{4,5}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,6,8},{2},{4,5},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7,8},{2},{3,4,6},{5}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,7,8},{2},{4,6},{5}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2},{3,4,6,7},{5}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,8},{2},{4,6,7},{5}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4,5,6},{2},{7,8}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,8},{2},{3,4,5,6},{7}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7,8},{2},{3,4,5,6}} => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,7},{2},{4,5,6},{8}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,8},{2},{4,5,6},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2},{3,4,7},{5,6}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4,8},{2},{5,6},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2},{3,4,5,7},{6}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,8},{2},{4,5,7},{6}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4,8},{2},{5,7},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2},{3,4,5,6,7}} => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5,8},{2},{6,7}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5,6,7,8},{2}} => [7,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3},{4},{5,6,8},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3},{4,6},{5},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3},{4,8},{5},{6,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3},{4,5,7,8},{6}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3},{4,5,6,7},{8}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3},{4,8},{5,6,7}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3},{4,5,8},{6,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,3},{4,5,6,8},{7}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3},{4,5,6,7,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,4},{2,3},{5},{6,7},{8}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,4},{2,3},{5},{6,8},{7}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,4},{2,3},{5,6,7,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5},{2,3},{4},{6,7},{8}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,5},{2,3},{4},{6,8},{7}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,5,6},{2,3},{4},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,3},{4},{5,6},{8}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,7,8},{2,3},{4},{5,6}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,8},{2,3},{4},{6,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6,7,8},{2,3},{4}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5},{2,3},{6},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6},{2,3},{5},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,8},{2,3},{5},{6,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6,7,8},{2,3},{5}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,7,8},{2,3},{6}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,6,7},{2,3},{8}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,8},{2,3},{5,6,7}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,6,8},{2,3},{7}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,6,7,8},{2,3}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,4},{3},{5,7,8},{6}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4},{3},{5,6,7},{8}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4},{3},{5,6,8},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4},{3},{5,6,7,8}} => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,4},{3},{6,7},{8}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,5},{2,4},{3},{6,8},{7}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,5,6},{2,4},{3},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,4},{3},{5,6},{8}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,7,8},{2,4},{3},{5,6}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,4},{3},{5,7},{6}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,5,8},{2,4},{3},{6,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6,7,8},{2,4},{3}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,4,5},{3},{7,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,4,5},{3},{6,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,6},{3},{4,5},{8}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,7,8},{2,6},{3},{4,5}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,7,8},{3},{4,5},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,6,7},{3},{4,5}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,6,8},{3},{4,5},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,7,8},{3},{4,6},{5}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,8},{3},{4,6,7},{5}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4,5,6},{3},{7,8}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7,8},{2,4,5,6},{3}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,8},{3},{4,5,6},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,7,8},{3},{4,5,6}} => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,7},{3},{5,6},{8}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,4,7},{3},{5,6}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4,8},{3},{5,6},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4,7,8},{3},{5,6}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,8},{3},{4,5,7},{6}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4,8},{3},{5,7},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,4,5,6,7},{3}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,8},{3},{4,5,6,7}} => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,5,8},{3},{6,7}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,5,6,7,8},{3}} => [7,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4},{5},{6,7},{8}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3,4},{5},{6,8},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3,4},{5,7,8},{6}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4},{5,6,7},{8}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4},{5,6,8},{7}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,3,4},{6,8},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,3,4},{5},{7,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,3,4},{5},{6,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,3,4},{5,6},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,3,4},{5,6},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,3,4},{5,7},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6,7},{2,3,4},{8}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,8},{2,3,4},{6,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5,6,8},{2,3,4},{7}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6,7,8},{2,3,4}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,5},{3,4},{6},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5},{3,4},{6,7,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3,4},{5},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,6,7},{3,4},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,8},{3,4},{5},{6,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,5,6},{3,4},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7,8},{2,5,6},{3,4}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,8},{2,5,7},{3,4},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5,6,8},{3,4},{7}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5,6,7,8},{3,4}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5},{4},{6,8},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3,5},{4},{6,7,8}} => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,3,5},{4},{7,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,3,5},{4},{6,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,7,8},{2,3,5},{4}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3,5},{4},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,6,7},{3,5},{4}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,8},{3,5},{4},{6,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,6,7,8},{3,5},{4}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,5,6},{4},{7,8}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,7},{4},{5,6},{8}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,3,7},{4},{5,6}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,8},{3,7},{4},{5,6}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3,8},{4},{5,6},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3,7,8},{4},{5,6}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,8},{4},{5,7},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,3,5,6,7},{4}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,8},{4},{5,6,7}} => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,5,6,7,8},{4}} => [7,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5},{6,7},{8}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5},{6,8},{7}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5},{6,7,8}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,6,8},{2,3,4,5},{7}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3,4,5},{7,8}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,7,8},{2,6},{3,4,5}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,8},{3,4,5},{6,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,6,7,8},{3,4,5}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,8},{2,3,6},{4,5},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7,8},{2,3,6},{4,5}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,8},{2,3,7},{4,5},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3,6,7},{4,5},{8}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,8},{2,3,6,7},{4,5}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,6,8},{4,5},{7}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,6,7,8},{4,5}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,6},{5},{7,8}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7,8},{2,3,4,6},{5}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,7,8},{3,4,6},{5}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,8},{2,3,7},{4,6},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3,7,8},{4,6},{5}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,8},{2,3,4,6,7},{5}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,8},{3,4,6,7},{5}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,8},{5},{6,7}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,6,7,8},{5}} => [7,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6},{7,8}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,7},{2,3,4,5,6},{8}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,8},{2,3,4,5,6},{7}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7,8},{2,3,4,5,6}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,2,7},{3,4,5,6},{8}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,7},{4,5,6},{8}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,8},{3,7},{4,5,6}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,8},{4,5,6},{7}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,7,8},{4,5,6}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,7},{5,6},{8}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,8},{2,3,4,7},{5,6}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,8},{3,4,7},{5,6}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,3,4,8},{5,6},{7}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,7,8},{5,6}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,8},{2,3,4,5,7},{6}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,8},{3,4,5,7},{6}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,8},{4,5,7},{6}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,8},{5,7},{6}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,7,8},{6}} => [7,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6,7},{8}} => [7,1] => [1,1] => ([(0,1)],2) => 2
