Identifier
-
Mp00106:
Standard tableaux
—catabolism⟶
Standard tableaux
St001712: Standard tableaux ⟶ ℤ
Values
[[1]] => [[1]] => 0
[[1,2]] => [[1,2]] => 0
[[1],[2]] => [[1,2]] => 0
[[1,2,3]] => [[1,2,3]] => 0
[[1,3],[2]] => [[1,2],[3]] => 0
[[1,2],[3]] => [[1,2,3]] => 0
[[1],[2],[3]] => [[1,2],[3]] => 0
[[1,2,3,4]] => [[1,2,3,4]] => 0
[[1,3,4],[2]] => [[1,2,4],[3]] => 1
[[1,2,4],[3]] => [[1,2,3],[4]] => 0
[[1,2,3],[4]] => [[1,2,3,4]] => 0
[[1,3],[2,4]] => [[1,2,4],[3]] => 1
[[1,2],[3,4]] => [[1,2,3,4]] => 0
[[1,4],[2],[3]] => [[1,2],[3],[4]] => 0
[[1,3],[2],[4]] => [[1,2,4],[3]] => 1
[[1,2],[3],[4]] => [[1,2,3],[4]] => 0
[[1],[2],[3],[4]] => [[1,2],[3],[4]] => 0
[[1,2,3,4,5]] => [[1,2,3,4,5]] => 0
[[1,3,4,5],[2]] => [[1,2,4,5],[3]] => 1
[[1,2,4,5],[3]] => [[1,2,3,5],[4]] => 1
[[1,2,3,5],[4]] => [[1,2,3,4],[5]] => 0
[[1,2,3,4],[5]] => [[1,2,3,4,5]] => 0
[[1,3,5],[2,4]] => [[1,2,4],[3,5]] => 1
[[1,2,5],[3,4]] => [[1,2,3,4],[5]] => 0
[[1,3,4],[2,5]] => [[1,2,4,5],[3]] => 1
[[1,2,4],[3,5]] => [[1,2,3,5],[4]] => 1
[[1,2,3],[4,5]] => [[1,2,3,4,5]] => 0
[[1,4,5],[2],[3]] => [[1,2,5],[3],[4]] => 1
[[1,3,5],[2],[4]] => [[1,2,4],[3],[5]] => 1
[[1,2,5],[3],[4]] => [[1,2,3],[4],[5]] => 0
[[1,3,4],[2],[5]] => [[1,2,4,5],[3]] => 1
[[1,2,4],[3],[5]] => [[1,2,3,5],[4]] => 1
[[1,2,3],[4],[5]] => [[1,2,3,4],[5]] => 0
[[1,4],[2,5],[3]] => [[1,2,5],[3],[4]] => 1
[[1,3],[2,5],[4]] => [[1,2,4,5],[3]] => 1
[[1,2],[3,5],[4]] => [[1,2,3,5],[4]] => 1
[[1,3],[2,4],[5]] => [[1,2,4],[3,5]] => 1
[[1,2],[3,4],[5]] => [[1,2,3,4],[5]] => 0
[[1,5],[2],[3],[4]] => [[1,2],[3],[4],[5]] => 0
[[1,4],[2],[3],[5]] => [[1,2,5],[3],[4]] => 1
[[1,3],[2],[4],[5]] => [[1,2,4],[3],[5]] => 1
[[1,2],[3],[4],[5]] => [[1,2,3],[4],[5]] => 0
[[1],[2],[3],[4],[5]] => [[1,2],[3],[4],[5]] => 0
[[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => 0
[[1,3,4,5,6],[2]] => [[1,2,4,5,6],[3]] => 1
[[1,2,4,5,6],[3]] => [[1,2,3,5,6],[4]] => 1
[[1,2,3,5,6],[4]] => [[1,2,3,4,6],[5]] => 1
[[1,2,3,4,6],[5]] => [[1,2,3,4,5],[6]] => 0
[[1,2,3,4,5],[6]] => [[1,2,3,4,5,6]] => 0
[[1,3,5,6],[2,4]] => [[1,2,4,6],[3,5]] => 2
[[1,2,5,6],[3,4]] => [[1,2,3,4],[5,6]] => 0
[[1,3,4,6],[2,5]] => [[1,2,4,5],[3,6]] => 1
[[1,2,4,6],[3,5]] => [[1,2,3,5],[4,6]] => 1
[[1,2,3,6],[4,5]] => [[1,2,3,4,5],[6]] => 0
[[1,3,4,5],[2,6]] => [[1,2,4,5,6],[3]] => 1
[[1,2,4,5],[3,6]] => [[1,2,3,5,6],[4]] => 1
[[1,2,3,5],[4,6]] => [[1,2,3,4,6],[5]] => 1
[[1,2,3,4],[5,6]] => [[1,2,3,4,5,6]] => 0
[[1,4,5,6],[2],[3]] => [[1,2,5,6],[3],[4]] => 1
[[1,3,5,6],[2],[4]] => [[1,2,4,6],[3],[5]] => 2
[[1,2,5,6],[3],[4]] => [[1,2,3,6],[4],[5]] => 1
[[1,3,4,6],[2],[5]] => [[1,2,4,5],[3],[6]] => 1
[[1,2,4,6],[3],[5]] => [[1,2,3,5],[4],[6]] => 1
[[1,2,3,6],[4],[5]] => [[1,2,3,4],[5],[6]] => 0
[[1,3,4,5],[2],[6]] => [[1,2,4,5,6],[3]] => 1
[[1,2,4,5],[3],[6]] => [[1,2,3,5,6],[4]] => 1
[[1,2,3,5],[4],[6]] => [[1,2,3,4,6],[5]] => 1
[[1,2,3,4],[5],[6]] => [[1,2,3,4,5],[6]] => 0
[[1,3,5],[2,4,6]] => [[1,2,4,6],[3,5]] => 2
[[1,2,5],[3,4,6]] => [[1,2,3,4,6],[5]] => 1
[[1,3,4],[2,5,6]] => [[1,2,4,5,6],[3]] => 1
[[1,2,4],[3,5,6]] => [[1,2,3,5,6],[4]] => 1
[[1,2,3],[4,5,6]] => [[1,2,3,4,5,6]] => 0
[[1,4,6],[2,5],[3]] => [[1,2,5],[3,6],[4]] => 1
[[1,3,6],[2,5],[4]] => [[1,2,4,5],[3],[6]] => 1
[[1,2,6],[3,5],[4]] => [[1,2,3,5],[4],[6]] => 1
[[1,3,6],[2,4],[5]] => [[1,2,4],[3,5],[6]] => 1
[[1,2,6],[3,4],[5]] => [[1,2,3,4],[5],[6]] => 0
[[1,4,5],[2,6],[3]] => [[1,2,5,6],[3],[4]] => 1
[[1,3,5],[2,6],[4]] => [[1,2,4,6],[3],[5]] => 2
[[1,2,5],[3,6],[4]] => [[1,2,3,6],[4],[5]] => 1
[[1,3,4],[2,6],[5]] => [[1,2,4,5,6],[3]] => 1
[[1,2,4],[3,6],[5]] => [[1,2,3,5,6],[4]] => 1
[[1,2,3],[4,6],[5]] => [[1,2,3,4,6],[5]] => 1
[[1,3,5],[2,4],[6]] => [[1,2,4,6],[3,5]] => 2
[[1,2,5],[3,4],[6]] => [[1,2,3,4],[5,6]] => 0
[[1,3,4],[2,5],[6]] => [[1,2,4,5],[3,6]] => 1
[[1,2,4],[3,5],[6]] => [[1,2,3,5],[4,6]] => 1
[[1,2,3],[4,5],[6]] => [[1,2,3,4,5],[6]] => 0
[[1,5,6],[2],[3],[4]] => [[1,2,6],[3],[4],[5]] => 1
[[1,4,6],[2],[3],[5]] => [[1,2,5],[3],[4],[6]] => 1
[[1,3,6],[2],[4],[5]] => [[1,2,4],[3],[5],[6]] => 1
[[1,2,6],[3],[4],[5]] => [[1,2,3],[4],[5],[6]] => 0
[[1,4,5],[2],[3],[6]] => [[1,2,5,6],[3],[4]] => 1
[[1,3,5],[2],[4],[6]] => [[1,2,4,6],[3],[5]] => 2
[[1,2,5],[3],[4],[6]] => [[1,2,3,6],[4],[5]] => 1
[[1,3,4],[2],[5],[6]] => [[1,2,4,5],[3],[6]] => 1
[[1,2,4],[3],[5],[6]] => [[1,2,3,5],[4],[6]] => 1
[[1,2,3],[4],[5],[6]] => [[1,2,3,4],[5],[6]] => 0
[[1,4],[2,5],[3,6]] => [[1,2,5],[3,6],[4]] => 1
[[1,3],[2,5],[4,6]] => [[1,2,4,5],[3,6]] => 1
>>> Load all 1115 entries. <<<[[1,2],[3,5],[4,6]] => [[1,2,3,5],[4,6]] => 1
[[1,3],[2,4],[5,6]] => [[1,2,4,6],[3,5]] => 2
[[1,2],[3,4],[5,6]] => [[1,2,3,4],[5,6]] => 0
[[1,5],[2,6],[3],[4]] => [[1,2,6],[3],[4],[5]] => 1
[[1,4],[2,6],[3],[5]] => [[1,2,5,6],[3],[4]] => 1
[[1,3],[2,6],[4],[5]] => [[1,2,4,6],[3],[5]] => 2
[[1,2],[3,6],[4],[5]] => [[1,2,3,6],[4],[5]] => 1
[[1,4],[2,5],[3],[6]] => [[1,2,5],[3,6],[4]] => 1
[[1,3],[2,5],[4],[6]] => [[1,2,4,5],[3],[6]] => 1
[[1,2],[3,5],[4],[6]] => [[1,2,3,5],[4],[6]] => 1
[[1,3],[2,4],[5],[6]] => [[1,2,4],[3,5],[6]] => 1
[[1,2],[3,4],[5],[6]] => [[1,2,3,4],[5],[6]] => 0
[[1,6],[2],[3],[4],[5]] => [[1,2],[3],[4],[5],[6]] => 0
[[1,5],[2],[3],[4],[6]] => [[1,2,6],[3],[4],[5]] => 1
[[1,4],[2],[3],[5],[6]] => [[1,2,5],[3],[4],[6]] => 1
[[1,3],[2],[4],[5],[6]] => [[1,2,4],[3],[5],[6]] => 1
[[1,2],[3],[4],[5],[6]] => [[1,2,3],[4],[5],[6]] => 0
[[1],[2],[3],[4],[5],[6]] => [[1,2],[3],[4],[5],[6]] => 0
[[1,2,3,4,5,6,7]] => [[1,2,3,4,5,6,7]] => 0
[[1,3,4,5,6,7],[2]] => [[1,2,4,5,6,7],[3]] => 1
[[1,2,4,5,6,7],[3]] => [[1,2,3,5,6,7],[4]] => 1
[[1,2,3,5,6,7],[4]] => [[1,2,3,4,6,7],[5]] => 1
[[1,2,3,4,6,7],[5]] => [[1,2,3,4,5,7],[6]] => 1
[[1,2,3,4,5,7],[6]] => [[1,2,3,4,5,6],[7]] => 0
[[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,6,7]] => 0
[[1,3,5,6,7],[2,4]] => [[1,2,4,6,7],[3,5]] => 2
[[1,2,5,6,7],[3,4]] => [[1,2,3,4,7],[5,6]] => 1
[[1,3,4,6,7],[2,5]] => [[1,2,4,5,7],[3,6]] => 2
[[1,2,4,6,7],[3,5]] => [[1,2,3,5,7],[4,6]] => 2
[[1,2,3,6,7],[4,5]] => [[1,2,3,4,5],[6,7]] => 0
[[1,3,4,5,7],[2,6]] => [[1,2,4,5,6],[3,7]] => 1
[[1,2,4,5,7],[3,6]] => [[1,2,3,5,6],[4,7]] => 1
[[1,2,3,5,7],[4,6]] => [[1,2,3,4,6],[5,7]] => 1
[[1,2,3,4,7],[5,6]] => [[1,2,3,4,5,6],[7]] => 0
[[1,3,4,5,6],[2,7]] => [[1,2,4,5,6,7],[3]] => 1
[[1,2,4,5,6],[3,7]] => [[1,2,3,5,6,7],[4]] => 1
[[1,2,3,5,6],[4,7]] => [[1,2,3,4,6,7],[5]] => 1
[[1,2,3,4,6],[5,7]] => [[1,2,3,4,5,7],[6]] => 1
[[1,2,3,4,5],[6,7]] => [[1,2,3,4,5,6,7]] => 0
