Identifier
-
Mp00295:
Standard tableaux
—valley composition⟶
Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001060: Graphs ⟶ ℤ
Values
[[1,3,5],[2,4]] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5],[2],[4]] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3],[2,5],[4]] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,6],[2,5]] => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,6],[3,5]] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,6],[2],[5]] => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,6],[3],[5]] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4],[2,5,6]] => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,5,6]] => [3,2,1] => [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
[[1,3,6],[2,4],[5]] => [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
[[1,3,4],[2,6],[5]] => [2,3,1] => [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
[[1,4,6],[2],[3],[5]] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6],[2],[4],[5]] => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2,4],[5,6]] => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2],[3,4],[5,6]] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4],[2,6],[3],[5]] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2,6],[4],[5]] => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6,7],[2,4]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,6,7],[2,5]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,7],[2,6]] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,7],[3,6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,5,7],[4,6]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6,7],[2],[4]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,6,7],[2],[5]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,7],[2],[6]] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,7],[3],[6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,5,7],[4],[6]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,7],[2,4,6]] => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,5,7],[3,4,6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,7],[2,5,6]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6],[2,4,7]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,6],[2,5,7]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,6,7]] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5],[3,6,7]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,5],[4,6,7]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,7],[2,5],[4]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,6,7],[2,4],[5]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5,7],[2,6],[3]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,7],[2,6],[4]] => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,5,7],[3,6],[4]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,7],[2,6],[5]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,7],[2,4],[6]] => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,5,7],[3,4],[6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,7],[2,5],[6]] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,7],[3,5],[6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,7],[4,5],[6]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6],[2,7],[4]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,6],[2,7],[5]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,7],[6]] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5],[3,7],[6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,5],[4,7],[6]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6],[2,4],[7]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,6],[2,5],[7]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,7],[2],[4],[5]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5,7],[2],[3],[6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,7],[2],[4],[6]] => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,5,7],[3],[4],[6]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,7],[2],[5],[6]] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,7],[3],[5],[6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,6],[2],[4],[7]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,6],[2],[5],[7]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6],[2,5,7],[4]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,6],[2,4,7],[5]] => [2,3,2] => [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) => 2
[[1,3,5],[2,6,7],[4]] => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,5],[3,6,7],[4]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4],[2,6,7],[5]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2,4,7],[6]] => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,5],[3,4,7],[6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4],[2,5,7],[6]] => [2,4,1] => [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) => 2
[[1,2,3],[4,5,7],[6]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2,4,6],[7]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4],[2,5,6],[7]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,7],[2,5],[3,6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,7],[2,5],[4,6]] => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,7],[3,5],[4,6]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,7],[2,4],[5,6]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6],[2,5],[4,7]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,6],[2,4],[5,7]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2,6],[4,7]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4],[2,6],[5,7]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2,4],[6,7]] => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,5],[3,4],[6,7]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4],[2,5],[6,7]] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,5],[6,7]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3],[4,5],[6,7]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,5,7],[2,6],[3],[4]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,7],[2,6],[4],[5]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,7],[2,5],[3],[6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,7],[2,5],[4],[6]] => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,7],[3,5],[4],[6]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,7],[2,4],[5],[6]] => [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) => 2
[[1,3,6],[2,7],[4],[5]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5],[2,7],[3],[6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5],[2,7],[4],[6]] => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,5],[3,7],[4],[6]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
>>> Load all 1113 entries. <<<[[1,3,4],[2,7],[5],[6]] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,7],[5],[6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,6],[2,5],[4],[7]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,6],[2,4],[5],[7]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2,6],[4],[7]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4],[2,6],[5],[7]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2,4],[6],[7]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,5,7],[2],[3],[4],[6]] => [4,2,1] => [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) => 2
[[1,3,7],[2],[4],[5],[6]] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6],[2],[4],[5],[7]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2],[4],[6],[7]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3],[2,6],[4,7],[5]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4],[2,5],[3,7],[6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3],[2,5],[4,7],[6]] => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2],[3,5],[4,7],[6]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2,4],[5,7],[6]] => [2,4,1] => [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) => 2
[[1,3],[2,5],[4,6],[7]] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3],[2,4],[5,6],[7]] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,5],[2,7],[3],[4],[6]] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4],[2,7],[3],[5],[6]] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3],[2,7],[4],[5],[6]] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2,6],[4],[5],[7]] => [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) => 2
[[1,3,5,6,7,8],[2,4]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,6,7,8],[3,5]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,7,8],[2,6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,7,8],[3,6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,5,6,8],[2,7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6,8],[3,7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,6,8],[4,7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,8],[5,7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6,7,8],[2],[4]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,6,7,8],[3],[5]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,7,8],[2],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,7,8],[3],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,5,6,8],[2],[7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6,8],[3],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,6,8],[4],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,8],[5],[7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,7,8],[3,4,6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,7,8],[3,5,6]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6,8],[2,4,7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,6,8],[3,4,7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,6,8],[2,5,7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6,8],[3,5,7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,6,8],[4,5,7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,8],[2,6,7]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,8],[3,6,7]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,6,7],[2,4,8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,6,7],[3,5,8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,7],[2,6,8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,7],[3,6,8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,5,6],[2,7,8]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6],[3,7,8]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,6],[4,7,8]] => [4,3,1] => [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