{{1,8},{2,3,4,5,6,7}} => [2,6] => [1,1] => ([(0,1)],2) => 2
{{1,2,8},{3,4,5,6,7}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,8},{5,6,7}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,8},{6,7}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6,8},{7}} => [7,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6,7,8}} => [8] => [1] => ([],1) => 1
{{1,3,5,6,7,8},{2,4}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,6,7,8},{2,5}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,6,7,8},{3,5}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,5,7,8},{2,6}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,5,7,8},{3,6}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5,7,8},{4,6}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,5,6,8},{2,7}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,5,6,8},{3,7}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5,6,8},{4,7}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,6,8},{5,7}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,5,6,7},{2,8}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,5,6,7},{3,8}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5,6,7},{4,8}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,6,7},{5,8}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,7},{6,8}} => [6,2] => [1,1] => ([(0,1)],2) => 2
{{1,3,5,7,8},{2,4,6}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,5,7,8},{3,4,6}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,7,8},{2,5,6}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,7,8},{3,5,6}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,5,6,8},{2,4,7}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,5,6,8},{3,4,7}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,6,8},{2,5,7}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,6,8},{3,5,7}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,6,8},{4,5,7}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,5,8},{3,6,7}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5,8},{4,6,7}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,5,6,7},{2,4,8}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,5,6,7},{3,4,8}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,6,7},{2,5,8}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,6,7},{3,5,8}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,6,7},{4,5,8}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,5,7},{2,6,8}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,5,7},{3,6,8}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5,7},{4,6,8}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,7},{5,6,8}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,5,6},{3,7,8}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5,6},{4,7,8}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,6},{5,7,8}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,4,6,7,8},{2,5},{3}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6,7,8},{2,5},{4}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6,7,8},{2,4},{5}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5,7,8},{3,6},{4}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,7,8},{2,6},{5}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,7,8},{3,6},{5}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,7,8},{2,5},{6}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5,6,8},{2,7},{4}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5,6,8},{3,7},{4}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,6,8},{2,7},{5}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,6,8},{3,7},{5}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5,8},{2,7},{6}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5,6,8},{2,4},{7}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,6,8},{2,5},{7}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,5,8},{3,6},{7}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,6,7},{2,8},{5}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,6,7},{3,8},{5}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5,7},{2,8},{6}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,5,7},{3,8},{6}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,5,7},{4,8},{6}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5,6},{2,8},{7}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,5,6},{4,8},{7}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,6},{5,8},{7}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5,6,7},{2,4},{8}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,6,7},{2,5},{8}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,6,7},{3,5},{8}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,5,7},{3,6},{8}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,5,7},{4,6},{8}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,5,6},{4,7},{8}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,6},{5,7},{8}} => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6,8},{2,5,7},{4}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6,8},{3,5,7},{4}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5,8},{3,6,7},{4}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5,8},{3,4,7},{6}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,8},{2,5,7},{6}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5,8},{3,4,6},{7}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,8},{3,5,6},{7}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6,7},{3,5,8},{4}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6,7},{2,4,8},{5}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,7},{2,6,8},{3}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5,7},{2,6,8},{4}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,7},{2,6,8},{5}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,7},{3,6,8},{5}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5,7},{2,4,8},{6}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5,7},{3,4,8},{6}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,7},{3,5,8},{6}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5},{2,7,8},{6}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,5},{3,7,8},{6}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5,6},{2,4,8},{7}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,6},{4,5,8},{7}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,5},{3,6,8},{7}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5,7},{2,4,6},{8}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,6},{2,5,7},{8}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,5},{4,6,7},{8}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,7},{2,5,8},{3,6}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,7},{2,4,8},{5,6}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,6},{2,5,8},{3,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,6},{2,5,8},{4,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,6},{3,4,8},{5,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,5},{2,6,8},{3,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,5},{2,6,8},{4,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,5},{3,6,8},{4,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,4},{2,6,8},{5,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,5},{2,4,8},{6,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,5},{3,4,8},{6,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,4},{2,5,8},{6,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,4},{3,5,8},{6,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,6},{2,5,7},{3,8}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,6},{2,5,7},{4,8}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,4},{3,5,7},{6,8}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,5},{3,4,6},{7,8}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,4},{2,5,6},{7,8}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,4},{3,5,6},{7,8}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,5,8},{2},{4,6},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,7},{2,4},{3},{6,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,4,8},{3},{6,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,5,8},{4,6},{7}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,5,8},{3},{6,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,7},{2,5},{3},{6,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,6,7},{5,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,6},{5,7,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,7},{5,6,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,5,8},{6,7}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,4,8},{6,7}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5},{3},{4,7,8},{6}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5,7},{3},{4,8},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,5,7},{4},{6,8}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,8},{5,6,7}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6},{3,4,7},{5,8}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,3,7},{4},{5,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