[[1,4,5,6,7],[2],[3]] => [[1,2,5,6,7],[3],[4]] => 1
[[1,3,5,6,7],[2],[4]] => [[1,2,4,6,7],[3],[5]] => 2
[[1,2,5,6,7],[3],[4]] => [[1,2,3,6,7],[4],[5]] => 1
[[1,3,4,6,7],[2],[5]] => [[1,2,4,5,7],[3],[6]] => 2
[[1,2,4,6,7],[3],[5]] => [[1,2,3,5,7],[4],[6]] => 2
[[1,2,3,6,7],[4],[5]] => [[1,2,3,4,7],[5],[6]] => 1
[[1,3,4,5,7],[2],[6]] => [[1,2,4,5,6],[3],[7]] => 1
[[1,2,4,5,7],[3],[6]] => [[1,2,3,5,6],[4],[7]] => 1
[[1,2,3,5,7],[4],[6]] => [[1,2,3,4,6],[5],[7]] => 1
[[1,2,3,4,7],[5],[6]] => [[1,2,3,4,5],[6],[7]] => 0
[[1,3,4,5,6],[2],[7]] => [[1,2,4,5,6,7],[3]] => 1
[[1,2,4,5,6],[3],[7]] => [[1,2,3,5,6,7],[4]] => 1
[[1,2,3,5,6],[4],[7]] => [[1,2,3,4,6,7],[5]] => 1
[[1,2,3,4,6],[5],[7]] => [[1,2,3,4,5,7],[6]] => 1
[[1,2,3,4,5],[6],[7]] => [[1,2,3,4,5,6],[7]] => 0
[[1,3,5,7],[2,4,6]] => [[1,2,4,6],[3,5,7]] => 2
[[1,2,5,7],[3,4,6]] => [[1,2,3,4,6],[5,7]] => 1
[[1,3,4,7],[2,5,6]] => [[1,2,4,5,6],[3,7]] => 1
[[1,2,4,7],[3,5,6]] => [[1,2,3,5,6],[4,7]] => 1
[[1,2,3,7],[4,5,6]] => [[1,2,3,4,5,6],[7]] => 0
[[1,3,5,6],[2,4,7]] => [[1,2,4,6,7],[3,5]] => 2
[[1,2,5,6],[3,4,7]] => [[1,2,3,4,7],[5,6]] => 1
[[1,3,4,6],[2,5,7]] => [[1,2,4,5,7],[3,6]] => 2
[[1,2,4,6],[3,5,7]] => [[1,2,3,5,7],[4,6]] => 2
[[1,2,3,6],[4,5,7]] => [[1,2,3,4,5,7],[6]] => 1
[[1,3,4,5],[2,6,7]] => [[1,2,4,5,6,7],[3]] => 1
[[1,2,4,5],[3,6,7]] => [[1,2,3,5,6,7],[4]] => 1
[[1,2,3,5],[4,6,7]] => [[1,2,3,4,6,7],[5]] => 1
[[1,2,3,4],[5,6,7]] => [[1,2,3,4,5,6,7]] => 0
[[1,4,6,7],[2,5],[3]] => [[1,2,5,7],[3,6],[4]] => 2
[[1,3,6,7],[2,5],[4]] => [[1,2,4,5],[3,7],[6]] => 2
[[1,2,6,7],[3,5],[4]] => [[1,2,3,5],[4,7],[6]] => 2
[[1,3,6,7],[2,4],[5]] => [[1,2,4,7],[3,5],[6]] => 2
[[1,2,6,7],[3,4],[5]] => [[1,2,3,4],[5,7],[6]] => 1
[[1,4,5,7],[2,6],[3]] => [[1,2,5,6],[3,7],[4]] => 1
[[1,3,5,7],[2,6],[4]] => [[1,2,4,6],[3,7],[5]] => 2
[[1,2,5,7],[3,6],[4]] => [[1,2,3,6],[4,7],[5]] => 1
[[1,3,4,7],[2,6],[5]] => [[1,2,4,5,6],[3],[7]] => 1
[[1,2,4,7],[3,6],[5]] => [[1,2,3,5,6],[4],[7]] => 1
[[1,2,3,7],[4,6],[5]] => [[1,2,3,4,6],[5],[7]] => 1
[[1,3,5,7],[2,4],[6]] => [[1,2,4,6],[3,5],[7]] => 2
[[1,2,5,7],[3,4],[6]] => [[1,2,3,4],[5,6],[7]] => 0
[[1,3,4,7],[2,5],[6]] => [[1,2,4,5],[3,6],[7]] => 1
[[1,2,4,7],[3,5],[6]] => [[1,2,3,5],[4,6],[7]] => 1
[[1,2,3,7],[4,5],[6]] => [[1,2,3,4,5],[6],[7]] => 0
[[1,4,5,6],[2,7],[3]] => [[1,2,5,6,7],[3],[4]] => 1
[[1,3,5,6],[2,7],[4]] => [[1,2,4,6,7],[3],[5]] => 2
[[1,2,5,6],[3,7],[4]] => [[1,2,3,6,7],[4],[5]] => 1
[[1,3,4,6],[2,7],[5]] => [[1,2,4,5,7],[3],[6]] => 2
[[1,2,4,6],[3,7],[5]] => [[1,2,3,5,7],[4],[6]] => 2
[[1,2,3,6],[4,7],[5]] => [[1,2,3,4,7],[5],[6]] => 1
[[1,3,4,5],[2,7],[6]] => [[1,2,4,5,6,7],[3]] => 1
[[1,2,4,5],[3,7],[6]] => [[1,2,3,5,6,7],[4]] => 1
[[1,2,3,5],[4,7],[6]] => [[1,2,3,4,6,7],[5]] => 1
[[1,2,3,4],[5,7],[6]] => [[1,2,3,4,5,7],[6]] => 1
[[1,3,5,6],[2,4],[7]] => [[1,2,4,6,7],[3,5]] => 2
[[1,2,5,6],[3,4],[7]] => [[1,2,3,4,7],[5,6]] => 1
[[1,3,4,6],[2,5],[7]] => [[1,2,4,5,7],[3,6]] => 2
[[1,2,4,6],[3,5],[7]] => [[1,2,3,5,7],[4,6]] => 2
[[1,2,3,6],[4,5],[7]] => [[1,2,3,4,5],[6,7]] => 0
[[1,3,4,5],[2,6],[7]] => [[1,2,4,5,6],[3,7]] => 1
[[1,2,4,5],[3,6],[7]] => [[1,2,3,5,6],[4,7]] => 1
[[1,2,3,5],[4,6],[7]] => [[1,2,3,4,6],[5,7]] => 1
[[1,2,3,4],[5,6],[7]] => [[1,2,3,4,5,6],[7]] => 0
[[1,5,6,7],[2],[3],[4]] => [[1,2,6,7],[3],[4],[5]] => 1
[[1,4,6,7],[2],[3],[5]] => [[1,2,5,7],[3],[4],[6]] => 2
[[1,3,6,7],[2],[4],[5]] => [[1,2,4,7],[3],[5],[6]] => 2
[[1,2,6,7],[3],[4],[5]] => [[1,2,3,7],[4],[5],[6]] => 1
[[1,4,5,7],[2],[3],[6]] => [[1,2,5,6],[3],[4],[7]] => 1
[[1,3,5,7],[2],[4],[6]] => [[1,2,4,6],[3],[5],[7]] => 2
[[1,2,5,7],[3],[4],[6]] => [[1,2,3,6],[4],[5],[7]] => 1
[[1,3,4,7],[2],[5],[6]] => [[1,2,4,5],[3],[6],[7]] => 1
[[1,2,4,7],[3],[5],[6]] => [[1,2,3,5],[4],[6],[7]] => 1
[[1,2,3,7],[4],[5],[6]] => [[1,2,3,4],[5],[6],[7]] => 0
[[1,4,5,6],[2],[3],[7]] => [[1,2,5,6,7],[3],[4]] => 1
[[1,3,5,6],[2],[4],[7]] => [[1,2,4,6,7],[3],[5]] => 2
[[1,2,5,6],[3],[4],[7]] => [[1,2,3,6,7],[4],[5]] => 1
[[1,3,4,6],[2],[5],[7]] => [[1,2,4,5,7],[3],[6]] => 2
[[1,2,4,6],[3],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 2
[[1,2,3,6],[4],[5],[7]] => [[1,2,3,4,7],[5],[6]] => 1
[[1,3,4,5],[2],[6],[7]] => [[1,2,4,5,6],[3],[7]] => 1
[[1,2,4,5],[3],[6],[7]] => [[1,2,3,5,6],[4],[7]] => 1
[[1,2,3,5],[4],[6],[7]] => [[1,2,3,4,6],[5],[7]] => 1
[[1,2,3,4],[5],[6],[7]] => [[1,2,3,4,5],[6],[7]] => 0
[[1,4,6],[2,5,7],[3]] => [[1,2,5,7],[3,6],[4]] => 2
[[1,3,6],[2,5,7],[4]] => [[1,2,4,5,7],[3],[6]] => 2
[[1,2,6],[3,5,7],[4]] => [[1,2,3,5,7],[4],[6]] => 2
[[1,3,6],[2,4,7],[5]] => [[1,2,4,7],[3,5],[6]] => 2
[[1,2,6],[3,4,7],[5]] => [[1,2,3,4,7],[5],[6]] => 1
[[1,4,5],[2,6,7],[3]] => [[1,2,5,6,7],[3],[4]] => 1
[[1,3,5],[2,6,7],[4]] => [[1,2,4,6,7],[3],[5]] => 2
[[1,2,5],[3,6,7],[4]] => [[1,2,3,6,7],[4],[5]] => 1
[[1,3,4],[2,6,7],[5]] => [[1,2,4,5,6,7],[3]] => 1
[[1,2,4],[3,6,7],[5]] => [[1,2,3,5,6,7],[4]] => 1
[[1,2,3],[4,6,7],[5]] => [[1,2,3,4,6,7],[5]] => 1
[[1,3,5],[2,4,7],[6]] => [[1,2,4,6,7],[3,5]] => 2
[[1,2,5],[3,4,7],[6]] => [[1,2,3,4,7],[5,6]] => 1
[[1,3,4],[2,5,7],[6]] => [[1,2,4,5,7],[3,6]] => 2
[[1,2,4],[3,5,7],[6]] => [[1,2,3,5,7],[4,6]] => 2
[[1,2,3],[4,5,7],[6]] => [[1,2,3,4,5,7],[6]] => 1
[[1,3,5],[2,4,6],[7]] => [[1,2,4,6],[3,5,7]] => 2
[[1,2,5],[3,4,6],[7]] => [[1,2,3,4,6],[5,7]] => 1
[[1,3,4],[2,5,6],[7]] => [[1,2,4,5,6],[3,7]] => 1
[[1,2,4],[3,5,6],[7]] => [[1,2,3,5,6],[4,7]] => 1
[[1,2,3],[4,5,6],[7]] => [[1,2,3,4,5,6],[7]] => 0
[[1,4,7],[2,5],[3,6]] => [[1,2,5],[3,6],[4,7]] => 1
[[1,3,7],[2,5],[4,6]] => [[1,2,4,5],[3,6],[7]] => 1
[[1,2,7],[3,5],[4,6]] => [[1,2,3,5],[4,6],[7]] => 1
[[1,3,7],[2,4],[5,6]] => [[1,2,4,6],[3,5],[7]] => 2
[[1,2,7],[3,4],[5,6]] => [[1,2,3,4],[5,6],[7]] => 0
[[1,4,6],[2,5],[3,7]] => [[1,2,5,7],[3,6],[4]] => 2
[[1,3,6],[2,5],[4,7]] => [[1,2,4,5],[3,7],[6]] => 2
[[1,2,6],[3,5],[4,7]] => [[1,2,3,5],[4,7],[6]] => 2
[[1,3,6],[2,4],[5,7]] => [[1,2,4,7],[3,5],[6]] => 2
[[1,2,6],[3,4],[5,7]] => [[1,2,3,4],[5,7],[6]] => 1
[[1,4,5],[2,6],[3,7]] => [[1,2,5,6],[3,7],[4]] => 1
[[1,3,5],[2,6],[4,7]] => [[1,2,4,6],[3,7],[5]] => 2
[[1,2,5],[3,6],[4,7]] => [[1,2,3,6],[4,7],[5]] => 1
[[1,3,4],[2,6],[5,7]] => [[1,2,4,5,6],[3,7]] => 1
[[1,2,4],[3,6],[5,7]] => [[1,2,3,5,6],[4,7]] => 1
[[1,2,3],[4,6],[5,7]] => [[1,2,3,4,6],[5,7]] => 1
[[1,3,5],[2,4],[6,7]] => [[1,2,4,6,7],[3,5]] => 2
[[1,2,5],[3,4],[6,7]] => [[1,2,3,4,7],[5,6]] => 1
[[1,3,4],[2,5],[6,7]] => [[1,2,4,5,7],[3,6]] => 2
[[1,2,4],[3,5],[6,7]] => [[1,2,3,5,7],[4,6]] => 2
[[1,2,3],[4,5],[6,7]] => [[1,2,3,4,5],[6,7]] => 0