[[1,4,6,7,8],[2,5],[3]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,7,8],[2,5],[4]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,6,7,8],[3,4],[5]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5,7,8],[2,6],[3]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,7,8],[3,6],[5]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,7,8],[3,4],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,7,8],[2,5],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,7,8],[3,5],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,5,6,8],[2,7],[3]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6,8],[2,7],[4]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,6,8],[3,7],[4]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,6,8],[2,7],[5]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6,8],[3,7],[5]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,6,8],[4,7],[5]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,8],[2,7],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,8],[3,7],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,6,8],[2,4],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,6,8],[3,4],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,6,8],[2,5],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6,8],[3,5],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,6,8],[4,5],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,8],[2,6],[7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,8],[3,6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,8],[4,6],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,8],[5,6],[7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6,7],[2,8],[4]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,6,7],[3,8],[5]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,7],[2,8],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,7],[3,8],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,5,6],[2,8],[7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6],[3,8],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,6],[4,8],[7]] => [4,3,1] => [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]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,6,7],[3,5],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,7],[2,6],[8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,7],[3,6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,6,7,8],[2],[3],[5]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5,7,8],[2],[3],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,7,8],[2],[5],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,7,8],[3],[5],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,5,6,8],[2],[3],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6,8],[2],[4],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,6,8],[3],[4],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,6,8],[2],[5],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6,8],[3],[5],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,6,8],[4],[5],[7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,8],[2],[6],[7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,8],[3],[6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,8],[4],[6],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6,7],[2],[4],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,6,7],[3],[5],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,7],[2],[6],[8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,7],[3],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,5,7],[3,4,6,8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,7],[3,5,6,8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6],[2,4,7,8]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,6],[3,4,7,8]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,6],[2,5,7,8]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6],[3,5,7,8]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,6],[4,5,7,8]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,6,7,8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5],[3,6,7,8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,6,8],[2,5,7],[3]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,6,8],[2,5,7],[4]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,6,8],[3,5,7],[4]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,8],[2,4,7],[5]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,6,8],[3,4,7],[5]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,4,5,8],[2,6,7],[3]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,8],[3,6,7],[5]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,8],[3,4,7],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,8],[2,5,7],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,8],[3,5,7],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,8],[2,4,6],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,8],[3,4,6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,8],[2,5,6],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,8],[3,5,6],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,8],[4,5,6],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,6,7],[2,5,8],[3]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,7],[2,5,8],[4]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,6,7],[3,4,8],[5]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5,7],[2,6,8],[3]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,7],[3,6,8],[5]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,7],[3,4,8],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,7],[2,5,8],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,7],[3,5,8],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,5,6],[2,7,8],[3]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6],[2,7,8],[4]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,6],[3,7,8],[4]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,6],[2,7,8],[5]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6],[3,7,8],[5]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,6],[4,7,8],[5]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,7,8],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5],[3,7,8],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,6],[2,4,8],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,6],[3,4,8],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,6],[2,5,8],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6],[3,5,8],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,6],[4,5,8],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,6,8],[7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5],[3,6,8],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5],[4,6,8],[7]] => [4,3,1] => [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
[[1,2,5,7],[3,4,6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,7],[3,5,6],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6],[2,4,7],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,6],[3,5,7],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,6,7],[8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5],[3,6,7],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,7,8],[2,5],[3,6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,7,8],[3,4],[5,6]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,6,8],[2,5],[3,7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,6,8],[2,5],[4,7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,6,8],[3,5],[4,7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,8],[2,4],[5,7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,6,8],[3,4],[5,7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,4,5,8],[2,6],[3,7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,8],[2,6],[4,7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,8],[3,6],[4,7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,8],[2,6],[5,7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,8],[3,6],[5,7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,8],[4,6],[5,7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,8],[3,4],[6,7]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,8],[2,5],[6,7]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,8],[3,5],[6,7]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,6,7],[2,5],[3,8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,7],[2,5],[4,8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,6,7],[3,4],[5,8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5,7],[2,6],[3,8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,7],[3,6],[5,8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,7],[3,4],[6,8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,7],[2,5],[6,8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,7],[3,5],[6,8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,6],[2,7],[4,8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,6],[3,7],[5,8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,7],[6,8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5],[3,7],[6,8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,6],[2,4],[7,8]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,6],[3,4],[7,8]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,6],[2,5],[7,8]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6],[3,5],[7,8]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,6],[4,5],[7,8]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,6],[7,8]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5],[3,6],[7,8]] => [3,4,1] => [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
[[1,2,3,4],[5,6],[7,8]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,7,8],[2,6],[3],[5]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,7,8],[2,5],[3],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,7,8],[2,4],[5],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,7,8],[3,4],[5],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,5,6,8],[2,7],[3],[4]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,6,8],[2,7],[3],[5]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,6,8],[2,7],[4],[5]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,6,8],[3,7],[4],[5]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5,8],[2,7],[3],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,8],[2,7],[5],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,8],[3,7],[5],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,6,8],[2,5],[3],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,6,8],[2,5],[4],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,6,8],[3,5],[4],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,8],[2,4],[5],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,6,8],[3,4],[5],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,4,5,8],[2,6],[3],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,8],[2,6],[4],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,8],[3,6],[4],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,8],[2,6],[5],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,8],[3,6],[5],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,8],[4,6],[5],[7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,8],[2,4],[6],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,8],[3,4],[6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,8],[2,5],[6],[7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,8],[3,5],[6],[7]] => [3,4,1] => [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