,6,7},{4,8},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,5,8},{4,7},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,3,8},{4,5},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3,4,8},{6,7}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4},{3,5,8},{6,7}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4},{3,6,7},{5,8}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,6,7},{4},{5,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,7,8},{4,5},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,6},{2,8},{4},{5,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,6},{2,7},{4},{5,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,8},{3,4,6},{5,7}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,3,6},{4},{5,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,3,6},{4},{5,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,7},{3,4,6},{5,8}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,6,8},{4,7},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,5,7},{4,8},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,8},{2,7},{3},{5,6}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,7},{2,8},{4},{5,6}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,7},{2},{4,5,8},{6}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,3,8},{4,6},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,3,8},{4},{5,6}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,4,5},{3,8},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6},{2,5},{3},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,7,8},{2},{3,6},{4}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,5,7},{3,6},{4}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5,7},{2},{3,8},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,5},{2,6},{4},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6,8},{2},{3,7},{5}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,4,6},{3,7},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,8},{2,5},{3},{6,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,5},{2,8},{4},{6,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,3,8},{4},{6,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,8},{2},{3,4,7},{5}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,3,8},{4,7},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,3,7},{4,8},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,3,6},{4},{7,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,8},{2,7},{3},{4,5}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,7},{2},{3,4,8},{6}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,6,8},{3,4},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,4,8},{3,7},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,4,7},{3,8},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,4,8},{3,6},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,4,8},{3,5},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,3,5},{4,8},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,3,6},{4,8},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,3,8},{4,7},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,3,6},{4,8},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,3,6},{4,7},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,3,5},{4,7},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,4,7},{3,5},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,4,7},{3,6},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,4,8},{3,6},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,4,8},{3,7},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,4,7},{3,8},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,4,6},{3,8},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,4,8},{3,5},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,3,5},{4,8},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,3,7},{4,8},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,5},{2},{4,6,8},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,6,8},{3},{5,7}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,6,8},{5,7}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,5,7},{2},{4,6},{8}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,7},{2},{4,6,8},{5}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,5,7},{2},{4,8},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,4,8},{5,7},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,5,7},{3,8},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,5,7},{4,8},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,4,6},{3},{5,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,8},{3,5,7},{4,6}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,4,6},{3,5},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,6,8},{3,5},{7}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,6,8},{3,5},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,4,8},{3},{5,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,4,7},{3},{5,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,4,7},{3},{6,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,6,8},{3,7},{5}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,5},{2,7},{4},{6,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,6,8},{3,5},{4}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,4,6},{5,8},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,5,6},{4,8},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5,6},{3},{4,8},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,6},{3},{4,5,8},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,3,8},{4,6},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4},{3,6},{5},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4,6},{3},{5,8},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4},{3,8},{5},{6,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,3,8},{5},{6,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4},{2,8},{5},{6,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,3,8},{5,7},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,3,6},{5},{7,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,3,6},{5,8},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,4,5},{3,7},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4},{2,6},{5},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,5,8},{3,4},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,4,5},{3,8},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,8},{2,5},{4},{6,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,7,8},{3,5},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,7},{2,8},{3},{5,6}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5},{3,7},{4},{6,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,3,7},{4},{6,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5},{2,7},{3},{6,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,6,7},{3},{5,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,6,8},{3},{4,5}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,8},{3,6},{4},{5,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,5,6},{3},{4,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7,8},{2,5},{3},{4,6}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,3,7},{5,8},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,6,7},{4,8},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,4,8},{3},{5,6}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,5,8},{3,4},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2},{3,4,6},{5,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2},{3,6},{4,5,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2},{3,5,6},{4,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,5},{4,7,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,7,8},{4,6}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,8},{4,6,7}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,8},{4,5,7}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,4,8},{5,7}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,6,8},{3},{4,7},{5}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6,8},{2},{3,7},{4}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,8},{2},{3,6,7},{4}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3,4,5,6,7,8},{9}} => [8,1] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3,4,5,6,7,8,9}} => [1,8] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6,7,8,9},{10}} => [9,1] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3,4,5,6,7,9},{8}} => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,5,6,7,8,9,10}} => [1,9] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6,7,8,9,10},{11}} => [10,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,8},{6,7},{9}} => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,5,6,9},{7,8}} => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,5,6,8,9},{7}} => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,5,6,7,8,10},{9}} => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,5,6,7,8,9,10,11}} => [1,10] => [1,1] => ([(0,1)],2) => 2
{{1,4,6,8},{2},{3,5},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,7,8},{2},{3,6},{5}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6,7},{2},{3,5},{8}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,5,8},{4,7},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,4,8},{5,6},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,5,8},{4,6},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,3,4},{5,8},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,5,6},{3,7},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,6,7},{3,8},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5},{3,6},{4},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,7},{2,8},{3},{4,5}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,3,6},{5,7},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,3,7},{5},{6,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4},{3,7},{5},{6,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4},{2,7},{5},{6,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,3,4},{5},{6,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,3,4},{5,7},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,5,7},{4,6},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,4,7},{5,6},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,7,8},{3},{4,6}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,4,5,6},{7,8}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,3,5,6},{7,8}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,3,5,7},{6,8}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,4,5,7},{6,8}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4,5,7},{6,8}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,4,5,6,7,8}} => [2,6] => [1,1] => ([(0,1)],2) => 2