[[1,5,7],[2,6],[3],[4]] => [[1,2,6],[3,7],[4],[5]] => 1
[[1,4,7],[2,6],[3],[5]] => [[1,2,5,6],[3],[4],[7]] => 1
[[1,3,7],[2,6],[4],[5]] => [[1,2,4,6],[3],[5],[7]] => 2
[[1,2,7],[3,6],[4],[5]] => [[1,2,3,6],[4],[5],[7]] => 1
[[1,4,7],[2,5],[3],[6]] => [[1,2,5],[3,6],[4],[7]] => 1
[[1,3,7],[2,5],[4],[6]] => [[1,2,4,5],[3],[6],[7]] => 1
[[1,2,7],[3,5],[4],[6]] => [[1,2,3,5],[4],[6],[7]] => 1
[[1,3,7],[2,4],[5],[6]] => [[1,2,4],[3,5],[6],[7]] => 1
[[1,2,7],[3,4],[5],[6]] => [[1,2,3,4],[5],[6],[7]] => 0
[[1,5,6],[2,7],[3],[4]] => [[1,2,6,7],[3],[4],[5]] => 1
[[1,4,6],[2,7],[3],[5]] => [[1,2,5,7],[3],[4],[6]] => 2
[[1,3,6],[2,7],[4],[5]] => [[1,2,4,7],[3],[5],[6]] => 2
[[1,2,6],[3,7],[4],[5]] => [[1,2,3,7],[4],[5],[6]] => 1
[[1,4,5],[2,7],[3],[6]] => [[1,2,5,6,7],[3],[4]] => 1
[[1,3,5],[2,7],[4],[6]] => [[1,2,4,6,7],[3],[5]] => 2
[[1,2,5],[3,7],[4],[6]] => [[1,2,3,6,7],[4],[5]] => 1
[[1,3,4],[2,7],[5],[6]] => [[1,2,4,5,7],[3],[6]] => 2
[[1,2,4],[3,7],[5],[6]] => [[1,2,3,5,7],[4],[6]] => 2
[[1,2,3],[4,7],[5],[6]] => [[1,2,3,4,7],[5],[6]] => 1
[[1,4,6],[2,5],[3],[7]] => [[1,2,5,7],[3,6],[4]] => 2
[[1,3,6],[2,5],[4],[7]] => [[1,2,4,5],[3,7],[6]] => 2
[[1,2,6],[3,5],[4],[7]] => [[1,2,3,5],[4,7],[6]] => 2
[[1,3,6],[2,4],[5],[7]] => [[1,2,4,7],[3,5],[6]] => 2
[[1,2,6],[3,4],[5],[7]] => [[1,2,3,4],[5,7],[6]] => 1
[[1,4,5],[2,6],[3],[7]] => [[1,2,5,6],[3,7],[4]] => 1
[[1,3,5],[2,6],[4],[7]] => [[1,2,4,6],[3,7],[5]] => 2
[[1,2,5],[3,6],[4],[7]] => [[1,2,3,6],[4,7],[5]] => 1
[[1,3,4],[2,6],[5],[7]] => [[1,2,4,5,6],[3],[7]] => 1
[[1,2,4],[3,6],[5],[7]] => [[1,2,3,5,6],[4],[7]] => 1
[[1,2,3],[4,6],[5],[7]] => [[1,2,3,4,6],[5],[7]] => 1
[[1,3,5],[2,4],[6],[7]] => [[1,2,4,6],[3,5],[7]] => 2
[[1,2,5],[3,4],[6],[7]] => [[1,2,3,4],[5,6],[7]] => 0
[[1,3,4],[2,5],[6],[7]] => [[1,2,4,5],[3,6],[7]] => 1
[[1,2,4],[3,5],[6],[7]] => [[1,2,3,5],[4,6],[7]] => 1
[[1,2,3],[4,5],[6],[7]] => [[1,2,3,4,5],[6],[7]] => 0
[[1,6,7],[2],[3],[4],[5]] => [[1,2,7],[3],[4],[5],[6]] => 1
[[1,5,7],[2],[3],[4],[6]] => [[1,2,6],[3],[4],[5],[7]] => 1
[[1,4,7],[2],[3],[5],[6]] => [[1,2,5],[3],[4],[6],[7]] => 1
[[1,3,7],[2],[4],[5],[6]] => [[1,2,4],[3],[5],[6],[7]] => 1
[[1,2,7],[3],[4],[5],[6]] => [[1,2,3],[4],[5],[6],[7]] => 0
[[1,5,6],[2],[3],[4],[7]] => [[1,2,6,7],[3],[4],[5]] => 1
[[1,4,6],[2],[3],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 2
[[1,3,6],[2],[4],[5],[7]] => [[1,2,4,7],[3],[5],[6]] => 2
[[1,2,6],[3],[4],[5],[7]] => [[1,2,3,7],[4],[5],[6]] => 1
[[1,4,5],[2],[3],[6],[7]] => [[1,2,5,6],[3],[4],[7]] => 1
[[1,3,5],[2],[4],[6],[7]] => [[1,2,4,6],[3],[5],[7]] => 2
[[1,2,5],[3],[4],[6],[7]] => [[1,2,3,6],[4],[5],[7]] => 1
[[1,3,4],[2],[5],[6],[7]] => [[1,2,4,5],[3],[6],[7]] => 1
[[1,2,4],[3],[5],[6],[7]] => [[1,2,3,5],[4],[6],[7]] => 1
[[1,2,3],[4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7]] => 0
[[1,5],[2,6],[3,7],[4]] => [[1,2,6],[3,7],[4],[5]] => 1
[[1,4],[2,6],[3,7],[5]] => [[1,2,5,6],[3,7],[4]] => 1
[[1,3],[2,6],[4,7],[5]] => [[1,2,4,6],[3,7],[5]] => 2
[[1,2],[3,6],[4,7],[5]] => [[1,2,3,6],[4,7],[5]] => 1
[[1,4],[2,5],[3,7],[6]] => [[1,2,5,7],[3,6],[4]] => 2
[[1,3],[2,5],[4,7],[6]] => [[1,2,4,5],[3,7],[6]] => 2
[[1,2],[3,5],[4,7],[6]] => [[1,2,3,5],[4,7],[6]] => 2
[[1,3],[2,4],[5,7],[6]] => [[1,2,4,7],[3,5],[6]] => 2
[[1,2],[3,4],[5,7],[6]] => [[1,2,3,4],[5,7],[6]] => 1
[[1,4],[2,5],[3,6],[7]] => [[1,2,5],[3,6],[4,7]] => 1
[[1,3],[2,5],[4,6],[7]] => [[1,2,4,5],[3,6],[7]] => 1
[[1,2],[3,5],[4,6],[7]] => [[1,2,3,5],[4,6],[7]] => 1
[[1,3],[2,4],[5,6],[7]] => [[1,2,4,6],[3,5],[7]] => 2
[[1,2],[3,4],[5,6],[7]] => [[1,2,3,4],[5,6],[7]] => 0
[[1,6],[2,7],[3],[4],[5]] => [[1,2,7],[3],[4],[5],[6]] => 1
[[1,5],[2,7],[3],[4],[6]] => [[1,2,6,7],[3],[4],[5]] => 1
[[1,4],[2,7],[3],[5],[6]] => [[1,2,5,7],[3],[4],[6]] => 2
[[1,3],[2,7],[4],[5],[6]] => [[1,2,4,7],[3],[5],[6]] => 2
[[1,2],[3,7],[4],[5],[6]] => [[1,2,3,7],[4],[5],[6]] => 1
[[1,5],[2,6],[3],[4],[7]] => [[1,2,6],[3,7],[4],[5]] => 1
[[1,4],[2,6],[3],[5],[7]] => [[1,2,5,6],[3],[4],[7]] => 1
[[1,3],[2,6],[4],[5],[7]] => [[1,2,4,6],[3],[5],[7]] => 2
[[1,2],[3,6],[4],[5],[7]] => [[1,2,3,6],[4],[5],[7]] => 1
[[1,4],[2,5],[3],[6],[7]] => [[1,2,5],[3,6],[4],[7]] => 1
[[1,3],[2,5],[4],[6],[7]] => [[1,2,4,5],[3],[6],[7]] => 1
[[1,2],[3,5],[4],[6],[7]] => [[1,2,3,5],[4],[6],[7]] => 1
[[1,3],[2,4],[5],[6],[7]] => [[1,2,4],[3,5],[6],[7]] => 1
[[1,2],[3,4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7]] => 0
[[1,7],[2],[3],[4],[5],[6]] => [[1,2],[3],[4],[5],[6],[7]] => 0
[[1,6],[2],[3],[4],[5],[7]] => [[1,2,7],[3],[4],[5],[6]] => 1
[[1,5],[2],[3],[4],[6],[7]] => [[1,2,6],[3],[4],[5],[7]] => 1
[[1,4],[2],[3],[5],[6],[7]] => [[1,2,5],[3],[4],[6],[7]] => 1
[[1,3],[2],[4],[5],[6],[7]] => [[1,2,4],[3],[5],[6],[7]] => 1
[[1,2],[3],[4],[5],[6],[7]] => [[1,2,3],[4],[5],[6],[7]] => 0
[[1],[2],[3],[4],[5],[6],[7]] => [[1,2],[3],[4],[5],[6],[7]] => 0
[[1,2,3,4,5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => 0
[[1,3,4,5,6,7,8],[2]] => [[1,2,4,5,6,7,8],[3]] => 1
[[1,2,4,5,6,7,8],[3]] => [[1,2,3,5,6,7,8],[4]] => 1
[[1,2,3,5,6,7,8],[4]] => [[1,2,3,4,6,7,8],[5]] => 1
[[1,2,3,4,6,7,8],[5]] => [[1,2,3,4,5,7,8],[6]] => 1
[[1,2,3,4,5,7,8],[6]] => [[1,2,3,4,5,6,8],[7]] => 1
[[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,6,7],[8]] => 0
[[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,7,8]] => 0
[[1,3,5,6,7,8],[2,4]] => [[1,2,4,6,7,8],[3,5]] => 2
[[1,2,5,6,7,8],[3,4]] => [[1,2,3,4,7,8],[5,6]] => 1
[[1,3,4,6,7,8],[2,5]] => [[1,2,4,5,7,8],[3,6]] => 2
[[1,2,4,6,7,8],[3,5]] => [[1,2,3,5,7,8],[4,6]] => 2
[[1,2,3,6,7,8],[4,5]] => [[1,2,3,4,5,8],[6,7]] => 1
[[1,3,4,5,7,8],[2,6]] => [[1,2,4,5,6,8],[3,7]] => 2
[[1,2,4,5,7,8],[3,6]] => [[1,2,3,5,6,8],[4,7]] => 2
[[1,2,3,5,7,8],[4,6]] => [[1,2,3,4,6,8],[5,7]] => 2
[[1,2,3,4,7,8],[5,6]] => [[1,2,3,4,5,6],[7,8]] => 0
[[1,3,4,5,6,8],[2,7]] => [[1,2,4,5,6,7],[3,8]] => 1
[[1,2,4,5,6,8],[3,7]] => [[1,2,3,5,6,7],[4,8]] => 1
[[1,2,3,5,6,8],[4,7]] => [[1,2,3,4,6,7],[5,8]] => 1
[[1,2,3,4,6,8],[5,7]] => [[1,2,3,4,5,7],[6,8]] => 1
[[1,2,3,4,5,8],[6,7]] => [[1,2,3,4,5,6,7],[8]] => 0
[[1,3,4,5,6,7],[2,8]] => [[1,2,4,5,6,7,8],[3]] => 1
[[1,2,4,5,6,7],[3,8]] => [[1,2,3,5,6,7,8],[4]] => 1
[[1,2,3,5,6,7],[4,8]] => [[1,2,3,4,6,7,8],[5]] => 1
[[1,2,3,4,6,7],[5,8]] => [[1,2,3,4,5,7,8],[6]] => 1
[[1,2,3,4,5,7],[6,8]] => [[1,2,3,4,5,6,8],[7]] => 1
[[1,2,3,4,5,6],[7,8]] => [[1,2,3,4,5,6,7,8]] => 0
[[1,4,5,6,7,8],[2],[3]] => [[1,2,5,6,7,8],[3],[4]] => 1
[[1,3,5,6,7,8],[2],[4]] => [[1,2,4,6,7,8],[3],[5]] => 2