[[1,4,6,7],[2,8],[3],[5]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5,7],[2,8],[3],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,7],[2,8],[5],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,7],[3,8],[5],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,5,6],[2,8],[3],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6],[2,8],[4],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,6],[3,8],[4],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,6],[2,8],[5],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6],[3,8],[5],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,6],[4,8],[5],[7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,8],[6],[7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5],[3,8],[6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5],[4,8],[6],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,6,7],[2,5],[3],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,7],[2,5],[4],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,6,7],[3,4],[5],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5,7],[2,6],[3],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,7],[3,6],[5],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,7],[3,4],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,7],[2,5],[6],[8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,7],[3,5],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,6],[2,7],[4],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,6],[3,7],[5],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,7],[6],[8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5],[3,7],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,6],[2,4],[7],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,6],[3,5],[7],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,7,8],[2],[3],[5],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,7,8],[2],[4],[5],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,5,6,8],[2],[3],[4],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,6,8],[2],[3],[5],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,6,8],[2],[4],[5],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,6,8],[3],[4],[5],[7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5,8],[2],[3],[6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,8],[2],[4],[6],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,8],[3],[4],[6],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,8],[2],[5],[6],[7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,8],[3],[5],[6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,6,7],[2],[3],[5],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5,7],[2],[3],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,7],[2],[5],[6],[8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,7],[3],[5],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,6],[2],[4],[7],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,6],[3],[5],[7],[8]] => [3,2,3] => [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) => 2
[[1,2,7],[3,4,8],[5,6]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,6],[2,5,8],[3,7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,6],[2,5,8],[4,7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,6],[3,5,8],[4,7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6],[2,4,8],[5,7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,6],[3,4,8],[5,7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,4,5],[2,6,8],[3,7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2,6,8],[4,7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5],[3,6,8],[4,7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4],[2,6,8],[5,7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4],[3,6,8],[5,7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3],[4,6,8],[5,7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5],[3,4,8],[6,7]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4],[2,5,8],[6,7]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,5,8],[6,7]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,6],[2,5,7],[3,8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6],[2,5,7],[4,8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,6],[3,4,7],[5,8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5],[2,6,7],[3,8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4],[3,6,7],[5,8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5],[3,4,7],[6,8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4],[2,5,7],[6,8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,5,7],[6,8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5],[2,4,6],[7,8]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5],[3,4,6],[7,8]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4],[2,5,6],[7,8]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4],[3,5,6],[7,8]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3],[4,5,6],[7,8]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,7],[2,6,8],[3],[5]] => [3,2,3] => [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) => 2
[[1,3,7],[2,4,8],[5],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,7],[3,4,8],[5],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,5,6],[2,7,8],[3],[4]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,6],[2,7,8],[3],[5]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,6],[2,7,8],[4],[5]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,6],[3,7,8],[4],[5]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5],[2,7,8],[3],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4],[2,7,8],[5],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,7,8],[5],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,6],[2,5,8],[3],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,6],[2,5,8],[4],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,6],[3,5,8],[4],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6],[2,4,8],[5],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,6],[3,4,8],[5],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,4,5],[2,6,8],[3],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2,6,8],[4],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5],[3,6,8],[4],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4],[2,6,8],[5],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4],[3,6,8],[5],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3],[4,6,8],[5],[7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2,4,8],[6],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5],[3,4,8],[6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4],[2,5,8],[6],[7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,5,8],[6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3],[4,5,8],[6],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,6],[2,5,7],[3],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6],[2,5,7],[4],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,6],[3,4,7],[5],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5],[2,6,7],[3],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4],[3,6,7],[5],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5],[3,4,7],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4],[2,5,7],[6],[8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,5,7],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5],[2,4,6],[7],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4],[3,5,6],[7],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,5,8],[2,6],[3,7],[4]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,8],[2,6],[3,7],[5]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,8],[2,6],[4,7],[5]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,8],[3,6],[4,7],[5]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,8],[2,5],[3,7],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,8],[2,4],[5,7],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,8],[3,4],[5,7],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,8],[2,5],[3,6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,8],[2,5],[4,6],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,8],[3,5],[4,6],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,8],[2,4],[5,6],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,8],[3,4],[5,6],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,4,7],[2,6],[3,8],[5]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,7],[2,5],[3,8],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,7],[2,4],[5,8],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,7],[3,4],[5,8],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,6],[2,7],[3,8],[5]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5],[2,7],[3,8],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4],[2,7],[5,8],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,7],[5,8],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,6],[2,5],[3,8],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,6],[2,5],[4,8],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,6],[3,5],[4,8],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6],[2,4],[5,8],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,6],[3,4],[5,8],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,4,5],[2,6],[3,8],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2,6],[4,8],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5],[3,6],[4,8],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4],[2,6],[5,8],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4],[3,6],[5,8],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[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],[2,4],[6,8],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5],[3,4],[6,8],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4],[2,5],[6,8],[7]] => [2,5,1] => [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],[4,5],[6,8],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,7],[2,5],[3,6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,7],[3,4],[5,6],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,6],[2,5],[3,7],