{{1,4},{2,3,5,6,7,8}} => [2,6] => [1,1] => ([(0,1)],2) => 2
{{1,5},{2,3,4,6,7,8}} => [2,6] => [1,1] => ([(0,1)],2) => 2
{{1,2},{3,4,6,7},{5,8}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,4,6,7},{5,8}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,3,6,7},{5,8}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,3,6,7},{4,8}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,4},{5,6,7,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4},{2,5},{3,6,7,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3},{2,5},{4,6,7,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3,5},{4,6,7,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3,6},{4,5,7,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3},{2,6},{4,5,7,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4},{2,6},{3,5,7,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5},{2,6},{3,4,7,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3,5,6,8},{4,7}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,5,6,8},{4,7}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,5,6,8},{3,7}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,4,6,8},{3,7}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2},{3,5,6},{7,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,4,6},{7,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,4,7,8},{5}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,4,7,8},{6}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5},{2},{3,7,8},{6}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,7},{2},{3,4,8},{5}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2},{3,4,8},{5,6}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6,7},{2},{3,8},{5}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6},{2},{3,7,8},{5}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,5,7,8},{6}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,7},{2,3},{4},{5,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,7},{2,4},{3},{5,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,6,7},{4},{5,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,4,5},{3},{6,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,4,5},{3,6},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,8},{2},{3,5,6},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,6,8},{5,7}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,7},{2,3},{4},{6,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,6},{3},{4,7,8}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,6,7},{4},{5,8}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3},{4,6,7,8}} => [1,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3,6,7},{4,8}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4},{3,6,8},{5,7}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,7},{3},{5,6,8}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2},{3,4,5},{6,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6},{3,5,7},{4,8}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,6,7},{4,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,6},{4,7,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6},{3},{4,5,7,8}} => [1,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,4},{5,7,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,6},{3},{4,7,8},{5}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,4,7},{5,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,7},{4,6,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,6},{2,5},{4},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,4,6},{3},{7,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5},{2,6},{3},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5},{2,8},{3},{6,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,5,8},{3},{4,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,5,6},{3,7},{4}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,8},{2,6},{4},{5,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,6,7},{3},{4,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6},{2,8},{3},{4,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,7},{2},{3,6,8},{4}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,6,8},{4,7}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,8},{2,5},{3},{4,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,6,8},{3},{4,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,7},{2,6},{3},{4,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,5,7},{3},{4,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,8},{2,6},{3},{4,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,5,8},{3,6},{4}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,5,8},{3},{4,6}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,5,6},{3},{4,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,7},{2,5},{3},{4,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6},{2,7},{3},{4,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,8},{2,7},{3},{4,6}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,5,8},{3,7},{4}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,7,8},{3,6},{4}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,5,7},{3},{4,6}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,6,8},{3,7},{4}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,5,7},{3,8},{4}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,7},{2,8},{3},{4,6}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,7,8},{3,5},{4}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,5,6},{3,8},{4}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,6,7},{3,8},{4}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,3,5},{4,6},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,4,6},{3,5},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,6},{2},{4,7,8},{5}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,7,8},{4,5}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,6,7},{2},{4,8},{5}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,8},{2},{3,6,7},{5}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6},{2},{3,4,8},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,5,7,8},{4}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,7},{2},{3,5,8},{4}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,6,8},{3},{5,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2,4,6},{3},{5,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2},{3,6,8},{4,5}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,8},{2},{3,5,7},{4}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,5,7},{6,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,5,7},{4},{6,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,8},{2},{3,4,7},{6}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,4,7},{5},{6,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5,8},{3},{4,7},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,4,7},{5,8},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,7},{2,6},{4},{5,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,6},{3,7},{4},{5,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5},{3},{4,6,8},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,5,6},{4,8},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4,7},{3},{5,8},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,7},{2,5},{4},{6,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,7},{3,4},{5},{6,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,4,7},{5},{6,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,5,8},{3,7},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,3,4},{5,8},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,4,7},{5,8},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,4,6},{5},{7,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,5,6},{3,8},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5,8},{3},{4,6},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,5,8},{4,6},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,5,7},{4},{6,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,7},{3,5},{4},{6,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,7},{2,4},{5},{6,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,4,7},{5},{6,8}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,5,7},{3},{6,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,4,6},{5,8},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,5,8},{3,6},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6},{2,3,4,7},{8}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6},{2,3,4,7,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,6,7},{2,3,4,8},{5}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6,7},{2,4,8},{3}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,7},{2,4,6,8},{3}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,3},{4,6,7,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5,6},{2,3,4,8},{7}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,4},{3,5,7,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,6},{2,5},{3,4,7,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1},{2,4,7},{3},{5,8},{6}} => [1,3,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,7},{3,4,5,8},{6}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6},{2,8},{3},{5,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,7},{3,5,8},{4,6}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,4,7},{3,5},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,3,7},{4,5},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,7},{3,4,8},{5,6}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,6,8},{3,4},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,5},{3},{6,8},{7}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,5,6,7},{3,8},{4}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6},{2},{3,5,8},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2},{3,4},{5,6,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,7},{3},{4,5,8},{6}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2},{3,4,6},{5,7}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,8},{2,7},{4},{5,6}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,7,8},{4},{5,6}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4},{3,7,8},{5,6}