[[1,2,5,6,7,8],[3],[4]] => [[1,2,3,6,7,8],[4],[5]] => 1
[[1,3,4,6,7,8],[2],[5]] => [[1,2,4,5,7,8],[3],[6]] => 2
[[1,2,4,6,7,8],[3],[5]] => [[1,2,3,5,7,8],[4],[6]] => 2
[[1,2,3,6,7,8],[4],[5]] => [[1,2,3,4,7,8],[5],[6]] => 1
[[1,3,4,5,7,8],[2],[6]] => [[1,2,4,5,6,8],[3],[7]] => 2
[[1,2,4,5,7,8],[3],[6]] => [[1,2,3,5,6,8],[4],[7]] => 2
[[1,2,3,5,7,8],[4],[6]] => [[1,2,3,4,6,8],[5],[7]] => 2
[[1,2,3,4,7,8],[5],[6]] => [[1,2,3,4,5,8],[6],[7]] => 1
[[1,3,4,5,6,8],[2],[7]] => [[1,2,4,5,6,7],[3],[8]] => 1
[[1,2,4,5,6,8],[3],[7]] => [[1,2,3,5,6,7],[4],[8]] => 1
[[1,2,3,5,6,8],[4],[7]] => [[1,2,3,4,6,7],[5],[8]] => 1
[[1,2,3,4,6,8],[5],[7]] => [[1,2,3,4,5,7],[6],[8]] => 1
[[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,5,6],[7],[8]] => 0
[[1,3,4,5,6,7],[2],[8]] => [[1,2,4,5,6,7,8],[3]] => 1
[[1,2,4,5,6,7],[3],[8]] => [[1,2,3,5,6,7,8],[4]] => 1
[[1,2,3,5,6,7],[4],[8]] => [[1,2,3,4,6,7,8],[5]] => 1
[[1,2,3,4,6,7],[5],[8]] => [[1,2,3,4,5,7,8],[6]] => 1
[[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,5,6,8],[7]] => 1
[[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,6,7],[8]] => 0
[[1,3,5,7,8],[2,4,6]] => [[1,2,4,6,8],[3,5,7]] => 3
[[1,2,5,7,8],[3,4,6]] => [[1,2,3,4,6],[5,7,8]] => 1
[[1,3,4,7,8],[2,5,6]] => [[1,2,4,5,6],[3,7,8]] => 1
[[1,2,4,7,8],[3,5,6]] => [[1,2,3,5,6],[4,7,8]] => 1
[[1,2,3,7,8],[4,5,6]] => [[1,2,3,4,5,6],[7,8]] => 0
[[1,3,5,6,8],[2,4,7]] => [[1,2,4,6,7],[3,5,8]] => 2
[[1,2,5,6,8],[3,4,7]] => [[1,2,3,4,7],[5,6,8]] => 1
[[1,3,4,6,8],[2,5,7]] => [[1,2,4,5,7],[3,6,8]] => 2
[[1,2,4,6,8],[3,5,7]] => [[1,2,3,5,7],[4,6,8]] => 2
[[1,2,3,6,8],[4,5,7]] => [[1,2,3,4,5,7],[6,8]] => 1
[[1,3,4,5,8],[2,6,7]] => [[1,2,4,5,6,7],[3,8]] => 1
[[1,2,4,5,8],[3,6,7]] => [[1,2,3,5,6,7],[4,8]] => 1
[[1,2,3,5,8],[4,6,7]] => [[1,2,3,4,6,7],[5,8]] => 1
[[1,2,3,4,8],[5,6,7]] => [[1,2,3,4,5,6,7],[8]] => 0
[[1,3,5,6,7],[2,4,8]] => [[1,2,4,6,7,8],[3,5]] => 2
[[1,2,5,6,7],[3,4,8]] => [[1,2,3,4,7,8],[5,6]] => 1
[[1,3,4,6,7],[2,5,8]] => [[1,2,4,5,7,8],[3,6]] => 2
[[1,2,4,6,7],[3,5,8]] => [[1,2,3,5,7,8],[4,6]] => 2
[[1,2,3,6,7],[4,5,8]] => [[1,2,3,4,5,8],[6,7]] => 1
[[1,3,4,5,7],[2,6,8]] => [[1,2,4,5,6,8],[3,7]] => 2
[[1,2,4,5,7],[3,6,8]] => [[1,2,3,5,6,8],[4,7]] => 2
[[1,2,3,5,7],[4,6,8]] => [[1,2,3,4,6,8],[5,7]] => 2
[[1,2,3,4,7],[5,6,8]] => [[1,2,3,4,5,6,8],[7]] => 1
[[1,3,4,5,6],[2,7,8]] => [[1,2,4,5,6,7,8],[3]] => 1
[[1,2,4,5,6],[3,7,8]] => [[1,2,3,5,6,7,8],[4]] => 1
[[1,2,3,5,6],[4,7,8]] => [[1,2,3,4,6,7,8],[5]] => 1
[[1,2,3,4,6],[5,7,8]] => [[1,2,3,4,5,7,8],[6]] => 1
[[1,2,3,4,5],[6,7,8]] => [[1,2,3,4,5,6,7,8]] => 0
[[1,4,6,7,8],[2,5],[3]] => [[1,2,5,7,8],[3,6],[4]] => 2
[[1,3,6,7,8],[2,5],[4]] => [[1,2,4,5,8],[3,7],[6]] => 3
[[1,2,6,7,8],[3,5],[4]] => [[1,2,3,5,8],[4,7],[6]] => 3
[[1,3,6,7,8],[2,4],[5]] => [[1,2,4,7,8],[3,5],[6]] => 2
[[1,2,6,7,8],[3,4],[5]] => [[1,2,3,4,8],[5,7],[6]] => 2
[[1,4,5,7,8],[2,6],[3]] => [[1,2,5,6,8],[3,7],[4]] => 2
[[1,3,5,7,8],[2,6],[4]] => [[1,2,4,6,8],[3,7],[5]] => 3
[[1,2,5,7,8],[3,6],[4]] => [[1,2,3,6,8],[4,7],[5]] => 2
[[1,3,4,7,8],[2,6],[5]] => [[1,2,4,5,6],[3,8],[7]] => 2
[[1,2,4,7,8],[3,6],[5]] => [[1,2,3,5,6],[4,8],[7]] => 2
[[1,2,3,7,8],[4,6],[5]] => [[1,2,3,4,6],[5,8],[7]] => 2
[[1,3,5,7,8],[2,4],[6]] => [[1,2,4,6,8],[3,5],[7]] => 3
[[1,2,5,7,8],[3,4],[6]] => [[1,2,3,4,8],[5,6],[7]] => 1
[[1,3,4,7,8],[2,5],[6]] => [[1,2,4,5,8],[3,6],[7]] => 2
[[1,2,4,7,8],[3,5],[6]] => [[1,2,3,5,8],[4,6],[7]] => 2
[[1,2,3,7,8],[4,5],[6]] => [[1,2,3,4,5],[6,8],[7]] => 1
[[1,4,5,6,8],[2,7],[3]] => [[1,2,5,6,7],[3,8],[4]] => 1
[[1,3,5,6,8],[2,7],[4]] => [[1,2,4,6,7],[3,8],[5]] => 2
[[1,2,5,6,8],[3,7],[4]] => [[1,2,3,6,7],[4,8],[5]] => 1
[[1,3,4,6,8],[2,7],[5]] => [[1,2,4,5,7],[3,8],[6]] => 2
[[1,2,4,6,8],[3,7],[5]] => [[1,2,3,5,7],[4,8],[6]] => 2
[[1,2,3,6,8],[4,7],[5]] => [[1,2,3,4,7],[5,8],[6]] => 1
[[1,3,4,5,8],[2,7],[6]] => [[1,2,4,5,6,7],[3],[8]] => 1
[[1,2,4,5,8],[3,7],[6]] => [[1,2,3,5,6,7],[4],[8]] => 1
[[1,2,3,5,8],[4,7],[6]] => [[1,2,3,4,6,7],[5],[8]] => 1
[[1,2,3,4,8],[5,7],[6]] => [[1,2,3,4,5,7],[6],[8]] => 1
[[1,3,5,6,8],[2,4],[7]] => [[1,2,4,6,7],[3,5],[8]] => 2
[[1,2,5,6,8],[3,4],[7]] => [[1,2,3,4,7],[5,6],[8]] => 1
[[1,3,4,6,8],[2,5],[7]] => [[1,2,4,5,7],[3,6],[8]] => 2
[[1,2,4,6,8],[3,5],[7]] => [[1,2,3,5,7],[4,6],[8]] => 2
[[1,2,3,6,8],[4,5],[7]] => [[1,2,3,4,5],[6,7],[8]] => 0
[[1,3,4,5,8],[2,6],[7]] => [[1,2,4,5,6],[3,7],[8]] => 1
[[1,2,4,5,8],[3,6],[7]] => [[1,2,3,5,6],[4,7],[8]] => 1
[[1,2,3,5,8],[4,6],[7]] => [[1,2,3,4,6],[5,7],[8]] => 1
[[1,2,3,4,8],[5,6],[7]] => [[1,2,3,4,5,6],[7],[8]] => 0
[[1,4,5,6,7],[2,8],[3]] => [[1,2,5,6,7,8],[3],[4]] => 1
[[1,3,5,6,7],[2,8],[4]] => [[1,2,4,6,7,8],[3],[5]] => 2
[[1,2,5,6,7],[3,8],[4]] => [[1,2,3,6,7,8],[4],[5]] => 1
[[1,3,4,6,7],[2,8],[5]] => [[1,2,4,5,7,8],[3],[6]] => 2
[[1,2,4,6,7],[3,8],[5]] => [[1,2,3,5,7,8],[4],[6]] => 2
[[1,2,3,6,7],[4,8],[5]] => [[1,2,3,4,7,8],[5],[6]] => 1
[[1,3,4,5,7],[2,8],[6]] => [[1,2,4,5,6,8],[3],[7]] => 2
[[1,2,4,5,7],[3,8],[6]] => [[1,2,3,5,6,8],[4],[7]] => 2
[[1,2,3,5,7],[4,8],[6]] => [[1,2,3,4,6,8],[5],[7]] => 2
[[1,2,3,4,7],[5,8],[6]] => [[1,2,3,4,5,8],[6],[7]] => 1
[[1,3,4,5,6],[2,8],[7]] => [[1,2,4,5,6,7,8],[3]] => 1
[[1,2,4,5,6],[3,8],[7]] => [[1,2,3,5,6,7,8],[4]] => 1
[[1,2,3,5,6],[4,8],[7]] => [[1,2,3,4,6,7,8],[5]] => 1
[[1,2,3,4,6],[5,8],[7]] => [[1,2,3,4,5,7,8],[6]] => 1
[[1,2,3,4,5],[6,8],[7]] => [[1,2,3,4,5,6,8],[7]] => 1
[[1,3,5,6,7],[2,4],[8]] => [[1,2,4,6,7,8],[3,5]] => 2
[[1,2,5,6,7],[3,4],[8]] => [[1,2,3,4,7,8],[5,6]] => 1
[[1,3,4,6,7],[2,5],[8]] => [[1,2,4,5,7,8],[3,6]] => 2
[[1,2,4,6,7],[3,5],[8]] => [[1,2,3,5,7,8],[4,6]] => 2
[[1,2,3,6,7],[4,5],[8]] => [[1,2,3,4,5,8],[6,7]] => 1
[[1,3,4,5,7],[2,6],[8]] => [[1,2,4,5,6,8],[3,7]] => 2
[[1,2,4,5,7],[3,6],[8]] => [[1,2,3,5,6,8],[4,7]] => 2
[[1,2,3,5,7],[4,6],[8]] => [[1,2,3,4,6,8],[5,7]] => 2
[[1,2,3,4,7],[5,6],[8]] => [[1,2,3,4,5,6],[7,8]] => 0
[[1,3,4,5,6],[2,7],[8]] => [[1,2,4,5,6,7],[3,8]] => 1
[[1,2,4,5,6],[3,7],[8]] => [[1,2,3,5,6,7],[4,8]] => 1
[[1,2,3,5,6],[4,7],[8]] => [[1,2,3,4,6,7],[5,8]] => 1
[[1,2,3,4,6],[5,7],[8]] => [[1,2,3,4,5,7],[6,8]] => 1
[[1,2,3,4,5],[6,7],[8]] => [[1,2,3,4,5,6,7],[8]] => 0
[[1,5,6,7,8],[2],[3],[4]] => [[1,2,6,7,8],[3],[4],[5]] => 1
[[1,4,6,7,8],[2],[3],[5]] => [[1,2,5,7,8],[3],[4],[6]] => 2
[[1,3,6,7,8],[2],[4],[5]] => [[1,2,4,7,8],[3],[5],[6]] => 2
[[1,2,6,7,8],[3],[4],[5]] => [[1,2,3,7,8],[4],[5],[6]] => 1
[[1,4,5,7,8],[2],[3],[6]] => [[1,2,5,6,8],[3],[4],[7]] => 2
[[1,3,5,7,8],[2],[4],[6]] => [[1,2,4,6,8],[3],[5],[7]] => 3