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6],[2,5],[4,7],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,6],[3,4],[5,7],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2,6],[4,7],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4],[3,6],[5,7],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5],[3,4],[6,7],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4],[2,5],[6,7],[8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,5],[6,7],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,6,8],[2,7],[3],[4],[5]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,8],[2,7],[3],[5],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,8],[2,7],[4],[5],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,5,8],[2,6],[3],[4],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,8],[2,6],[3],[5],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,8],[2,6],[4],[5],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,8],[3,6],[4],[5],[7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,8],[2,5],[3],[6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,8],[2,5],[4],[6],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,8],[3,5],[4],[6],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,8],[2,4],[5],[6],[7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,8],[3,4],[5],[6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,7],[2,8],[3],[5],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,7],[2,8],[4],[5],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,5,6],[2,8],[3],[4],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,6],[2,8],[3],[5],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,6],[2,8],[4],[5],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,6],[3,8],[4],[5],[7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5],[2,8],[3],[6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2,8],[4],[6],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5],[3,8],[4],[6],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4],[2,8],[5],[6],[7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,8],[5],[6],[7]] => [3,4,1] => [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
[[1,4,7],[2,5],[3],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,7],[2,4],[5],[6],[8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,7],[3,4],[5],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,6],[2,7],[3],[5],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5],[2,7],[3],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4],[2,7],[5],[6],[8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,7],[5],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,6],[2,5],[3],[7],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6],[2,5],[4],[7],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,6],[3,4],[5],[7],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2,6],[4],[7],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4],[3,6],[5],[7],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5],[2,4],[6],[7],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,6,8],[2],[3],[4],[5],[7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,5,8],[2],[3],[4],[6],[7]] => [4,3,1] => [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
[[1,3,8],[2],[4],[5],[6],[7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,7],[2],[3],[5],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,7],[2],[4],[5],[6],[8]] => [2,4,2] => [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
[[1,3,5],[2],[4],[6],[7],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4],[2,6],[3,7],[5,8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4],[2,5],[3,7],[6,8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[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]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4],[2,5],[3,6],[7,8]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2,5],[4,6],[7,8]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2],[3,5],[4,6],[7,8]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[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) => 3
[[1,2],[3,4],[5,6],[7,8]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,4],[2,7],[3,8],[5],[6]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3],[2,7],[4,8],[5],[6]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,5],[2,6],[3,8],[4],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4],[2,6],[3,8],[5],[7]] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3],[2,6],[4,8],[5],[7]] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2],[3,6],[4,8],[5],[7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4],[2,5],[3,8],[6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2,5],[4,8],[6],[7]] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2],[3,5],[4,8],[6],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2,4],[5,8],[6],[7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2],[3,4],[5,8],[6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4],[2,6],[3,7],[5],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4],[2,5],[3,7],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[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]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3],[2,5],[4,6],[7],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2],[3,4],[5,6],[7],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,6],[2,8],[3],[4],[5],[7]] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,5],[2,8],[3],[4],[6],[7]] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4],[2,8],[3],[5],[6],[7]] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2,8],[4],[5],[6],[7]] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4],[2,7],[3],[5],[6],[8]] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3],[2,7],[4],[5],[6],[8]] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4],[2,6],[3],[5],[7],[8]] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2,5],[4],[6],[7],[8]] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,7,8],[2,4,6,9,10]] => [2,2,2,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,5,6,9],[2,4,7,8,10]] => [2,2,3,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,3,5,6,8],[2,4,7,9,10]] => [2,2,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,5,6,7],[2,4,8,9,10]] => [2,2,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,4,7,9],[2,5,6,8,10]] => [2,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,4,7,8],[2,5,6,9,10]] => [2,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,6,9],[2,5,7,8,10]] => [2,3,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,6,8],[2,5,7,9,10]] => [2,3,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,4,6,7],[2,5,8,9,10]] => [2,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,4,5,8],[2,6,7,9,10]] => [2,4,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5,7],[2,6,8,9,10]] => [2,4,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5,6],[2,7,8,9,10]] => [2,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,7,9],[3,4,6,8,10]] => [3,3,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,2,5,7,8],[3,4,6,9,10]] => [3,3,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,5,6,9],[3,4,7,8,10]] => [3,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,6,8],[3,4,7,9,10]] => [3,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,5,6,7],[3,4,8,9,10]] => [3,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,7,9],[3,5,6,8,10]] => [3,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,7,8],[3,5,6,9,10]] => [3,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6,9],[3,5,7,8,10]] => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,4,6,8],[3,5,7,9,10]] => [3,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,6,7],[3,5,8,9,10]] => [3,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,5,9],[3,6,7,8,10]] => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,5,8],[3,6,7,9,10]] => [3,3,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,4,5,7],[3,6,8,9,10]] => [3,3,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,2,4,5,6],[3,7,8,9,10]] => [3,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,7,9],[4,5,6,8,10]] => [4,4,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,7,8],[4,5,6,9,10]] => [4,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,6,8],[4,5,7,9,10]] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,6,7],[4,5,8,9,10]] => [4,4,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,5,9],[4,6,7,8,10]] => [4,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,8],[4,6,7,9,10]] => [4,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4,8],[5,6,7,9,10]] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,7],[5,6,8,9,10]] => [5,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6],[5,7,8,9,10]] => [5,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,7,9,10],[2,4,6,8,11,12]] => [2,2,2,2,3,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,5,7,8,11],[2,4,6,9,10,12]] => [2,2,2,3,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[[1,3,5,7,8,9],[2,4,6,10,11,12]] => [2,2,2,4,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,5,6,9,11],[2,4,7,8,10,12]] => [2,2,3,3,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,5,6,9,10],[2,4,7,8,11,12]] => [2,2,3,4,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,5,6,8,11],[2,4,7,9,10,12]] => [2,2,3,2,3] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,5,6,8,10],[2,4,7,9,11,12]] => [2,2,3,2,2,1] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,5,6,8,9],[2,4,7,10,11,12]] => [2,2,3,3,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,5,6,7,11],[2,4,8,9,10,12]] => [2,2,4,4] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,3,5,6,7,10],[2,4,8,9,11,12]] => [2,2,4,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,5,6,7,9],[2,4,8,10,11,12]] => [2,2,4,2,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,5,6,7,8],[2,4,9,10,11,12]] => [2,2,5,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,4,7,9,11],[2,5,6,8,10,12]] => [2,3,3,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,4,7,9,10],[2,5,6,8,11,12]] => [2,3,3,3,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,4,7,8,11],[2,5,6,9,10,12]] => [2,3,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,7,8,10],[2,5,6,9,11,12]] => [2,3,4,2,1] => [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) => 3
[[1,3,4,7,8,9],[2,5,6,10,11,12]] => [2,3,5,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,6,9,11],[2,5,7,8,10,12]] => [2,3,2,3,2] => [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) => 3
[[1,3,4,6,9,10],[2,5,7,8,11,12]] => [2,3,2,4,1] => [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) => 3