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,6,8},{4},{5,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,8},{2,3},{4},{5,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,6,8},{4,7},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,6,8},{2},{4,7},{5}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,7},{2,6},{3},{5,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,5,6},{3},{7,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,6,7,8},{4}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5,8},{2},{3,7},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,4,6},{3,8},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,3,8},{4},{5,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6},{3,4,8},{5,7}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3},{4,5,7},{6,8}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3},{4,6,8},{5,7}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,5,6},{4,7},{8}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,5,7},{4,8},{6}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,4,6,7},{8}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,6,7},{3,4},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,5,7,8},{4,6}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,7},{2},{3,6},{8}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,5,6,8},{7}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,8},{2},{3,5,7},{6}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,8},{2,4},{3},{5,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,8},{2,6},{3},{5,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2},{3,4,6,8},{5}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,7},{3,4,5},{6,8}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6},{3,4,5,8},{7}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,4,5,7},{8}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,4},{3,5,6,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4},{2,7},{3,5,6,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,8},{2,6},{3,5,7}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6,8},{2,4},{3,5,7}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,8},{2,5,7},{4,6}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,6},{2,4,5},{3,7},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,7},{3,5,6},{4,8}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,3,8},{5,6},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,6},{3,8},{4},{5,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,6,7},{3,4,8}} => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6,7},{2,3,8},{4}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,7},{2,3,4,8},{6}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6,7},{2},{3,4,8}} => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2},{3,8},{4},{5,7}} => [2,1,2,1,2] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,5},{2,4,6},{3,7},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,3,5},{4,7},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6},{2,7},{3},{5,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,7},{2,3},{5},{6,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3,6,8},{4,7}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,6,7},{4,8},{5}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,5,8},{2},{4,7},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6},{2},{3,7,8},{4}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,7},{2},{3,5,8},{6}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,6,8},{3,7},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,6,8},{4},{5,7}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3},{4,6},{5,7,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,6,8},{3},{4,7}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,5,7},{3,8},{6}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6},{3,7,8},{4,5}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,6},{5,7,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,6,7},{3},{5,8}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3,7,8},{4,6}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,7},{2},{3,6,8},{5}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,4,5},{6,8},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,4,5},{6,7},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,7,8},{3},{5,6}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,8},{2,4},{5},{6,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,3,7},{4,6},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,4,5},{3,6},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,6,7},{5,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,8},{3,5,6},{4,7}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,6,7},{3},{4,8}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,7,8},{3,4},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,7},{3,4,6,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,7},{2},{3,8},{4,5,6}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,5,8},{3,7},{6}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5,6},{2},{3,8},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,5,6},{2},{4,8},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,6,7},{3,8},{5}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,7,8},{3,4},{6}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,5},{2},{4,7,8},{6}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,7,8},{4,6},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,6},{2,4},{5},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,6},{2},{4,5,8},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,4,7},{5,8},{6}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,4,6},{5,8},{7}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,5,8},{3,6},{7}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,4,5,8},{7}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,5},{4},{6,8},{7}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,4,5,6},{3,8},{7}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6},{3,5,7,8},{4}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,7,8},{3,6},{4}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4},{3,6,7,8},{5}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,3,7},{5,6},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,6},{2},{4,5,7},{8}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,3,5},{6,7},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,5,7},{3,4},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,3,5},{6,8},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3,6,8},{4},{5,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2},{3,6},{4,5,7}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2},{3,5,6},{4,7}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,8},{2},{3,4,6},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,4,8},{5},{6,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,3,6},{4,7},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,5,7},{3,6},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3,4,5,6,7,8,9}} => [9] => [1] => ([],1) => 1
{{1,2,3,4,5,6,7},{8,9}} => [7,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6},{7,8,9}} => [6,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6},{7,8},{9}} => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5},{6,7,8,9}} => [5,4] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5},{6,7,8},{9}} => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,6,7,8,9,10}} => [10] => [1] => ([],1) => 1
{{1,2,3,4,5,6,7,8},{9,10}} => [8,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6,7},{8,9,10}} => [7,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6,7},{8,9},{10}} => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,6},{7,8,9,10}} => [6,4] => [1,1] => ([(0,1)],2) => 2
{{1,2,3},{4,7},{5},{6,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5},{3},{4,6,7},{8}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5},{3,8},{4},{6,7}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,6},{3},{4,5,7},{8}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5,6},{3},{4,7},{8}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6},{3,4,7,8},{5}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,7},{5,6,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,6,7,8},{5}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,7},{4},{5,6,8}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,6},{4},{5,7,8}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3},{4,6,7},{5,8}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,5,6},{4,8},{7}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3,4,7,8},{6}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,3,6,8},{4,7}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,5},{3,4,7},{6,8}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,7},{2,6},{3,4,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,7},{2,3,6},{4,8}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5,7},{2,3,8},{4,6}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,7},{2,4,5,8},{3,6}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,4,5,8},{3,7}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,5,7},{3,6},{8}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5},{2,7},{3,6,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7},{2,5},{3,4,6,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1},{2,6},{3,4,5,7},{8}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,7},{3,6,8},{4,5}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,4,5,7},{3,8}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,7},{2,8},{3,4,6}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,6,8},{3},{4,7},{5}} => [1,3,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,3},{2},{4,7},{5},{6,8}} => [2,1,2,1,2] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,6},{2,4},{3},{5,7},{8}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,7},{3,5,6,8},{4}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,5},{3},{4,6},{8}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,7},{3,4,6,8},{5}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5,8},{2},{3,6},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4,6},{2},{5,8},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6},{3,5,8},{4,7}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,4,7},{3,6},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3,4,6,8},{7}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,6,8},{3,7},{4}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2},{3,4,7},{6,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4},{3,5,7},{6,8}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2,5},{3},{4,8},{6}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,7},{2,3,5},{4},{6,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,5,7},{3},{6,8}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,7,8},{3},{4,6}} => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4,5,6,7,8,9},{2}} => [8,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,9},{5,6,7,8}} => [5,4] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,5,6,7,8,9,10},{2}} => [9,1] => [1,1] => ([(0,1)],2) => 2