[[1,2,5,7,8],[3],[4],[6]] => [[1,2,3,6,8],[4],[5],[7]] => 2
[[1,3,4,7,8],[2],[5],[6]] => [[1,2,4,5,8],[3],[6],[7]] => 2
[[1,2,4,7,8],[3],[5],[6]] => [[1,2,3,5,8],[4],[6],[7]] => 2
[[1,2,3,7,8],[4],[5],[6]] => [[1,2,3,4,8],[5],[6],[7]] => 1
[[1,4,5,6,8],[2],[3],[7]] => [[1,2,5,6,7],[3],[4],[8]] => 1
[[1,3,5,6,8],[2],[4],[7]] => [[1,2,4,6,7],[3],[5],[8]] => 2
[[1,2,5,6,8],[3],[4],[7]] => [[1,2,3,6,7],[4],[5],[8]] => 1
[[1,3,4,6,8],[2],[5],[7]] => [[1,2,4,5,7],[3],[6],[8]] => 2
[[1,2,4,6,8],[3],[5],[7]] => [[1,2,3,5,7],[4],[6],[8]] => 2
[[1,2,3,6,8],[4],[5],[7]] => [[1,2,3,4,7],[5],[6],[8]] => 1
[[1,3,4,5,8],[2],[6],[7]] => [[1,2,4,5,6],[3],[7],[8]] => 1
[[1,2,4,5,8],[3],[6],[7]] => [[1,2,3,5,6],[4],[7],[8]] => 1
[[1,2,3,5,8],[4],[6],[7]] => [[1,2,3,4,6],[5],[7],[8]] => 1
[[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,4,5],[6],[7],[8]] => 0
[[1,4,5,6,7],[2],[3],[8]] => [[1,2,5,6,7,8],[3],[4]] => 1
[[1,3,5,6,7],[2],[4],[8]] => [[1,2,4,6,7,8],[3],[5]] => 2
[[1,2,5,6,7],[3],[4],[8]] => [[1,2,3,6,7,8],[4],[5]] => 1
[[1,3,4,6,7],[2],[5],[8]] => [[1,2,4,5,7,8],[3],[6]] => 2
[[1,2,4,6,7],[3],[5],[8]] => [[1,2,3,5,7,8],[4],[6]] => 2
[[1,2,3,6,7],[4],[5],[8]] => [[1,2,3,4,7,8],[5],[6]] => 1
[[1,3,4,5,7],[2],[6],[8]] => [[1,2,4,5,6,8],[3],[7]] => 2
[[1,2,4,5,7],[3],[6],[8]] => [[1,2,3,5,6,8],[4],[7]] => 2
[[1,2,3,5,7],[4],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 2
[[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,4,5,8],[6],[7]] => 1
[[1,3,4,5,6],[2],[7],[8]] => [[1,2,4,5,6,7],[3],[8]] => 1
[[1,2,4,5,6],[3],[7],[8]] => [[1,2,3,5,6,7],[4],[8]] => 1
[[1,2,3,5,6],[4],[7],[8]] => [[1,2,3,4,6,7],[5],[8]] => 1
[[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,4,5,7],[6],[8]] => 1
[[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,5,6],[7],[8]] => 0
[[1,3,5,7],[2,4,6,8]] => [[1,2,4,6,8],[3,5,7]] => 3
[[1,2,5,7],[3,4,6,8]] => [[1,2,3,4,6,8],[5,7]] => 2
[[1,3,4,7],[2,5,6,8]] => [[1,2,4,5,6,8],[3,7]] => 2
[[1,2,4,7],[3,5,6,8]] => [[1,2,3,5,6,8],[4,7]] => 2
[[1,2,3,7],[4,5,6,8]] => [[1,2,3,4,5,6,8],[7]] => 1
[[1,3,5,6],[2,4,7,8]] => [[1,2,4,6,7,8],[3,5]] => 2
[[1,2,5,6],[3,4,7,8]] => [[1,2,3,4,7,8],[5,6]] => 1
[[1,3,4,6],[2,5,7,8]] => [[1,2,4,5,7,8],[3,6]] => 2
[[1,2,4,6],[3,5,7,8]] => [[1,2,3,5,7,8],[4,6]] => 2
[[1,2,3,6],[4,5,7,8]] => [[1,2,3,4,5,7,8],[6]] => 1
[[1,3,4,5],[2,6,7,8]] => [[1,2,4,5,6,7,8],[3]] => 1
[[1,2,4,5],[3,6,7,8]] => [[1,2,3,5,6,7,8],[4]] => 1
[[1,2,3,5],[4,6,7,8]] => [[1,2,3,4,6,7,8],[5]] => 1
[[1,2,3,4],[5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => 0
[[1,4,6,8],[2,5,7],[3]] => [[1,2,5,7],[3,6,8],[4]] => 2
[[1,3,6,8],[2,5,7],[4]] => [[1,2,4,5,7],[3,8],[6]] => 2
[[1,2,6,8],[3,5,7],[4]] => [[1,2,3,5,7],[4,8],[6]] => 2
[[1,3,6,8],[2,4,7],[5]] => [[1,2,4,7],[3,5,8],[6]] => 2
[[1,2,6,8],[3,4,7],[5]] => [[1,2,3,4,7],[5,8],[6]] => 1
[[1,4,5,8],[2,6,7],[3]] => [[1,2,5,6,7],[3,8],[4]] => 1
[[1,3,5,8],[2,6,7],[4]] => [[1,2,4,6,7],[3,8],[5]] => 2
[[1,2,5,8],[3,6,7],[4]] => [[1,2,3,6,7],[4,8],[5]] => 1
[[1,3,4,8],[2,6,7],[5]] => [[1,2,4,5,6,7],[3],[8]] => 1
[[1,2,4,8],[3,6,7],[5]] => [[1,2,3,5,6,7],[4],[8]] => 1
[[1,2,3,8],[4,6,7],[5]] => [[1,2,3,4,6,7],[5],[8]] => 1
[[1,3,5,8],[2,4,7],[6]] => [[1,2,4,6,7],[3,5],[8]] => 2
[[1,2,5,8],[3,4,7],[6]] => [[1,2,3,4,7],[5,6],[8]] => 1
[[1,3,4,8],[2,5,7],[6]] => [[1,2,4,5,7],[3,6],[8]] => 2
[[1,2,4,8],[3,5,7],[6]] => [[1,2,3,5,7],[4,6],[8]] => 2
[[1,2,3,8],[4,5,7],[6]] => [[1,2,3,4,5,7],[6],[8]] => 1
[[1,3,5,8],[2,4,6],[7]] => [[1,2,4,6],[3,5,7],[8]] => 2
[[1,2,5,8],[3,4,6],[7]] => [[1,2,3,4,6],[5,7],[8]] => 1
[[1,3,4,8],[2,5,6],[7]] => [[1,2,4,5,6],[3,7],[8]] => 1
[[1,2,4,8],[3,5,6],[7]] => [[1,2,3,5,6],[4,7],[8]] => 1
[[1,2,3,8],[4,5,6],[7]] => [[1,2,3,4,5,6],[7],[8]] => 0
[[1,4,6,7],[2,5,8],[3]] => [[1,2,5,7,8],[3,6],[4]] => 2
[[1,3,6,7],[2,5,8],[4]] => [[1,2,4,5,8],[3,7],[6]] => 3
[[1,2,6,7],[3,5,8],[4]] => [[1,2,3,5,8],[4,7],[6]] => 3
[[1,3,6,7],[2,4,8],[5]] => [[1,2,4,7,8],[3,5],[6]] => 2
[[1,2,6,7],[3,4,8],[5]] => [[1,2,3,4,8],[5,7],[6]] => 2
[[1,4,5,7],[2,6,8],[3]] => [[1,2,5,6,8],[3,7],[4]] => 2
[[1,3,5,7],[2,6,8],[4]] => [[1,2,4,6,8],[3,7],[5]] => 3
[[1,2,5,7],[3,6,8],[4]] => [[1,2,3,6,8],[4,7],[5]] => 2
[[1,3,4,7],[2,6,8],[5]] => [[1,2,4,5,6,8],[3],[7]] => 2
[[1,2,4,7],[3,6,8],[5]] => [[1,2,3,5,6,8],[4],[7]] => 2
[[1,2,3,7],[4,6,8],[5]] => [[1,2,3,4,6,8],[5],[7]] => 2
[[1,3,5,7],[2,4,8],[6]] => [[1,2,4,6,8],[3,5],[7]] => 3
[[1,2,5,7],[3,4,8],[6]] => [[1,2,3,4,8],[5,6],[7]] => 1
[[1,3,4,7],[2,5,8],[6]] => [[1,2,4,5,8],[3,6],[7]] => 2
[[1,2,4,7],[3,5,8],[6]] => [[1,2,3,5,8],[4,6],[7]] => 2
[[1,2,3,7],[4,5,8],[6]] => [[1,2,3,4,5,8],[6],[7]] => 1
[[1,4,5,6],[2,7,8],[3]] => [[1,2,5,6,7,8],[3],[4]] => 1
[[1,3,5,6],[2,7,8],[4]] => [[1,2,4,6,7,8],[3],[5]] => 2
[[1,2,5,6],[3,7,8],[4]] => [[1,2,3,6,7,8],[4],[5]] => 1
[[1,3,4,6],[2,7,8],[5]] => [[1,2,4,5,7,8],[3],[6]] => 2
[[1,2,4,6],[3,7,8],[5]] => [[1,2,3,5,7,8],[4],[6]] => 2
[[1,2,3,6],[4,7,8],[5]] => [[1,2,3,4,7,8],[5],[6]] => 1
[[1,3,4,5],[2,7,8],[6]] => [[1,2,4,5,6,7,8],[3]] => 1
[[1,2,4,5],[3,7,8],[6]] => [[1,2,3,5,6,7,8],[4]] => 1
[[1,2,3,5],[4,7,8],[6]] => [[1,2,3,4,6,7,8],[5]] => 1
[[1,2,3,4],[5,7,8],[6]] => [[1,2,3,4,5,7,8],[6]] => 1
[[1,3,5,6],[2,4,8],[7]] => [[1,2,4,6,7,8],[3,5]] => 2
[[1,2,5,6],[3,4,8],[7]] => [[1,2,3,4,7,8],[5,6]] => 1
[[1,3,4,6],[2,5,8],[7]] => [[1,2,4,5,7,8],[3,6]] => 2
[[1,2,4,6],[3,5,8],[7]] => [[1,2,3,5,7,8],[4,6]] => 2
[[1,2,3,6],[4,5,8],[7]] => [[1,2,3,4,5,8],[6,7]] => 1
[[1,3,4,5],[2,6,8],[7]] => [[1,2,4,5,6,8],[3,7]] => 2
[[1,2,4,5],[3,6,8],[7]] => [[1,2,3,5,6,8],[4,7]] => 2
[[1,2,3,5],[4,6,8],[7]] => [[1,2,3,4,6,8],[5,7]] => 2
[[1,2,3,4],[5,6,8],[7]] => [[1,2,3,4,5,6,8],[7]] => 1
[[1,3,5,7],[2,4,6],[8]] => [[1,2,4,6,8],[3,5,7]] => 3
[[1,2,5,7],[3,4,6],[8]] => [[1,2,3,4,6],[5,7,8]] => 1
[[1,3,4,7],[2,5,6],[8]] => [[1,2,4,5,6],[3,7,8]] => 1
[[1,2,4,7],[3,5,6],[8]] => [[1,2,3,5,6],[4,7,8]] => 1
[[1,2,3,7],[4,5,6],[8]] => [[1,2,3,4,5,6],[7,8]] => 0
[[1,3,5,6],[2,4,7],[8]] => [[1,2,4,6,7],[3,5,8]] => 2
[[1,2,5,6],[3,4,7],[8]] => [[1,2,3,4,7],[5,6,8]] => 1
[[1,3,4,6],[2,5,7],[8]] => [[1,2,4,5,7],[3,6,8]] => 2
[[1,2,4,6],[3,5,7],[8]] => [[1,2,3,5,7],[4,6,8]] => 2
[[1,2,3,6],[4,5,7],[8]] => [[1,2,3,4,5,7],[6,8]] => 1
[[1,3,4,5],[2,6,7],[8]] => [[1,2,4,5,6,7],[3,8]] => 1
[[1,2,4,5],[3,6,7],[8]] => [[1,2,3,5,6,7],[4,8]] => 1
[[1,2,3,5],[4,6,7],[8]] => [[1,2,3,4,6,7],[5,8]] => 1
[[1,2,3,4],[5,6,7],[8]] => [[1,2,3,4,5,6,7],[8]] => 0
[[1,4,7,8],[2,5],[3,6]] => [[1,2,5,8],[3,6],[4,7]] => 2
[[1,3,7,8],[2,5],[4,6]] => [[1,2,4,5],[3,6],[7,8]] => 1