[[1,3,4,6,8,11],[2,5,7,9,10,12]] => [2,3,2,2,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,4,6,8,10],[2,5,7,9,11,12]] => [2,3,2,2,2,1] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,4,6,8,9],[2,5,7,10,11,12]] => [2,3,2,3,2] => [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) => 3
[[1,3,4,6,7,11],[2,5,8,9,10,12]] => [2,3,3,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,4,6,7,10],[2,5,8,9,11,12]] => [2,3,3,3,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,4,6,7,9],[2,5,8,10,11,12]] => [2,3,3,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,4,6,7,8],[2,5,9,10,11,12]] => [2,3,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5,9,11],[2,6,7,8,10,12]] => [2,4,4,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,4,5,9,10],[2,6,7,8,11,12]] => [2,4,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5,8,11],[2,6,7,9,10,12]] => [2,4,3,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5,8,10],[2,6,7,9,11,12]] => [2,4,3,2,1] => [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) => 3
[[1,3,4,5,8,9],[2,6,7,10,11,12]] => [2,4,4,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,4,5,7,11],[2,6,8,9,10,12]] => [2,4,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5,7,10],[2,6,8,9,11,12]] => [2,4,2,3,1] => [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) => 3
[[1,3,4,5,7,8],[2,6,9,10,11,12]] => [2,4,3,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5,6,10],[2,7,8,9,11,12]] => [2,5,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5,6,9],[2,7,8,10,11,12]] => [2,5,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5,6,8],[2,7,9,10,11,12]] => [2,5,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5,6,7],[2,8,9,10,11,12]] => [2,6,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,7,9,10],[3,4,6,8,11,12]] => [3,3,2,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,5,7,8,10],[3,4,6,9,11,12]] => [3,3,3,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,5,7,8,9],[3,4,6,10,11,12]] => [3,3,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,6,9,11],[3,4,7,8,10,12]] => [3,4,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,5,6,9,10],[3,4,7,8,11,12]] => [3,4,4,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5,6,8,11],[3,4,7,9,10,12]] => [3,4,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,5,6,8,10],[3,4,7,9,11,12]] => [3,4,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,5,6,8,9],[3,4,7,10,11,12]] => [3,4,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,5,6,7,11],[3,4,8,9,10,12]] => [3,5,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,6,7,10],[3,4,8,9,11,12]] => [3,5,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,5,6,7,9],[3,4,8,10,11,12]] => [3,5,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,5,6,7,8],[3,4,9,10,11,12]] => [3,6,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,7,9,11],[3,5,6,8,10,12]] => [3,2,3,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2,4,7,9,10],[3,5,6,8,11,12]] => [3,2,3,3,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,7,8,11],[3,5,6,9,10,12]] => [3,2,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,7,8,10],[3,5,6,9,11,12]] => [3,2,4,2,1] => [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) => 3
[[1,2,4,7,8,9],[3,5,6,10,11,12]] => [3,2,5,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6,9,11],[3,5,7,8,10,12]] => [3,2,2,3,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,6,9,10],[3,5,7,8,11,12]] => [3,2,2,4,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,6,8,11],[3,5,7,9,10,12]] => [3,2,2,2,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,6,8,10],[3,5,7,9,11,12]] => [3,2,2,2,2,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,4,6,8,9],[3,5,7,10,11,12]] => [3,2,2,3,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,6,7,11],[3,5,8,9,10,12]] => [3,2,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6,7,10],[3,5,8,9,11,12]] => [3,2,3,3,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,6,7,9],[3,5,8,10,11,12]] => [3,2,3,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2,4,6,7,8],[3,5,9,10,11,12]] => [3,2,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,5,9,11],[3,6,7,8,10,12]] => [3,3,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,4,5,9,10],[3,6,7,8,11,12]] => [3,3,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,4,5,8,10],[3,6,7,9,11,12]] => [3,3,3,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,5,8,9],[3,6,7,10,11,12]] => [3,3,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,4,5,7,11],[3,6,8,9,10,12]] => [3,3,2,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,4,5,7,10],[3,6,8,9,11,12]] => [3,3,2,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,5,6,11],[3,7,8,9,10,12]] => [3,4,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6,10],[3,7,8,9,11,12]] => [3,4,4,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,4,5,6,9],[3,7,8,10,11,12]] => [3,4,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,5,6,8],[3,7,9,10,11,12]] => [3,4,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,5,6,7],[3,8,9,10,11,12]] => [3,5,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,7,9,11],[4,5,6,8,10,12]] => [4,4,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,2,3,7,9,10],[4,5,6,8,11,12]] => [4,4,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,7,8,11],[4,5,6,9,10,12]] => [4,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,7,8,10],[4,5,6,9,11,12]] => [4,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,7,8,9],[4,5,6,10,11,12]] => [4,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,6,9,11],[4,5,7,8,10,12]] => [4,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,6,9,10],[4,5,7,8,11,12]] => [4,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,6,8,11],[4,5,7,9,10,12]] => [4,3,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,6,8,10],[4,5,7,9,11,12]] => [4,3,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,3,6,8,9],[4,5,7,10,11,12]] => [4,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,6,7,10],[4,5,8,9,11,12]] => [4,4,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,6,7,9],[4,5,8,10,11,12]] => [4,4,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,2,3,6,7,8],[4,5,9,10,11,12]] => [4,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,9,11],[4,6,7,8,10,12]] => [4,2,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,9,10],[4,6,7,8,11,12]] => [4,2,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,8,11],[4,6,7,9,10,12]] => [4,2,3,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,8,10],[4,6,7,9,11,12]] => [4,2,3,2,1] => [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) => 3
[[1,2,3,5,8,9],[4,6,7,10,11,12]] => [4,2,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,7,11],[4,6,8,9,10,12]] => [4,2,2,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,5,7,10],[4,6,8,9,11,12]] => [4,2,2,3,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,3,5,7,8],[4,6,9,10,11,12]] => [4,2,3,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,6,11],[4,7,8,9,10,12]] => [4,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,6,10],[4,7,8,9,11,12]] => [4,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,6,9],[4,7,8,10,11,12]] => [4,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,5,6,8],[4,7,9,10,11,12]] => [4,3,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4,9,11],[5,6,7,8,10,12]] => [5,5,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,4,9,10],[5,6,7,8,11,12]] => [5,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,8,11],[5,6,7,9,10,12]] => [5,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,8,10],[5,6,7,9,11,12]] => [5,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4,8,9],[5,6,7,10,11,12]] => [5,5,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,4,7,11],[5,6,8,9,10,12]] => [5,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,7,10],[5,6,8,9,11,12]] => [5,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,4,7,9],[5,6,8,10,11,12]] => [5,3,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4,7,8],[5,6,9,10,11,12]] => [5,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,11],[5,7,8,9,10,12]] => [5,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,10],[5,7,8,9,11,12]] => [5,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4,6,9],[5,7,8,10,11,12]] => [5,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4,6,8],[5,7,9,10,11,12]] => [5,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,4,6,7],[5,8,9,10,11,12]] => [5,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,10],[6,7,8,9,11,12]] => [6,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,9],[6,7,8,10,11,12]] => [6,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,7],[6,8,9,10,11,12]] => [6,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[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]] => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3],[4,5,6],[7,8,9]] => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3],[4,5,6],[7,8],[9]] => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3],[4,5],[6,7],[8,9]] => [4,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3],[4,5],[6,7],[8],[9]] => [4,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2],[3,4],[5,6],[7],[8],[9]] => [3,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[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]] => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4],[5,6,7,8],[9,10]] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4],[5,6,7],[8,9,10]] => [5,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4],[5,6,7],[8,9],[10]] => [5,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4],[5,6],[7,8],[9,10]] => [5,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,4],[5,6],[7,8],[9],[10]] => [5,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3],[4,5,6],[7,8],[9,10]] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3],[4,5],[6,7],[8],[9],[10]] => [4,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2],[3,4],[5,6],[7,8],[9,10]] => [3,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2],[3,4],[5,6],[7,8],[9],[10]] => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [3,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,6],[7,8,9,10],[11,12]] => [7,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5],[6,7,8,9],[10,11,12]] => [6,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => [6,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => [5,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => [5,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4],[5,6,7,8],[9,10],[11],[12]] => [5,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => [5,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => [5,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => [5,3,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => [4,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [4,3,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,6,7,8,9],[2,5],[4]] => [2,2,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,8,9],[2,6,7],[5]] => [2,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,7,8,9],[3,4],[5,6]] => [3,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,7,8,9],[2,6],[3],[5]] => [3,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,7,8,9],[6]] => [2,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,8,9],[2,5],[4,7],[6]] => [2,2,2,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,5,8,9],[2,7],[3],[4],[6]] => [4,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6],[2,5,9],[4,8],[7]] => [2,2,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,5,6],[2,8,9],[3],[4],[7]] => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2,5],[4,7],[6,9],[8]] => [2,2,2,2,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[[1,5],[2,7],[3,9],[4],[6],[8]] => [4,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,7],[2,9],[3],[4],[5],[6],[8]] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,7,8,9,10],[2,5],[4]] => [2,2,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,8,9,10],[2,6,7],[5]] => [2,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,7,8,9,10],[3,4],[5,6]] => [3,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,7,8,9,10],[2,6],[3],[5]] => [3,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,9,10],[3,4,8],[6,7]] => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,5,9,10],[2,7,8],[3],[6]] => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,8,9,10],[2,5],[4,7],[6]] => [2,2,2,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,5,8,9,10],[2,7],[3],[4],[6]] => [4,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,6],[3,4,9,10],[7,8]] => [3,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,5,6],[2,8,9,10],[3],[7]] => [3,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,10],[2,5,9],[4,8],[7]] => [2,2,3,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,2,9,10],[3,4],[5,6],[7,8]] => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,4,9,10],[2,6],[3,8],[5],[7]] => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,6,9,10],[2,8],[3],[4],[5],[7]] => [5,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4],[2,6,7],[5,9,10],[8]] => [2,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,7],[3,4,10],[5,6],[8,9]] => [3,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,4,7],[2,6,10],[3,9],[5],[8]] => [3,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,6,7],[2,9,10],[3],[4],[5],[8]] => [5,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4],[2,6],[3,8],[5,10],[7],[9]] => [3,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,6],[2,8],[3,10],[4],[5],[7],[9]] => [5,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,7],[4,5,6,11],[8,9,10]] => [4,4,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,5,6,7],[2,9,10,11],[3],[4],[8]] => [4,4,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,5],[3,4,8],[6,7,11],[9,10]] => [3,3,3,2] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,4,5],[2,7,8],[3,10,11],[6],[9]] => [3,3,3,2] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,5,6,11,12],[3,4,9,10],[7,8]] => [3,4,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => [2,2,4,4] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,3,4,11,12],[2,6,7],[5,9,10],[8]] => [2,3,3,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,7,11,12],[3,4,10],[5,6],[8,9]] => [3,2,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,4,7,11,12],[2,6,10],[3,9],[5],[8]] => [3,2,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,10,11,12],[2,5],[4,7],[6,9],[8]] => [2,2,2,2,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => [2,3,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => [3,2,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,4,7,8],[2,6,11,12],[3,10],[5],[9]] => [3,2,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => [2,2,2,3,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => [2,2,3,3,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => [3,2,2,3,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,7],[3,5,8],[6,9],[10]] => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,4,5,9],[6,7],[8]] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,9],[5,6,7],[8]] => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,9],[5,6],[7],[8]] => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,7],[4,5,6,9],[8]] => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,9],[4,5,6],[7,8]] => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,9],[4,5,6],[7],[8]] => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,9],[4,5],[6,7],[8]] => [4,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,9],[4,5],[6],[7],[8]] => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,5],[3,4,9],[6,7],[8]] => [3,3,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,5],[3,4,9],[6],[7],[8]] => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,9],[3,4],[5,6],[7],[8]] => [3,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,9],[3,4],[5],[6],[7],[8]] => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2,5],[4,9],[6],[7],[8]] => [2,2,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3],[2,9],[4],[5],[6],[7],[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]] => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,10],[6,7,8],[9]] => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,10],[6,7],[8],[9]] => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,10],[5,6,7,8],[9]] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,10],[5,6,7],[8,9]] => [5,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,10],[5,6,7],[8],[9]] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,10],[5,6],[7,8],[9]] => [5,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,4,10],[5,6],[7],[8],[9]] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,7],[4,5,6,10],[8,9]] => [4,4,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,7],[4,5,6,10],[8],[9]] => [4,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,10],[4,5,6],[7,8],[9]] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,10],[4,5,6],[7],[8],[9]] => [4,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,10],[4,5],[6,7],[8],[9]] => [4,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,10],[4,5],[6],[7],[8],[9]] => [4,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5],[3,4,8],[6,7,10],[9]] => [3,3,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,5],[3,4,10],[6,7],[8,9]] => [3,3,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,2,5],[3,4,10],[6,7],[8],[9]] => [3,3,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,5],[3,4,10],[6],[7],[8],[9]] => [3,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,10],[3,4],[5,6],[7,8],[9]] => [3,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,10],[3,4],[5,6],[7],[8],[9]] => [3,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,10],[3,4],[5],[6],[7],[8],[9]] => [3,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2,5],[4,7],[6,10],[8],[9]] => [2,2,2,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3],[2,5],[4,10],[6],[7],[8],[9]] => [2,2,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3],[2,10],[4],[5],[6],[7],[8],[9]] => [2,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,6,7,8,9],[2,5]] => [2,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6,7,8,9],[2],[4]] => [2,2,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,6,8,9],[2,4,7]] => [2,2,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,4,6,7,8,9],[2],[3],[5]] => [3,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,7,8],[2,4,6,9]] => [2,2,2,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,5,7,9],[3,6,8],[4]] => [4,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,5,8,9],[2,6],[4],[7]] => [2,2,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,5,7,8,9],[2],[3],[4],[6]] => [4,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,6],[3,7,8,9],[4]] => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,7],[2,6,8],[5,9]] => [2,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,8],[2,7,9],[4],[5]] => [2,3,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,6,9],[3,4],[5,7],[8]] => [3,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,4,6,9],[2,7],[3],[5],[8]] => [3,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,4,7],[2,8,9],[3],[5],[6]] => [3,3,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,5,8],[2,6],[3,7],[4,9]] => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,7],[2,5],[4,8],[6],[9]] => [2,2,2,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,5,7],[2,8],[3],[4],[6],[9]] => [4,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,7,9],[2],[3],[4],[5],[6],[8]] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,6,7,8,9,10],[2,5]] => [2,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,6,7,8,9,10],[2],[4]] => [2,2,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,5,6,8,9,10],[2,4,7]] => [2,2,3,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,2,4,7,8,9,10],[3,5],[6]] => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,6,7,8,9,10],[2],[3],[5]] => [3,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,5,7,8,10],[2,4,6,9]] => [2,2,2,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,4,6,8,9,10],[2,5],[3,7]] => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,5,8,9,10],[2,6],[4],[7]] => [2,2,3,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,5,7,8,9,10],[2],[3],[4],[6]] => [4,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,7,10],[2,6,8],[5,9]] => [2,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,6,8,10],[2,7,9],[4],[5]] => [2,3,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,6,9,10],[3,4],[5,7],[8]] => [3,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,4,6,9,10],[2,7],[3],[5],[8]] => [3,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,6,8,9,10],[2],[3],[4],[5],[7]] => [5,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,8],[2,6,9,10],[5,7]] => [2,3,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,6,7],[2,8,9,10],[4],[5]] => [2,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,4,7,9],[2,5,8],[3,6,10]] => [3,3,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,4,7,9],[2,8,10],[3],[5],[6]] => [3,3,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,5,8,10],[2,6],[3,7],[4,9]] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