{{1,5,6,7},{2},{3,8},{4}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,5,6,7,8,9},{3}} => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,5,6,7,8,9,10},{3}} => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,5,6,7,8,9},{3,4}} => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,6,7,8},{2,3},{9}} => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,5},{4,6,7,8}} => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,6,8},{2,3,7}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,4},{2},{3,5,6,7,8}} => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4,5,6,7,8,9,10}} => [2,8] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4},{5,6,7,8,9,10}} => [4,6] => [1,1] => ([(0,1)],2) => 2
{{1,3},{2,5,6},{4},{7,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,7},{4,5,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2},{3,5},{4,6,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2},{3,5,6,8},{4}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,7},{2},{3,5,8},{4,6}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,5,7},{4,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2},{3,5,7},{4,6}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5,6},{2},{3,4,7},{8}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,7},{2,3,5,6},{8}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,3,5,7,8},{4}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,6},{2,3,7,8},{5}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5,6,8},{2},{4,7}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,5,7,8},{3,6}} => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,6,8},{3,5,7}} => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,7},{2,6},{3,5,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5,7},{2},{4,6,8}} => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6},{2},{4,5,7,8}} => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,5,8},{3,4,6,7}} => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6,8},{2,4,7},{3}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,4,5,7,8},{3}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,6,7},{3},{5,8}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5},{2,4,6,8},{7}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,3,5,6,8},{7}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,6,7},{2},{5,8}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,5,6,8},{4,7}} => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,7},{2,4,6,8},{5}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,3,5,7,8},{6}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2},{4,5,7},{6,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3},{4,5,7},{6,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3},{4,6,8},{5,7}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3},{4,6,7},{5,8}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6,7},{3},{4,5,8}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4,6},{3},{5,7},{8}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4,6},{2},{5,7},{8}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,5},{6,7,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,4,6},{5,7},{8}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,7,8},{3},{4,5}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,8},{2},{3,5},{4,6,7}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2},{3,5,8},{4,7}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,6,8},{3},{4,5,7}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,9},{2,3,4,5,6,7,8}} => [2,7] => [1,1] => ([(0,1)],2) => 2
{{1,8},{2,3,4,5,6,7},{9}} => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,7},{3,6},{4},{5,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,10},{2,3,4,5,6,7,8,9}} => [2,8] => [1,1] => ([(0,1)],2) => 2
{{1,9},{2,3,4,5,6,8},{7}} => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,11},{2,3,4,5,6,7,8,9,10}} => [2,9] => [1,1] => ([(0,1)],2) => 2
{{1,10},{2,3,4,5,6,7,9},{8}} => [2,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,9},{2,3,4,5,8},{6,7}} => [2,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,9},{2,3,4,5,7,8},{6}} => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7},{2,3,5},{4,6},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,5,6},{4,7},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5,8},{3},{4,6,7}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,6,7},{3,5},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,7,8},{3,6},{5}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4},{3,5,6},{7,8}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6},{2,3,8},{5,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4},{2},{3,5,6,7},{8}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,6},{2,7},{4,5,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,6},{2,3,5,7,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,6},{3},{5,7,8}} => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6},{2,4,7},{3,8}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,3,6,7},{4},{5,8}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,6,7,8},{3,5}} => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3,4,5,7,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,5,8},{2},{3,4,6,7}} => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,5,8},{4,7},{6}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,7},{2,3,5,6,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6,7,9},{8}} => [8,1] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3,4,5,6,7,8},{9}} => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,6,7,8,10},{9}} => [9,1] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3,4,5,6,7,8,9},{10}} => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2},{3,4,5,6,7,8},{9}} => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,6,7,8,9,11},{10}} => [10,1] => [1,1] => ([(0,1)],2) => 2
{{1,6},{2,3,4,5,7,8}} => [2,6] => [1,1] => ([(0,1)],2) => 2
{{1,2,6},{3,4,5,8},{7}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,8},{2,3,5,6},{7}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,3,4,8},{6,7}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,8},{2,3,5},{6,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,4},{3,5,6,7,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,5,8},{2,3,4,6,7}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,3,4},{2,5,6,7,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,4,6,7},{2,3,8},{5}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,8},{2,4,6,7},{5}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5},{2,8},{4,6,7}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,7,8},{2,3,6},{5}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3,5},{4,7,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5},{3,6},{4,7,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7,8},{2,3,5},{4,6}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,7,8},{2,5},{3,4,6}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7,8},{2,4,6},{3,5}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,3,5,6,7,8,9,10},{4}} => [9,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,6,7,8,9,10},{5}} => [9,1] => [1,1] => ([(0,1)],2) => 2
{{1,4,8},{2,3,5,7},{6}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5},{3,4,6,7,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,5,6,7},{2,9},{8}} => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,7},{6,8},{9}} => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5,6,8},{2,9},{7}} => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5,6,9},{2,8},{7}} => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5,6,7,8},{2,10},{9}} => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5,6,7,8,9,10,11},{2}} => [10,1] => [1,1] => ([(0,1)],2) => 2
{{1,2},{3,4,5,6,7,8,9}} => [2,7] => [1,1] => ([(0,1)],2) => 2
{{1,2,3},{4,5,6,7,8,9}} => [3,6] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4},{5,6,7,8,9}} => [4,5] => [1,1] => ([(0,1)],2) => 2
{{1},{2},{3,4,5,6,7,8,9}} => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3,5,6,7,8,9},{4}} => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,5,6,7},{3},{8,9}} => [6,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3},{4,5,6,7,8,9,10}} => [3,7] => [1,1] => ([(0,1)],2) => 2
{{1,2,3},{4,5,7,8,9},{6}} => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,5,6},{4},{7,8,9}} => [5,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4},{5,6,7,9},{8}} => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1},{2},{3,5,6},{4,8},{7}} => [1,1,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,2,5,7},{3},{4,6,8}} => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7},{2,3,4,5,6,8}} => [2,6] => [1,1] => ([(0,1)],2) => 2
{{1,4,6,7,8},{2,3,5}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,6,7,8},{2,4,5}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,6},{2,5,7,8},{3,4}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5},{2,6},{4,7,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,7,8},{2,3,6}} => [5,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,7},{2,4,6},{5,8}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5,7},{2,3,6,8},{4}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,7},{2,4,5,8},{6}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,7},{2,4,5,6,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,5,8},{2,4,6},{3,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,6},{2,3,4,7,8},{5}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,5,7,8},{4,6}} => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,5,7},{4,6},{8}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,5,7},{4,6,8}} => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,5,7},{6,8}} => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,5,8},{4,6,7}} => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,6,8},{4,5},{7}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,7,8},{2},{3,5},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,7,8},{3,5},{6}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,7,8},{3,6},{5}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,7,8},{5,6}} => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,4,6,8},{5,7}} => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,5,6,8},{7,9}} => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6,8},{2,3,7},{4}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6},{2,3},{4,7,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6,7,8,9},{2,3,4,5}} => [5,4] => [1,1] => ([(0,1)],2) => 2