[[1,2,7,8],[3,5],[4,6]] => [[1,2,3,5],[4,6],[7,8]] => 1
[[1,3,7,8],[2,4],[5,6]] => [[1,2,4,6],[3,5],[7,8]] => 2
[[1,2,7,8],[3,4],[5,6]] => [[1,2,3,4],[5,6],[7,8]] => 0
[[1,4,6,8],[2,5],[3,7]] => [[1,2,5,7],[3,6],[4,8]] => 2
[[1,3,6,8],[2,5],[4,7]] => [[1,2,4,5],[3,7],[6,8]] => 2
[[1,2,6,8],[3,5],[4,7]] => [[1,2,3,5],[4,7],[6,8]] => 2
[[1,3,6,8],[2,4],[5,7]] => [[1,2,4,7],[3,5],[6,8]] => 2
[[1,2,6,8],[3,4],[5,7]] => [[1,2,3,4],[5,7],[6,8]] => 1
[[1,4,5,8],[2,6],[3,7]] => [[1,2,5,6],[3,7],[4,8]] => 1
[[1,3,5,8],[2,6],[4,7]] => [[1,2,4,6],[3,7],[5,8]] => 2
[[1,2,5,8],[3,6],[4,7]] => [[1,2,3,6],[4,7],[5,8]] => 1
[[1,3,4,8],[2,6],[5,7]] => [[1,2,4,5,6],[3,7],[8]] => 1
[[1,2,4,8],[3,6],[5,7]] => [[1,2,3,5,6],[4,7],[8]] => 1
[[1,2,3,8],[4,6],[5,7]] => [[1,2,3,4,6],[5,7],[8]] => 1
[[1,3,5,8],[2,4],[6,7]] => [[1,2,4,6,7],[3,5],[8]] => 2
[[1,2,5,8],[3,4],[6,7]] => [[1,2,3,4,7],[5,6],[8]] => 1
[[1,3,4,8],[2,5],[6,7]] => [[1,2,4,5,7],[3,6],[8]] => 2
[[1,2,4,8],[3,5],[6,7]] => [[1,2,3,5,7],[4,6],[8]] => 2
[[1,2,3,8],[4,5],[6,7]] => [[1,2,3,4,5],[6,7],[8]] => 0
[[1,4,6,7],[2,5],[3,8]] => [[1,2,5,7,8],[3,6],[4]] => 2
[[1,3,6,7],[2,5],[4,8]] => [[1,2,4,5,8],[3,7],[6]] => 3
[[1,2,6,7],[3,5],[4,8]] => [[1,2,3,5,8],[4,7],[6]] => 3
[[1,3,6,7],[2,4],[5,8]] => [[1,2,4,7,8],[3,5],[6]] => 2
[[1,2,6,7],[3,4],[5,8]] => [[1,2,3,4,8],[5,7],[6]] => 2
[[1,4,5,7],[2,6],[3,8]] => [[1,2,5,6,8],[3,7],[4]] => 2
[[1,3,5,7],[2,6],[4,8]] => [[1,2,4,6,8],[3,7],[5]] => 3
[[1,2,5,7],[3,6],[4,8]] => [[1,2,3,6,8],[4,7],[5]] => 2
[[1,3,4,7],[2,6],[5,8]] => [[1,2,4,5,6],[3,8],[7]] => 2
[[1,2,4,7],[3,6],[5,8]] => [[1,2,3,5,6],[4,8],[7]] => 2
[[1,2,3,7],[4,6],[5,8]] => [[1,2,3,4,6],[5,8],[7]] => 2
[[1,3,5,7],[2,4],[6,8]] => [[1,2,4,6,8],[3,5],[7]] => 3
[[1,2,5,7],[3,4],[6,8]] => [[1,2,3,4,8],[5,6],[7]] => 1
[[1,3,4,7],[2,5],[6,8]] => [[1,2,4,5,8],[3,6],[7]] => 2
[[1,2,4,7],[3,5],[6,8]] => [[1,2,3,5,8],[4,6],[7]] => 2
[[1,2,3,7],[4,5],[6,8]] => [[1,2,3,4,5],[6,8],[7]] => 1
[[1,4,5,6],[2,7],[3,8]] => [[1,2,5,6,7],[3,8],[4]] => 1
[[1,3,5,6],[2,7],[4,8]] => [[1,2,4,6,7],[3,8],[5]] => 2
[[1,2,5,6],[3,7],[4,8]] => [[1,2,3,6,7],[4,8],[5]] => 1
[[1,3,4,6],[2,7],[5,8]] => [[1,2,4,5,7],[3,8],[6]] => 2
[[1,2,4,6],[3,7],[5,8]] => [[1,2,3,5,7],[4,8],[6]] => 2
[[1,2,3,6],[4,7],[5,8]] => [[1,2,3,4,7],[5,8],[6]] => 1
[[1,3,4,5],[2,7],[6,8]] => [[1,2,4,5,6,7],[3,8]] => 1
[[1,2,4,5],[3,7],[6,8]] => [[1,2,3,5,6,7],[4,8]] => 1
[[1,2,3,5],[4,7],[6,8]] => [[1,2,3,4,6,7],[5,8]] => 1
[[1,2,3,4],[5,7],[6,8]] => [[1,2,3,4,5,7],[6,8]] => 1
[[1,3,5,6],[2,4],[7,8]] => [[1,2,4,6,7,8],[3,5]] => 2
[[1,2,5,6],[3,4],[7,8]] => [[1,2,3,4,7,8],[5,6]] => 1
[[1,3,4,6],[2,5],[7,8]] => [[1,2,4,5,7,8],[3,6]] => 2
[[1,2,4,6],[3,5],[7,8]] => [[1,2,3,5,7,8],[4,6]] => 2
[[1,2,3,6],[4,5],[7,8]] => [[1,2,3,4,5,8],[6,7]] => 1
[[1,3,4,5],[2,6],[7,8]] => [[1,2,4,5,6,8],[3,7]] => 2
[[1,2,4,5],[3,6],[7,8]] => [[1,2,3,5,6,8],[4,7]] => 2
[[1,2,3,5],[4,6],[7,8]] => [[1,2,3,4,6,8],[5,7]] => 2
[[1,2,3,4],[5,6],[7,8]] => [[1,2,3,4,5,6],[7,8]] => 0
[[1,5,7,8],[2,6],[3],[4]] => [[1,2,6,8],[3,7],[4],[5]] => 2
[[1,4,7,8],[2,6],[3],[5]] => [[1,2,5,6],[3,8],[4],[7]] => 2
[[1,3,7,8],[2,6],[4],[5]] => [[1,2,4,6],[3,8],[5],[7]] => 3
[[1,2,7,8],[3,6],[4],[5]] => [[1,2,3,6],[4,8],[5],[7]] => 2
[[1,4,7,8],[2,5],[3],[6]] => [[1,2,5,8],[3,6],[4],[7]] => 2
[[1,3,7,8],[2,5],[4],[6]] => [[1,2,4,5],[3,8],[6],[7]] => 2
[[1,2,7,8],[3,5],[4],[6]] => [[1,2,3,5],[4,8],[6],[7]] => 2
[[1,3,7,8],[2,4],[5],[6]] => [[1,2,4,8],[3,5],[6],[7]] => 2
[[1,2,7,8],[3,4],[5],[6]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[[1,5,6,8],[2,7],[3],[4]] => [[1,2,6,7],[3,8],[4],[5]] => 1
[[1,4,6,8],[2,7],[3],[5]] => [[1,2,5,7],[3,8],[4],[6]] => 2
[[1,3,6,8],[2,7],[4],[5]] => [[1,2,4,7],[3,8],[5],[6]] => 2
[[1,2,6,8],[3,7],[4],[5]] => [[1,2,3,7],[4,8],[5],[6]] => 1
[[1,4,5,8],[2,7],[3],[6]] => [[1,2,5,6,7],[3],[4],[8]] => 1
[[1,3,5,8],[2,7],[4],[6]] => [[1,2,4,6,7],[3],[5],[8]] => 2
[[1,2,5,8],[3,7],[4],[6]] => [[1,2,3,6,7],[4],[5],[8]] => 1
[[1,3,4,8],[2,7],[5],[6]] => [[1,2,4,5,7],[3],[6],[8]] => 2
[[1,2,4,8],[3,7],[5],[6]] => [[1,2,3,5,7],[4],[6],[8]] => 2
[[1,2,3,8],[4,7],[5],[6]] => [[1,2,3,4,7],[5],[6],[8]] => 1
[[1,4,6,8],[2,5],[3],[7]] => [[1,2,5,7],[3,6],[4],[8]] => 2
[[1,3,6,8],[2,5],[4],[7]] => [[1,2,4,5],[3,7],[6],[8]] => 2
[[1,2,6,8],[3,5],[4],[7]] => [[1,2,3,5],[4,7],[6],[8]] => 2
[[1,3,6,8],[2,4],[5],[7]] => [[1,2,4,7],[3,5],[6],[8]] => 2
[[1,2,6,8],[3,4],[5],[7]] => [[1,2,3,4],[5,7],[6],[8]] => 1
[[1,4,5,8],[2,6],[3],[7]] => [[1,2,5,6],[3,7],[4],[8]] => 1
[[1,3,5,8],[2,6],[4],[7]] => [[1,2,4,6],[3,7],[5],[8]] => 2
[[1,2,5,8],[3,6],[4],[7]] => [[1,2,3,6],[4,7],[5],[8]] => 1
[[1,3,4,8],[2,6],[5],[7]] => [[1,2,4,5,6],[3],[7],[8]] => 1
[[1,2,4,8],[3,6],[5],[7]] => [[1,2,3,5,6],[4],[7],[8]] => 1
[[1,2,3,8],[4,6],[5],[7]] => [[1,2,3,4,6],[5],[7],[8]] => 1
[[1,3,5,8],[2,4],[6],[7]] => [[1,2,4,6],[3,5],[7],[8]] => 2
[[1,2,5,8],[3,4],[6],[7]] => [[1,2,3,4],[5,6],[7],[8]] => 0
[[1,3,4,8],[2,5],[6],[7]] => [[1,2,4,5],[3,6],[7],[8]] => 1
[[1,2,4,8],[3,5],[6],[7]] => [[1,2,3,5],[4,6],[7],[8]] => 1
[[1,2,3,8],[4,5],[6],[7]] => [[1,2,3,4,5],[6],[7],[8]] => 0
[[1,5,6,7],[2,8],[3],[4]] => [[1,2,6,7,8],[3],[4],[5]] => 1
[[1,4,6,7],[2,8],[3],[5]] => [[1,2,5,7,8],[3],[4],[6]] => 2
[[1,3,6,7],[2,8],[4],[5]] => [[1,2,4,7,8],[3],[5],[6]] => 2
[[1,2,6,7],[3,8],[4],[5]] => [[1,2,3,7,8],[4],[5],[6]] => 1
[[1,4,5,7],[2,8],[3],[6]] => [[1,2,5,6,8],[3],[4],[7]] => 2
[[1,3,5,7],[2,8],[4],[6]] => [[1,2,4,6,8],[3],[5],[7]] => 3
[[1,2,5,7],[3,8],[4],[6]] => [[1,2,3,6,8],[4],[5],[7]] => 2
[[1,3,4,7],[2,8],[5],[6]] => [[1,2,4,5,8],[3],[6],[7]] => 2
[[1,2,4,7],[3,8],[5],[6]] => [[1,2,3,5,8],[4],[6],[7]] => 2
[[1,2,3,7],[4,8],[5],[6]] => [[1,2,3,4,8],[5],[6],[7]] => 1
[[1,4,5,6],[2,8],[3],[7]] => [[1,2,5,6,7,8],[3],[4]] => 1
[[1,3,5,6],[2,8],[4],[7]] => [[1,2,4,6,7,8],[3],[5]] => 2
[[1,2,5,6],[3,8],[4],[7]] => [[1,2,3,6,7,8],[4],[5]] => 1
[[1,3,4,6],[2,8],[5],[7]] => [[1,2,4,5,7,8],[3],[6]] => 2
[[1,2,4,6],[3,8],[5],[7]] => [[1,2,3,5,7,8],[4],[6]] => 2
[[1,2,3,6],[4,8],[5],[7]] => [[1,2,3,4,7,8],[5],[6]] => 1
[[1,3,4,5],[2,8],[6],[7]] => [[1,2,4,5,6,8],[3],[7]] => 2
[[1,2,4,5],[3,8],[6],[7]] => [[1,2,3,5,6,8],[4],[7]] => 2
[[1,2,3,5],[4,8],[6],[7]] => [[1,2,3,4,6,8],[5],[7]] => 2
[[1,2,3,4],[5,8],[6],[7]] => [[1,2,3,4,5,8],[6],[7]] => 1
[[1,4,6,7],[2,5],[3],[8]] => [[1,2,5,7,8],[3,6],[4]] => 2
[[1,3,6,7],[2,5],[4],[8]] => [[1,2,4,5,8],[3,7],[6]] => 3
[[1,2,6,7],[3,5],[4],[8]] => [[1,2,3,5,8],[4,7],[6]] => 3