,7,10],[2,5],[4,8],[6],[9]] => [2,2,2,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,5,7,10],[2,8],[3],[4],[6],[9]] => [4,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,5],[3,7,8],[4,9,10],[6]] => [4,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,4,6],[2,5,9],[3,8],[7,10]] => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,5],[2,6,8],[4,9],[7],[10]] => [2,2,3,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,5,8],[2,9,10],[3],[4],[6],[7]] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,8],[3,4],[5,6],[7,9],[10]] => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,4,8],[2,6],[3,9],[5],[7],[10]] => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,6,8],[2,9],[3],[4],[5],[7],[10]] => [5,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,8,10],[2],[3],[4],[5],[6],[7],[9]] => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6,7],[2,8,9]] => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6,7],[2,9],[8]] => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6],[2,7,8,9]] => [2,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6],[2,8,9],[7]] => [2,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6],[2,8],[7,9]] => [2,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6],[2,8],[7],[9]] => [2,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,7,8],[6,9]] => [2,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,7,8],[6],[9]] => [2,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,7],[6,9],[8]] => [2,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5],[2,7],[6],[8],[9]] => [2,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4],[2,6,7],[5,8,9]] => [2,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,4],[2,6,7],[5,9],[8]] => [2,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,4],[2,6,7],[5],[8],[9]] => [2,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4],[2,6],[5,8],[7,9]] => [2,3,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3,4],[2,6],[5,8],[7],[9]] => [2,3,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3,4],[2,6],[5],[7],[8],[9]] => [2,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2,5],[4,7],[6],[8],[9]] => [2,2,2,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,3],[2,5],[4],[6],[7],[8],[9]] => [2,2,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,5,6,7,8],[2,9,10]] => [2,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6,7,8],[2,10],[9]] => [2,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6,7],[2,8,9,10]] => [2,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6,7],[2,9,10],[8]] => [2,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6,7],[2,9],[8,10]] => [2,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6,7],[2,9],[8],[10]] => [2,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6],[2,8,9,10],[7]] => [2,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6],[2,8,9],[7,10]] => [2,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6],[2,8,9],[7],[10]] => [2,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5,6],[2,8],[7,10],[9]] => [2,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5,6],[2,8],[7],[9],[10]] => [2,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,5],[2,7,8],[6,9,10]] => [2,4,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5],[2,7,8],[6,10],[9]] => [2,4,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5],[2,7],[6,9],[8,10]] => [2,4,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3,4,5],[2,7],[6,9],[8],[10]] => [2,4,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3,4],[2,6,7],[5,9],[8,10]] => [2,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,4],[2,6,7],[5,9],[8],[10]] => [2,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,3,4],[2,6,7],[5],[8],[9],[10]] => [2,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4],[2,6],[5,8],[7,10],[9]] => [2,3,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,4],[2,6],[5,8],[7],[9],[10]] => [2,3,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,4],[2,6],[5],[7],[8],[9],[10]] => [2,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3],[2,5],[4,7],[6],[8],[9],[10]] => [2,2,2,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,3],[2,5],[4],[6],[7],[8],[9],[10]] => [2,2,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,6,8,10],[3,5,7,9]] => [3,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,6,8,9,10],[3,5,7]] => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,4,6,7,8,10],[3,5,9]] => [3,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6,7,9,10],[3,5,8]] => [3,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6,7,8,9,10],[3,5]] => [3,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6,8,10],[3,7,9]] => [3,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,5,6,9,10],[3,7,8]] => [3,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,7,8,10],[3,6,9]] => [3,3,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,2,4,5,7,9,10],[3,6,8]] => [3,3,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,2,4,5,7,8,9,10],[3,6]] => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,5,6,7,8,10],[3,9]] => [3,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6,7,9,10],[3,8]] => [3,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6,8,9,10],[3,7]] => [3,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,8,10],[5,7,9]] => [5,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,4,6,9,10],[5,7,8]] => [5,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,7,8,10],[5,6,9]] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,7,9,10],[5,6,8]] => [5,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,6,8,10],[4,7,9]] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,7,8,10],[4,6,9]] => [4,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,7,8,9,10],[4,6]] => [4,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,6,7,8,10],[4,9]] => [4,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,6,7,9,10],[4,8]] => [4,4,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,4,5,6,8,10],[7,9]] => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,7,8,10],[6,9]] => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,7,8,10],[5,9]] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,7,9,10],[5,8]] => [5,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,8,9,10],[5,7]] => [5,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,6,8,10,12],[3,5,7,9,11]] => [3,2,2,2,2,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,4,6,8,10,11,12],[3,5,7,9]] => [3,2,2,2,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,6,8,9,10,12],[3,5,7,11]] => [3,2,2,4,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,6,8,9,11,12],[3,5,7,10]] => [3,2,2,3,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,6,7,8,10,12],[3,5,9,11]] => [3,2,4,2,1] => [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) => 3
[[1,2,4,6,7,8,11,12],[3,5,9,10]] => [3,2,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6,7,9,10,12],[3,5,8,11]] => [3,2,3,3,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,6,7,9,11,12],[3,5,8,10]] => [3,2,3,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2,4,6,7,9,10,11,12],[3,5,8]] => [3,2,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6,7,8,9,11,12],[3,5,10]] => [3,2,5,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6,7,8,10,11,12],[3,5,9]] => [3,2,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,6,7,8,9,10,11,12],[3,5]] => [3,2,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6,8,10,12],[3,7,9,11]] => [3,4,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,5,6,8,11,12],[3,7,9,10]] => [3,4,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,5,6,9,10,12],[3,7,8,11]] => [3,4,4,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,4,5,6,9,11,12],[3,7,8,10]] => [3,4,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,5,6,9,10,11,12],[3,7,8]] => [3,4,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,7,8,10,12],[3,6,9,11]] => [3,3,3,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,5,7,9,10,12],[3,6,8,11]] => [3,3,2,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,5,7,9,10,11,12],[3,6,8]] => [3,3,2,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,4,5,7,8,9,10,12],[3,6,11]] => [3,3,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,4,5,7,8,9,11,12],[3,6,10]] => [3,3,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,4,5,6,7,8,11,12],[3,9,10]] => [3,6,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6,7,9,10,12],[3,8,11]] => [3,5,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,5,6,7,9,11,12],[3,8,10]] => [3,5,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,5,6,7,10,11,12],[3,8,9]] => [3,5,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6,8,9,10,12],[3,7,11]] => [3,4,4,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,4,5,6,8,9,11,12],[3,7,10]] => [3,4,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,5,6,8,10,11,12],[3,7,9]] => [3,4,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4,5,6,8,9,10,11,12],[3,7]] => [3,4,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6,7,8,9,10,12],[3,11]] => [3,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6,7,8,10,11,12],[3,9]] => [3,6,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6,7,9,10,11,12],[3,8]] => [3,5,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,8,10,12],[5,7,9,11]] => [5,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,3,4,6,8,11,12],[5,7,9,10]] => [5,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,4,6,9,10,12],[5,7,8,11]] => [5,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4,6,9,11,12],[5,7,8,10]] => [5,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4,6,9,10,11,12],[5,7,8]] => [5,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,7,8,10,12],[5,6,9,11]] => [5,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4,7,8,11,12],[5,6,9,10]] => [5,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,7,9,10,12],[5,6,8,11]] => [5,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,4,7,9,11,12],[5,6,8,10]] => [5,3,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4,7,9,10,11,12],[5,6,8]] => [5,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,7,8,9,10,12],[5,6,11]] => [5,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,7,8,9,11,12],[5,6,10]] => [5,5,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,4,7,8,10,11,12],[5,6,9]] => [5,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,6,8,10,12],[4,7,9,11]] => [4,3,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,3,5,6,8,11,12],[4,7,9,10]] => [4,3,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,6,9,10,12],[4,7,8,11]] => [4,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,6,9,11,12],[4,7,8,10]] => [4,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,5,6,9,10,11,12],[4,7,8]] => [4,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,7,8,10,12],[4,6,9,11]] => [4,2,3,2,1] => [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) => 3