{{1,3},{2,4,5,6,8},{7}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6,7},{2,3,4,5,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,4,5},{2,3,7,8},{6}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,8},{2,3,6,7},{5}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,7},{2,6},{4,5,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3,7},{4,5,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3},{4,7},{5,6,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,6,7,8},{3,4}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3,5,7,8},{4}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,6},{4,5,7,8}} => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7,8},{2,4},{3,5,6}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,6,8,9},{7}} => [8,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,7,8,9},{6}} => [8,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,6,7,8,9},{5}} => [8,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,5,6,7,8,9},{4}} => [8,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,4,5,6,7,8,9},{3}} => [8,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6,7,9,10},{8}} => [9,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,9},{6},{7,8}} => [6,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,6,8,9,10},{7}} => [9,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,9},{5},{6,7,8}} => [5,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,7,8,9,10},{6}} => [9,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,9},{4},{5,6,7,8}} => [4,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,9},{3},{4,5,6,7,8}} => [3,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,9},{2},{3,4,5,6,7,8}} => [2,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,5,6,7,8,9,10},{3}} => [9,1] => [1,1] => ([(0,1)],2) => 2
{{1,3},{2,5,8},{4},{6,7}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4},{3,5,6,7,8}} => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,6},{3},{5,8},{7}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,5},{2,6},{3},{4,8},{7}} => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,4,6},{2},{3,5,7},{8}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2},{3,7},{5},{6,8}} => [2,1,2,1,2] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,4,5,8},{2,3,7},{6}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,8},{2,3,4,6},{5,7}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7},{2,3},{4,5,6,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,7},{2,3,5,6},{4,8}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2},{3,4,6,8},{7}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3,6,7,8},{4}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,4,7},{2},{5,8},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6},{2,3,5},{7,8}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,6,8},{2,3,4,5,7}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,6,7},{2,4,5,8},{3}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,7},{3,6,8},{4,5}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,5,8},{2,3,6},{7}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,7},{2,3,4,6,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,5},{2,4,6,7,8},{3}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7},{2,4,5,6,8},{3}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,8},{2,3,5,6,7}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,3},{2,4,5,6,7},{8}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4},{3,5,6,7,8,9}} => [1,2,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,5},{3,4,6,7,8}} => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,3,5,6,7},{8}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4},{3,5,6,7},{8}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,4,5,6,7,8},{9}} => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4},{3,5,6,7,8,9,10}} => [1,2,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,5},{3,4,6,7,8,9}} => [1,2,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,5},{4,6,7,8,9}} => [1,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,6},{3,4,5,7,8}} => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,6},{5,7,8}} => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5},{2,3,4,6,7},{8}} => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,3,5,6,7,8},{9}} => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4},{3,5,6,7,8},{9}} => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,4,5,6,7,8,9},{10}} => [2,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,7},{3},{4,6,8},{5}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,5,8},{3,9},{4},{6,10},{7}} => [4,2,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,2,6,9},{3,7},{4},{5,10},{8}} => [4,2,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,3,6,10},{2,7},{4},{5,8},{9}} => [4,2,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,3,6,8},{2},{4,9},{5},{7,10}} => [4,1,2,1,2] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,4,7,10},{2,5},{3},{6,8},{9}} => [4,2,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,4,6,9},{2},{3,7},{5},{8,10}} => [4,1,2,1,2] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,3,6,9},{2,10},{4},{5,11},{7},{8,12}} => [4,2,1,2,1,2] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
{{1,3,7,10},{2,8},{4},{5,11},{6},{9,12}} => [4,2,1,2,1,2] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
{{1,4,7,11},{2,8},{3},{5,9},{6},{10,12}} => [4,2,1,2,1,2] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
{{1,5,8,11},{2,6},{3},{4,9},{7},{10,12}} => [4,2,1,2,1,2] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
{{1},{2,4,6},{3},{5,7,8}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,4,5,7},{3},{6,8}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5},{2},{3,6,7,8}} => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,6,8},{2},{5,7}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,5,7},{3},{4,6,8}} => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3},{4,6},{5,7,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5,7},{2},{6,8}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,7,8},{2},{3,6}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5,6,7},{3},{4,8}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,6,8},{2},{3,5,7}} => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,6,9},{7,8}} => [7,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6,7,10},{8,9}} => [8,2] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6,7,8,11},{9,10}} => [9,2] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3,4,5,6,7,10},{8,9}} => [1,7,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5,6,9},{2},{7,8}} => [6,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2},{3,5,8},{4,6},{7}} => [1,1,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,4,5,6,7,8,9},{2,3}} => [7,2] => [1,1] => ([(0,1)],2) => 2
{{1,5,6,7,8,9},{2,3,4}} => [6,3] => [1,1] => ([(0,1)],2) => 2
{{1,7,8,9},{2,3,4,5,6}} => [4,5] => [1,1] => ([(0,1)],2) => 2
{{1,8,9},{2,3,4,5,6,7}} => [3,6] => [1,1] => ([(0,1)],2) => 2
{{1,4,5,6,7,8,9,10},{2,3}} => [8,2] => [1,1] => ([(0,1)],2) => 2
{{1,5,6,7,8,9},{2,4},{3}} => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6,7,8,9,10},{2,3,4}} => [7,3] => [1,1] => ([(0,1)],2) => 2
{{1,6,7,8,9},{2,3,5},{4}} => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6,7,8,9,10},{2,3,4,5}} => [6,4] => [1,1] => ([(0,1)],2) => 2
{{1,7,8,9},{2,3,4,6},{5}} => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,8,9},{2,3,4,5,7},{6}} => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,8,9,10},{2,3,4,5,6,7}} => [4,6] => [1,1] => ([(0,1)],2) => 2
{{1,9,10},{2,3,4,5,6,7,8}} => [3,7] => [1,1] => ([(0,1)],2) => 2
{{1,2,9},{3,4,5,6,7,8}} => [3,6] => [1,1] => ([(0,1)],2) => 2
{{1},{2,3,4,5,6,7},{8,9}} => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,6},{2,3},{5,7,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,8},{2,4,5},{6,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2,7},{3},{4,5,6,8}} => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,8},{3,5,6,7}} => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,6,7},{2},{3,8}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,5},{2,4,6,7,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,5},{2},{3,7},{4},{6,8}} => [2,1,2,1,2] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,5,6},{2,4,8},{3,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1},{2,3,4,5,9},{6,7},{8}} => [1,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,7},{3,8},{4},{5,6}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,6,7},{3},{4,8},{5}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,5},{2,3,4,7},{6,8}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4,6,8},{3},{5,7}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,8},{2,4,5,6,7}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,3},{2,7},{4,5,6,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1},{2,7},{3},{4,5,6,8}} => [1,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,8},{2,6},{4,5,7}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4},{3,6},{5,7,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,7},{3,4,6,8},{5}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,8},{2,3,7},{5,6}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,7},{2,3},{5,6,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,7},{2,4},{5,6,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,7},{2,6,8},{4,5}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,7},{2,3,5,8},{4,6}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6},{3,8},{4,5,7}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,8},{3,4,6},{5,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3,5,7,8},{4,6}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,8},{2,7},{3,4,6}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6,8},{2,3},{4,5,7}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6,8},{2,5,7},{3,4}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,6,8},{2,4,7},{3,5}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5},{2,3,4,6},{7,8}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4},{2,8},{5,6,7}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,7},{3,4,5,6,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,5,6},{2,7,8},{3,4}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,5},{2,7,8},{3,6}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,7},{2,6},{3,4,5,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3,7},{4,5,6,8}} => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,7},{2,5,6,8},{3,4}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,7},{4},{5,8},{6}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2,3,9},{4,5,6,7,8}} => [4,5] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,9},{6,7,8}} => [6,3] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5,6},{7,9},{8}} => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,10},{3,4,5,6,7,8,9}} => [3,7] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,5},{6,7,9},{8}} => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,10},{4,5,6,7,8,9}} => [4,6] => [1,1] => ([(0,1)],2) => 2