[[1,3,6,7],[2,4],[5],[8]] => [[1,2,4,7,8],[3,5],[6]] => 2
[[1,2,6,7],[3,4],[5],[8]] => [[1,2,3,4,8],[5,7],[6]] => 2
[[1,4,5,7],[2,6],[3],[8]] => [[1,2,5,6,8],[3,7],[4]] => 2
[[1,3,5,7],[2,6],[4],[8]] => [[1,2,4,6,8],[3,7],[5]] => 3
[[1,2,5,7],[3,6],[4],[8]] => [[1,2,3,6,8],[4,7],[5]] => 2
[[1,3,4,7],[2,6],[5],[8]] => [[1,2,4,5,6],[3,8],[7]] => 2
[[1,2,4,7],[3,6],[5],[8]] => [[1,2,3,5,6],[4,8],[7]] => 2
[[1,2,3,7],[4,6],[5],[8]] => [[1,2,3,4,6],[5,8],[7]] => 2
[[1,3,5,7],[2,4],[6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 3
[[1,2,5,7],[3,4],[6],[8]] => [[1,2,3,4,8],[5,6],[7]] => 1
[[1,3,4,7],[2,5],[6],[8]] => [[1,2,4,5,8],[3,6],[7]] => 2
[[1,2,4,7],[3,5],[6],[8]] => [[1,2,3,5,8],[4,6],[7]] => 2
[[1,2,3,7],[4,5],[6],[8]] => [[1,2,3,4,5],[6,8],[7]] => 1
[[1,4,5,6],[2,7],[3],[8]] => [[1,2,5,6,7],[3,8],[4]] => 1
[[1,3,5,6],[2,7],[4],[8]] => [[1,2,4,6,7],[3,8],[5]] => 2
[[1,2,5,6],[3,7],[4],[8]] => [[1,2,3,6,7],[4,8],[5]] => 1
[[1,3,4,6],[2,7],[5],[8]] => [[1,2,4,5,7],[3,8],[6]] => 2
[[1,2,4,6],[3,7],[5],[8]] => [[1,2,3,5,7],[4,8],[6]] => 2
[[1,2,3,6],[4,7],[5],[8]] => [[1,2,3,4,7],[5,8],[6]] => 1
[[1,3,4,5],[2,7],[6],[8]] => [[1,2,4,5,6,7],[3],[8]] => 1
[[1,2,4,5],[3,7],[6],[8]] => [[1,2,3,5,6,7],[4],[8]] => 1
[[1,2,3,5],[4,7],[6],[8]] => [[1,2,3,4,6,7],[5],[8]] => 1
[[1,2,3,4],[5,7],[6],[8]] => [[1,2,3,4,5,7],[6],[8]] => 1
[[1,3,5,6],[2,4],[7],[8]] => [[1,2,4,6,7],[3,5],[8]] => 2
[[1,2,5,6],[3,4],[7],[8]] => [[1,2,3,4,7],[5,6],[8]] => 1
[[1,3,4,6],[2,5],[7],[8]] => [[1,2,4,5,7],[3,6],[8]] => 2
[[1,2,4,6],[3,5],[7],[8]] => [[1,2,3,5,7],[4,6],[8]] => 2
[[1,2,3,6],[4,5],[7],[8]] => [[1,2,3,4,5],[6,7],[8]] => 0
[[1,3,4,5],[2,6],[7],[8]] => [[1,2,4,5,6],[3,7],[8]] => 1
[[1,2,4,5],[3,6],[7],[8]] => [[1,2,3,5,6],[4,7],[8]] => 1
[[1,2,3,5],[4,6],[7],[8]] => [[1,2,3,4,6],[5,7],[8]] => 1
[[1,2,3,4],[5,6],[7],[8]] => [[1,2,3,4,5,6],[7],[8]] => 0
[[1,6,7,8],[2],[3],[4],[5]] => [[1,2,7,8],[3],[4],[5],[6]] => 1
[[1,5,7,8],[2],[3],[4],[6]] => [[1,2,6,8],[3],[4],[5],[7]] => 2
[[1,4,7,8],[2],[3],[5],[6]] => [[1,2,5,8],[3],[4],[6],[7]] => 2
[[1,3,7,8],[2],[4],[5],[6]] => [[1,2,4,8],[3],[5],[6],[7]] => 2
[[1,2,7,8],[3],[4],[5],[6]] => [[1,2,3,8],[4],[5],[6],[7]] => 1
[[1,5,6,8],[2],[3],[4],[7]] => [[1,2,6,7],[3],[4],[5],[8]] => 1
[[1,4,6,8],[2],[3],[5],[7]] => [[1,2,5,7],[3],[4],[6],[8]] => 2
[[1,3,6,8],[2],[4],[5],[7]] => [[1,2,4,7],[3],[5],[6],[8]] => 2
[[1,2,6,8],[3],[4],[5],[7]] => [[1,2,3,7],[4],[5],[6],[8]] => 1
[[1,4,5,8],[2],[3],[6],[7]] => [[1,2,5,6],[3],[4],[7],[8]] => 1
[[1,3,5,8],[2],[4],[6],[7]] => [[1,2,4,6],[3],[5],[7],[8]] => 2
[[1,2,5,8],[3],[4],[6],[7]] => [[1,2,3,6],[4],[5],[7],[8]] => 1
[[1,3,4,8],[2],[5],[6],[7]] => [[1,2,4,5],[3],[6],[7],[8]] => 1
[[1,2,4,8],[3],[5],[6],[7]] => [[1,2,3,5],[4],[6],[7],[8]] => 1
[[1,2,3,8],[4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[[1,5,6,7],[2],[3],[4],[8]] => [[1,2,6,7,8],[3],[4],[5]] => 1
[[1,4,6,7],[2],[3],[5],[8]] => [[1,2,5,7,8],[3],[4],[6]] => 2
[[1,3,6,7],[2],[4],[5],[8]] => [[1,2,4,7,8],[3],[5],[6]] => 2
[[1,2,6,7],[3],[4],[5],[8]] => [[1,2,3,7,8],[4],[5],[6]] => 1
[[1,4,5,7],[2],[3],[6],[8]] => [[1,2,5,6,8],[3],[4],[7]] => 2
[[1,3,5,7],[2],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => 3
[[1,2,5,7],[3],[4],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 2
[[1,3,4,7],[2],[5],[6],[8]] => [[1,2,4,5,8],[3],[6],[7]] => 2
[[1,2,4,7],[3],[5],[6],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 2
[[1,2,3,7],[4],[5],[6],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 1
[[1,4,5,6],[2],[3],[7],[8]] => [[1,2,5,6,7],[3],[4],[8]] => 1
[[1,3,5,6],[2],[4],[7],[8]] => [[1,2,4,6,7],[3],[5],[8]] => 2
[[1,2,5,6],[3],[4],[7],[8]] => [[1,2,3,6,7],[4],[5],[8]] => 1
[[1,3,4,6],[2],[5],[7],[8]] => [[1,2,4,5,7],[3],[6],[8]] => 2
[[1,2,4,6],[3],[5],[7],[8]] => [[1,2,3,5,7],[4],[6],[8]] => 2
[[1,2,3,6],[4],[5],[7],[8]] => [[1,2,3,4,7],[5],[6],[8]] => 1
[[1,3,4,5],[2],[6],[7],[8]] => [[1,2,4,5,6],[3],[7],[8]] => 1
[[1,2,4,5],[3],[6],[7],[8]] => [[1,2,3,5,6],[4],[7],[8]] => 1
[[1,2,3,5],[4],[6],[7],[8]] => [[1,2,3,4,6],[5],[7],[8]] => 1
[[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,4,5],[6],[7],[8]] => 0
[[1,4,7],[2,5,8],[3,6]] => [[1,2,5,8],[3,6],[4,7]] => 2
[[1,3,7],[2,5,8],[4,6]] => [[1,2,4,5,8],[3,6],[7]] => 2
[[1,2,7],[3,5,8],[4,6]] => [[1,2,3,5,8],[4,6],[7]] => 2
[[1,3,7],[2,4,8],[5,6]] => [[1,2,4,6,8],[3,5],[7]] => 3
[[1,2,7],[3,4,8],[5,6]] => [[1,2,3,4,8],[5,6],[7]] => 1
[[1,4,6],[2,5,8],[3,7]] => [[1,2,5,7,8],[3,6],[4]] => 2
[[1,3,6],[2,5,8],[4,7]] => [[1,2,4,5,8],[3,7],[6]] => 3
[[1,2,6],[3,5,8],[4,7]] => [[1,2,3,5,8],[4,7],[6]] => 3
[[1,3,6],[2,4,8],[5,7]] => [[1,2,4,7,8],[3,5],[6]] => 2
[[1,2,6],[3,4,8],[5,7]] => [[1,2,3,4,8],[5,7],[6]] => 2
[[1,4,5],[2,6,8],[3,7]] => [[1,2,5,6,8],[3,7],[4]] => 2
[[1,3,5],[2,6,8],[4,7]] => [[1,2,4,6,8],[3,7],[5]] => 3
[[1,2,5],[3,6,8],[4,7]] => [[1,2,3,6,8],[4,7],[5]] => 2
[[1,3,4],[2,6,8],[5,7]] => [[1,2,4,5,6,8],[3,7]] => 2
[[1,2,4],[3,6,8],[5,7]] => [[1,2,3,5,6,8],[4,7]] => 2
[[1,2,3],[4,6,8],[5,7]] => [[1,2,3,4,6,8],[5,7]] => 2
[[1,3,5],[2,4,8],[6,7]] => [[1,2,4,6,7,8],[3,5]] => 2
[[1,2,5],[3,4,8],[6,7]] => [[1,2,3,4,7,8],[5,6]] => 1
[[1,3,4],[2,5,8],[6,7]] => [[1,2,4,5,7,8],[3,6]] => 2
[[1,2,4],[3,5,8],[6,7]] => [[1,2,3,5,7,8],[4,6]] => 2
[[1,2,3],[4,5,8],[6,7]] => [[1,2,3,4,5,8],[6,7]] => 1
[[1,4,6],[2,5,7],[3,8]] => [[1,2,5,7],[3,6,8],[4]] => 2
[[1,3,6],[2,5,7],[4,8]] => [[1,2,4,5,7],[3,8],[6]] => 2
[[1,2,6],[3,5,7],[4,8]] => [[1,2,3,5,7],[4,8],[6]] => 2
[[1,3,6],[2,4,7],[5,8]] => [[1,2,4,7],[3,5,8],[6]] => 2
[[1,2,6],[3,4,7],[5,8]] => [[1,2,3,4,7],[5,8],[6]] => 1
[[1,4,5],[2,6,7],[3,8]] => [[1,2,5,6,7],[3,8],[4]] => 1
[[1,3,5],[2,6,7],[4,8]] => [[1,2,4,6,7],[3,8],[5]] => 2
[[1,2,5],[3,6,7],[4,8]] => [[1,2,3,6,7],[4,8],[5]] => 1
[[1,3,4],[2,6,7],[5,8]] => [[1,2,4,5,6,7],[3,8]] => 1
[[1,2,4],[3,6,7],[5,8]] => [[1,2,3,5,6,7],[4,8]] => 1
[[1,2,3],[4,6,7],[5,8]] => [[1,2,3,4,6,7],[5,8]] => 1
[[1,3,5],[2,4,7],[6,8]] => [[1,2,4,6,7],[3,5,8]] => 2
[[1,2,5],[3,4,7],[6,8]] => [[1,2,3,4,7],[5,6,8]] => 1
[[1,3,4],[2,5,7],[6,8]] => [[1,2,4,5,7],[3,6,8]] => 2
[[1,2,4],[3,5,7],[6,8]] => [[1,2,3,5,7],[4,6,8]] => 2
[[1,2,3],[4,5,7],[6,8]] => [[1,2,3,4,5,7],[6,8]] => 1
[[1,3,5],[2,4,6],[7,8]] => [[1,2,4,6,8],[3,5,7]] => 3
[[1,2,5],[3,4,6],[7,8]] => [[1,2,3,4,6],[5,7,8]] => 1
[[1,3,4],[2,5,6],[7,8]] => [[1,2,4,5,6],[3,7,8]] => 1
[[1,2,4],[3,5,6],[7,8]] => [[1,2,3,5,6],[4,7,8]] => 1
[[1,2,3],[4,5,6],[7,8]] => [[1,2,3,4,5,6],[7,8]] => 0