[[1,2,3,5,7,8,11,12],[4,6,9,10]] => [4,2,3,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,7,9,10,12],[4,6,8,11]] => [4,2,2,3,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,3,5,7,9,10,11,12],[4,6,8]] => [4,2,2,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,5,7,8,9,10,12],[4,6,11]] => [4,2,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,7,8,9,11,12],[4,6,10]] => [4,2,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,7,8,10,11,12],[4,6,9]] => [4,2,3,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,6,7,8,10,12],[4,9,11]] => [4,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,6,7,8,11,12],[4,9,10]] => [4,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,6,7,9,10,12],[4,8,11]] => [4,4,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,5,6,7,9,11,12],[4,8,10]] => [4,4,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,2,3,5,6,8,9,10,12],[4,7,11]] => [4,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,6,8,9,11,12],[4,7,10]] => [4,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,5,6,8,10,11,12],[4,7,9]] => [4,3,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,5,6,8,9,10,11,12],[4,7]] => [4,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,6,7,8,9,11,12],[4,10]] => [4,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,5,6,7,8,10,11,12],[4,9]] => [4,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,6,8,11,12],[7,9,10]] => [7,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,6,9,10,12],[7,8,11]] => [7,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,7,10,11,12],[6,8,9]] => [6,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,8,9,10,12],[6,7,11]] => [6,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,8,9,11,12],[6,7,10]] => [6,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,7,8,10,12],[5,9,11]] => [5,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4,6,7,8,11,12],[5,9,10]] => [5,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,7,9,10,12],[5,8,11]] => [5,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,4,6,7,9,11,12],[5,8,10]] => [5,3,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4,6,7,10,11,12],[5,8,9]] => [5,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,8,9,10,12],[5,7,11]] => [5,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4,6,8,9,11,12],[5,7,10]] => [5,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,3,4,6,8,10,11,12],[5,7,9]] => [5,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,3,4,6,8,9,10,11,12],[5,7]] => [5,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,7,8,9,10,12],[5,11]] => [5,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,7,8,9,11,12],[5,10]] => [5,5,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,4,6,7,8,10,11,12],[5,9]] => [5,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,6,7,9,10,11,12],[5,8]] => [5,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,6,7,8,10,12],[9,11]] => [9,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,6,8,9,10,12],[7,11]] => [7,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,6,8,10,11,12],[7,9]] => [7,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,7,8,9,10,12],[6,11]] => [6,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,7,8,9,11,12],[6,10]] => [6,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,5,7,9,10,11,12],[6,8]] => [6,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,7,8],[2,5],[4,9]] => [2,2,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,6,7,8],[2,5],[4],[9]] => [2,2,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,8],[2,6,7],[5,9]] => [2,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,8],[2,6,7],[5],[9]] => [2,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,7,8],[3,4],[5,6],[9]] => [3,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,7,8],[2,6],[3],[5],[9]] => [3,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,8],[2,5],[4,7],[6,9]] => [2,2,2,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,3,8],[2,5],[4,7],[6],[9]] => [2,2,2,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,5,8],[2,7],[3],[4],[6],[9]] => [4,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6,7,8,9],[2,5],[4,10]] => [2,2,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,6,7,8,9],[2,5],[4],[10]] => [2,2,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4,8,9],[2,6,7],[5,10]] => [2,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,4,8,9],[2,6,7],[5],[10]] => [2,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,7,8,9],[3,4],[5,6],[10]] => [3,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,4,7,8,9],[2,6],[3],[5],[10]] => [3,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,9],[3,4,8],[6,7,10]] => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,5,9],[3,4,8],[6,7],[10]] => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,4,5,9],[2,7,8],[3],[6],[10]] => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,8,9],[2,5],[4,7],[6,10]] => [2,2,2,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,3,8,9],[2,5],[4,7],[6],[10]] => [2,2,2,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,5,8,9],[2,7],[3],[4],[6],[10]] => [4,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,3,6],[2,5,9],[4,8],[7,10]] => [2,2,3,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,3,6],[2,5,9],[4,8],[7],[10]] => [2,2,3,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,2,9],[3,4],[5,6],[7,8],[10]] => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,4,9],[2,6],[3,8],[5],[7],[10]] => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,6,9],[2,8],[3],[4],[5],[7],[10]] => [5,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,7,8,9],[3,6],[5]] => [3,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,8,9],[4,5],[6,7]] => [4,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,8,9],[3,7],[4],[6]] => [4,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,6],[3,4,8,9],[7]] => [3,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,6],[4,5,9],[7,8]] => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,6],[3,8,9],[4],[7]] => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,6,7],[5,9],[8]] => [3,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,7],[3,6,9],[4],[5],[8]] => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5],[3,7],[4,9],[6],[8]] => [4,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,7],[3,9],[4],[5],[6],[8]] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,7,8,9,10],[3,6],[5]] => [3,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,9,10],[3,7,8],[6]] => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,3,8,9,10],[4,5],[6,7]] => [4,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,8,9,10],[3,7],[4],[6]] => [4,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6],[3,8,9,10],[7]] => [3,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,9,10],[3,6],[5,8],[7]] => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,6,9,10],[3,8],[4],[5],[7]] => [5,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,6,7],[3,5,9,10],[4],[8]] => [4,4,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,7],[3,6,10],[5,9],[8]] => [3,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,6,7],[3,9,10],[4],[5],[8]] => [5,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3],[4,5,8],[6,7],[9,10]] => [4,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,5],[3,7,8],[4,10],[6],[9]] => [4,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,8],[3,7,10],[4],[5],[6],[9]] => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4],[3,6],[5,8],[7,10],[9]] => [3,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,2,6],[3,8],[4,10],[5],[7],[9]] => [5,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,8],[3,10],[4],[5],[6],[7],[9]] => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,6,7],[3,9],[8]] => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,6,9],[3,8],[4],[7]] => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5],[3,7],[6,9],[8]] => [3,3,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2,6,7],[3,9],[4],[5],[8]] => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,6],[3,8],[4],[7],[9]] => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,8,9,10],[3,7],[6]] => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,4,5,6,7],[3,9,10],[8]] => [3,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,9,10],[5,6],[7,8]] => [5,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4,7,8],[5,6],[9,10]] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,5,6,7,8],[3,10],[4],[9]] => [4,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,10],[3,7],[6,9],[8]] => [3,3,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,2,6,7,10],[3,9],[4],[5],[8]] => [5,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5,8,9],[3,7],[6],[10]] => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,2,5,6],[3,8],[4,10],[7],[9]] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,7,8],[3,10],[4],[5],[6],[9]] => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,4,5],[3,7],[6,9],[8],[10]] => [3,3,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,2,6,7],[3,9],[4],[5],[8],[10]] => [5,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
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Description
The distinguishing index of a graph.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
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
valley composition
Description
The composition corresponding to the valley set of a standard tableau.
Let $T$ be a standard tableau of size $n$.
An entry $i$ of $T$ is a descent if $i+1$ is in a lower row (in English notation), otherwise $i$ is an ascent.
An entry $2 \leq i \leq n-1$ is a valley if $i-1$ is a descent and $i$ is an ascent.
This map returns the composition $c_1,\dots,c_k$ of $n$ such that $\{c_1, c_1+c_2,\dots, c_1+\dots+c_k\}$ is the valley set of $T$.
Let $T$ be a standard tableau of size $n$.
An entry $i$ of $T$ is a descent if $i+1$ is in a lower row (in English notation), otherwise $i$ is an ascent.
An entry $2 \leq i \leq n-1$ is a valley if $i-1$ is a descent and $i$ is an ascent.
This map returns the composition $c_1,\dots,c_k$ of $n$ such that $\{c_1, c_1+c_2,\dots, c_1+\dots+c_k\}$ is the valley set of $T$.
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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