{{1,2,3},{4,5,6,7,9},{8}} => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,10},{6,7,8,9}} => [6,4] => [1,1] => ([(0,1)],2) => 2
{{1,2},{3,4,5,6,7,9},{8}} => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,6,10},{7,8,9}} => [7,3] => [1,1] => ([(0,1)],2) => 2
{{1,3,4,5,6,7},{2},{8,9}} => [6,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4},{2,6},{5,7,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5,6},{2,8,9},{7}} => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5,6},{2},{7,8,9}} => [5,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,5,6,7,8},{2},{9,10}} => [7,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7},{2},{3,4,5,8},{6}} => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,5},{2,4},{6},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6},{2,4,7,8},{3,5}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4},{2,5},{6},{7,8}} => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2,4,5},{6},{7,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4},{2,3,5},{6},{7,8}} => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5},{2},{3,6,7},{8}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3,4,6,7},{8}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4,5,6},{3,7},{8}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,5},{2},{3,6,8},{7}} => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,3,6},{4},{5,8},{7}} => [1,3,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,3,7},{4},{5,8},{6}} => [1,3,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,5},{3},{4,6,8},{7}} => [1,2,1,3,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,5},{3},{4,6,7},{8}} => [1,2,1,3,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,5,8},{2,3,7},{4,6}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,2},{3,4,6,8},{5,7}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,9},{6,7},{8}} => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,6,7,8,10,11},{9}} => [10,1] => [1,1] => ([(0,1)],2) => 2
{{1,2,3,4,8,9},{5,7},{6}} => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,7,9},{5,6},{8}} => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,6,10},{7,8},{9}} => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3},{2,6,7},{4,5},{8}} => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,4,6,7,8},{2},{3,5}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4},{2,3,6,8},{5,7}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5},{2,3,6,7,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,6},{2},{3,4,5,7,8}} => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5},{2,3,6},{7,8}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,5},{2,3,8},{6,7}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,7},{2,3,8},{5,6}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,4},{2,7},{5,6,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,8},{3,6},{4,5,7}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,6},{2,4},{3,7,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,7,8},{2,4,5},{3,6}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,6,7},{2,3},{4,5,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6,7},{2,5,8},{3,4}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,4,8},{2,6,7},{3,5}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,5,6},{2,8},{3,4,7}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6,7},{2,4,5},{3,8}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1},{2,6,10},{3,5},{4},{7,9},{8}} => [1,3,2,1,2,1] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
{{1},{2,10},{3,5,9},{4},{6,8},{7}} => [1,2,3,1,2,1] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
{{1,3},{2},{4,6,10},{5},{7,9},{8}} => [2,1,3,1,2,1] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
{{1,3,7},{2},{4,6},{5},{8,10},{9}} => [3,1,2,1,2,1] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
{{1,7},{2,6},{3,5},{4},{8,10},{9}} => [2,2,2,1,2,1] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
{{1},{2,4,8,12},{3},{5,7},{6},{9,11},{10}} => [1,4,1,2,1,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
{{1},{2,4,12},{3},{5,7,11},{6},{8,10},{9}} => [1,3,1,3,1,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
{{1},{2,8,12},{3,7},{4,6},{5},{9,11},{10}} => [1,3,2,2,1,2,1] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
{{1},{2,12},{3,7,11},{4,6},{5},{8,10},{9}} => [1,2,3,2,1,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
{{1},{2,12},{3,11},{4,6,10},{5},{7,9},{8}} => [1,2,2,3,1,2,1] => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
{{1,3},{2},{4,8,12},{5,7},{6},{9,11},{10}} => [2,1,3,2,1,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
{{1,3},{2},{4,12},{5,7,11},{6},{8,10},{9}} => [2,1,2,3,1,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
{{1,3,5},{2},{4},{6,8,12},{7},{9,11},{10}} => [3,1,1,3,1,2,1] => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
{{1,5},{2,4},{3},{6,8,12},{7},{9,11},{10}} => [2,2,1,3,1,2,1] => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
{{1,3,5,9},{2},{4},{6,8},{7},{10,12},{11}} => [4,1,1,2,1,2,1] => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
{{1,3,9},{2},{4,8},{5,7},{6},{10,12},{11}} => [3,1,2,2,1,2,1] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
{{1,5,9},{2,4},{3},{6,8},{7},{10,12},{11}} => [3,2,1,2,1,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
{{1,9},{2,4,8},{3},{5,7},{6},{10,12},{11}} => [2,3,1,2,1,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
{{1,9},{2,8},{3,7},{4,6},{5},{10,12},{11}} => [2,2,2,2,1,2,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
{{1,2,4},{3,6,7,8},{5}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4},{3,5,6,8},{7}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,6},{4},{5,8},{7}} => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,4},{3,5,6,8},{7}} => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1},{2,5},{3,4,6},{7,8}} => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,2},{3},{4,7},{5,6,8}} => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,6,7},{2,3,5,8},{4}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,7,8},{2,3,6},{4}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,6},{4},{5,7,8}} => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,5,7,8},{2},{3,4,6}} => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,4,6},{2},{5,7,8}} => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4},{3,5,7,8},{6}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,6},{3},{5,7},{8}} => [1,3,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1,4,6},{2,3,5,8},{7}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,6},{2,3,5,8},{4,7}} => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6},{2,4,5,7,8}} => [3,5] => [1,1] => ([(0,1)],2) => 2
{{1,3,5},{2,7,8},{4,6}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1,3,4},{2,5,7,8},{6}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,5,6},{2},{3,7,8}} => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,5,7,8},{3},{4,6}} => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,6,8},{4,7},{5}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3,6},{2,4},{5,7,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,8},{2,5,7},{3,6}} => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 4
{{1},{2,4,7},{3,5,6,8}} => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,4,5,7},{3,6,8}} => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,6,8},{3},{4,5,7}} => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,6,8},{2,3,5},{7}} => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,3,6},{2,4,5,7},{8}} => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,4,7},{2,5},{3,6,8}} => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,3,4,6,7},{5,8}} => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,5,7},{6},{8,9}} => [6,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1},{2,5,7},{3},{4,8},{6}} => [1,3,1,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
{{1},{2,4,6,7},{3,5},{8}} => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
{{1,3},{2},{4,5,6,7,8,9}} => [2,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,4},{3},{5,6,7,8,9}} => [3,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,5},{4},{6,7,8,9}} => [4,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
{{1,2,3,4,6},{5},{7,8,9}} => [5,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
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Generating function
$F_{1} = q$
Description
The pebbling number of a connected graph.
Map
to composition
Description
The integer composition of block sizes of a set partition.
For a set partition of $\{1,2,\dots,n\}$, this is the integer composition of $n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.
For a set partition of $\{1,2,\dots,n\}$, this is the integer composition of $n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
Map
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
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