[[1,5,7],[2,6,8],[3],[4]] => [[1,2,6,8],[3,7],[4],[5]] => 2
[[1,4,7],[2,6,8],[3],[5]] => [[1,2,5,6,8],[3],[4],[7]] => 2
[[1,3,7],[2,6,8],[4],[5]] => [[1,2,4,6,8],[3],[5],[7]] => 3
[[1,2,7],[3,6,8],[4],[5]] => [[1,2,3,6,8],[4],[5],[7]] => 2
[[1,4,7],[2,5,8],[3],[6]] => [[1,2,5,8],[3,6],[4],[7]] => 2
[[1,3,7],[2,5,8],[4],[6]] => [[1,2,4,5,8],[3],[6],[7]] => 2
[[1,2,7],[3,5,8],[4],[6]] => [[1,2,3,5,8],[4],[6],[7]] => 2
[[1,3,7],[2,4,8],[5],[6]] => [[1,2,4,8],[3,5],[6],[7]] => 2
[[1,2,7],[3,4,8],[5],[6]] => [[1,2,3,4,8],[5],[6],[7]] => 1
[[1,5,6],[2,7,8],[3],[4]] => [[1,2,6,7,8],[3],[4],[5]] => 1
[[1,4,6],[2,7,8],[3],[5]] => [[1,2,5,7,8],[3],[4],[6]] => 2
[[1,3,6],[2,7,8],[4],[5]] => [[1,2,4,7,8],[3],[5],[6]] => 2
[[1,2,6],[3,7,8],[4],[5]] => [[1,2,3,7,8],[4],[5],[6]] => 1
[[1,4,5],[2,7,8],[3],[6]] => [[1,2,5,6,7,8],[3],[4]] => 1
[[1,3,5],[2,7,8],[4],[6]] => [[1,2,4,6,7,8],[3],[5]] => 2
[[1,2,5],[3,7,8],[4],[6]] => [[1,2,3,6,7,8],[4],[5]] => 1
[[1,3,4],[2,7,8],[5],[6]] => [[1,2,4,5,7,8],[3],[6]] => 2
[[1,2,4],[3,7,8],[5],[6]] => [[1,2,3,5,7,8],[4],[6]] => 2
[[1,2,3],[4,7,8],[5],[6]] => [[1,2,3,4,7,8],[5],[6]] => 1
[[1,4,6],[2,5,8],[3],[7]] => [[1,2,5,7,8],[3,6],[4]] => 2
[[1,3,6],[2,5,8],[4],[7]] => [[1,2,4,5,8],[3,7],[6]] => 3
[[1,2,6],[3,5,8],[4],[7]] => [[1,2,3,5,8],[4,7],[6]] => 3
[[1,3,6],[2,4,8],[5],[7]] => [[1,2,4,7,8],[3,5],[6]] => 2
[[1,2,6],[3,4,8],[5],[7]] => [[1,2,3,4,8],[5,7],[6]] => 2
[[1,4,5],[2,6,8],[3],[7]] => [[1,2,5,6,8],[3,7],[4]] => 2
[[1,3,5],[2,6,8],[4],[7]] => [[1,2,4,6,8],[3,7],[5]] => 3
[[1,2,5],[3,6,8],[4],[7]] => [[1,2,3,6,8],[4,7],[5]] => 2
[[1,3,4],[2,6,8],[5],[7]] => [[1,2,4,5,6,8],[3],[7]] => 2
[[1,2,4],[3,6,8],[5],[7]] => [[1,2,3,5,6,8],[4],[7]] => 2
[[1,2,3],[4,6,8],[5],[7]] => [[1,2,3,4,6,8],[5],[7]] => 2
[[1,3,5],[2,4,8],[6],[7]] => [[1,2,4,6,8],[3,5],[7]] => 3
[[1,2,5],[3,4,8],[6],[7]] => [[1,2,3,4,8],[5,6],[7]] => 1
[[1,3,4],[2,5,8],[6],[7]] => [[1,2,4,5,8],[3,6],[7]] => 2
[[1,2,4],[3,5,8],[6],[7]] => [[1,2,3,5,8],[4,6],[7]] => 2
[[1,2,3],[4,5,8],[6],[7]] => [[1,2,3,4,5,8],[6],[7]] => 1
[[1,4,6],[2,5,7],[3],[8]] => [[1,2,5,7],[3,6,8],[4]] => 2
[[1,3,6],[2,5,7],[4],[8]] => [[1,2,4,5,7],[3,8],[6]] => 2
[[1,2,6],[3,5,7],[4],[8]] => [[1,2,3,5,7],[4,8],[6]] => 2
[[1,3,6],[2,4,7],[5],[8]] => [[1,2,4,7],[3,5,8],[6]] => 2
[[1,2,6],[3,4,7],[5],[8]] => [[1,2,3,4,7],[5,8],[6]] => 1
[[1,4,5],[2,6,7],[3],[8]] => [[1,2,5,6,7],[3,8],[4]] => 1
[[1,3,5],[2,6,7],[4],[8]] => [[1,2,4,6,7],[3,8],[5]] => 2
[[1,2,5],[3,6,7],[4],[8]] => [[1,2,3,6,7],[4,8],[5]] => 1
[[1,3,4],[2,6,7],[5],[8]] => [[1,2,4,5,6,7],[3],[8]] => 1
[[1,2,4],[3,6,7],[5],[8]] => [[1,2,3,5,6,7],[4],[8]] => 1
[[1,2,3],[4,6,7],[5],[8]] => [[1,2,3,4,6,7],[5],[8]] => 1
[[1,3,5],[2,4,7],[6],[8]] => [[1,2,4,6,7],[3,5],[8]] => 2
[[1,2,5],[3,4,7],[6],[8]] => [[1,2,3,4,7],[5,6],[8]] => 1
[[1,3,4],[2,5,7],[6],[8]] => [[1,2,4,5,7],[3,6],[8]] => 2
[[1,2,4],[3,5,7],[6],[8]] => [[1,2,3,5,7],[4,6],[8]] => 2
[[1,2,3],[4,5,7],[6],[8]] => [[1,2,3,4,5,7],[6],[8]] => 1
[[1,3,5],[2,4,6],[7],[8]] => [[1,2,4,6],[3,5,7],[8]] => 2
[[1,2,5],[3,4,6],[7],[8]] => [[1,2,3,4,6],[5,7],[8]] => 1
[[1,3,4],[2,5,6],[7],[8]] => [[1,2,4,5,6],[3,7],[8]] => 1
[[1,2,4],[3,5,6],[7],[8]] => [[1,2,3,5,6],[4,7],[8]] => 1
[[1,2,3],[4,5,6],[7],[8]] => [[1,2,3,4,5,6],[7],[8]] => 0
[[1,5,8],[2,6],[3,7],[4]] => [[1,2,6],[3,7],[4,8],[5]] => 1
[[1,4,8],[2,6],[3,7],[5]] => [[1,2,5,6],[3,7],[4],[8]] => 1
[[1,3,8],[2,6],[4,7],[5]] => [[1,2,4,6],[3,7],[5],[8]] => 2
[[1,2,8],[3,6],[4,7],[5]] => [[1,2,3,6],[4,7],[5],[8]] => 1
[[1,4,8],[2,5],[3,7],[6]] => [[1,2,5,7],[3,6],[4],[8]] => 2
[[1,3,8],[2,5],[4,7],[6]] => [[1,2,4,5],[3,7],[6],[8]] => 2
[[1,2,8],[3,5],[4,7],[6]] => [[1,2,3,5],[4,7],[6],[8]] => 2
[[1,3,8],[2,4],[5,7],[6]] => [[1,2,4,7],[3,5],[6],[8]] => 2
[[1,2,8],[3,4],[5,7],[6]] => [[1,2,3,4],[5,7],[6],[8]] => 1
[[1,4,8],[2,5],[3,6],[7]] => [[1,2,5],[3,6],[4,7],[8]] => 1
[[1,3,8],[2,5],[4,6],[7]] => [[1,2,4,5],[3,6],[7],[8]] => 1
[[1,2,8],[3,5],[4,6],[7]] => [[1,2,3,5],[4,6],[7],[8]] => 1
[[1,3,8],[2,4],[5,6],[7]] => [[1,2,4,6],[3,5],[7],[8]] => 2
[[1,2,8],[3,4],[5,6],[7]] => [[1,2,3,4],[5,6],[7],[8]] => 0
[[1,5,7],[2,6],[3,8],[4]] => [[1,2,6,8],[3,7],[4],[5]] => 2
[[1,4,7],[2,6],[3,8],[5]] => [[1,2,5,6],[3,8],[4],[7]] => 2
[[1,3,7],[2,6],[4,8],[5]] => [[1,2,4,6],[3,8],[5],[7]] => 3
[[1,2,7],[3,6],[4,8],[5]] => [[1,2,3,6],[4,8],[5],[7]] => 2
[[1,4,7],[2,5],[3,8],[6]] => [[1,2,5,8],[3,6],[4],[7]] => 2
[[1,3,7],[2,5],[4,8],[6]] => [[1,2,4,5],[3,8],[6],[7]] => 2
[[1,2,7],[3,5],[4,8],[6]] => [[1,2,3,5],[4,8],[6],[7]] => 2
[[1,3,7],[2,4],[5,8],[6]] => [[1,2,4,8],[3,5],[6],[7]] => 2
[[1,2,7],[3,4],[5,8],[6]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[[1,5,6],[2,7],[3,8],[4]] => [[1,2,6,7],[3,8],[4],[5]] => 1
[[1,4,6],[2,7],[3,8],[5]] => [[1,2,5,7],[3,8],[4],[6]] => 2
[[1,3,6],[2,7],[4,8],[5]] => [[1,2,4,7],[3,8],[5],[6]] => 2
[[1,2,6],[3,7],[4,8],[5]] => [[1,2,3,7],[4,8],[5],[6]] => 1
[[1,4,5],[2,7],[3,8],[6]] => [[1,2,5,6,7],[3,8],[4]] => 1
[[1,3,5],[2,7],[4,8],[6]] => [[1,2,4,6,7],[3,8],[5]] => 2
[[1,2,5],[3,7],[4,8],[6]] => [[1,2,3,6,7],[4,8],[5]] => 1
[[1,3,4],[2,7],[5,8],[6]] => [[1,2,4,5,7],[3,8],[6]] => 2
[[1,2,4],[3,7],[5,8],[6]] => [[1,2,3,5,7],[4,8],[6]] => 2
[[1,2,3],[4,7],[5,8],[6]] => [[1,2,3,4,7],[5,8],[6]] => 1
[[1,4,6],[2,5],[3,8],[7]] => [[1,2,5,7,8],[3,6],[4]] => 2
[[1,3,6],[2,5],[4,8],[7]] => [[1,2,4,5,8],[3,7],[6]] => 3
[[1,2,6],[3,5],[4,8],[7]] => [[1,2,3,5,8],[4,7],[6]] => 3
[[1,3,6],[2,4],[5,8],[7]] => [[1,2,4,7,8],[3,5],[6]] => 2
[[1,2,6],[3,4],[5,8],[7]] => [[1,2,3,4,8],[5,7],[6]] => 2
[[1,4,5],[2,6],[3,8],[7]] => [[1,2,5,6,8],[3,7],[4]] => 2
[[1,3,5],[2,6],[4,8],[7]] => [[1,2,4,6,8],[3,7],[5]] => 3
[[1,2,5],[3,6],[4,8],[7]] => [[1,2,3,6,8],[4,7],[5]] => 2
[[1,3,4],[2,6],[5,8],[7]] => [[1,2,4,5,6],[3,8],[7]] => 2
[[1,2,4],[3,6],[5,8],[7]] => [[1,2,3,5,6],[4,8],[7]] => 2
[[1,2,3],[4,6],[5,8],[7]] => [[1,2,3,4,6],[5,8],[7]] => 2
[[1,3,5],[2,4],[6,8],[7]] => [[1,2,4,6,8],[3,5],[7]] => 3
[[1,2,5],[3,4],[6,8],[7]] => [[1,2,3,4,8],[5,6],[7]] => 1
[[1,3,4],[2,5],[6,8],[7]] => [[1,2,4,5,8],[3,6],[7]] => 2
[[1,2,4],[3,5],[6,8],[7]] => [[1,2,3,5,8],[4,6],[7]] => 2
[[1,2,3],[4,5],[6,8],[7]] => [[1,2,3,4,5],[6,8],[7]] => 1
[[1,4,7],[2,5],[3,6],[8]] => [[1,2,5,8],[3,6],[4,7]] => 2
[[1,3,7],[2,5],[4,6],[8]] => [[1,2,4,5],[3,6],[7,8]] => 1
[[1,2,7],[3,5],[4,6],[8]] => [[1,2,3,5],[4,6],[7,8]] => 1
[[1,3,7],[2,4],[5,6],[8]] => [[1,2,4,6],[3,5],[7,8]] => 2
[[1,2,7],[3,4],[5,6],[8]] => [[1,2,3,4],[5,6],[7,8]] => 0
[[1,4,6],[2,5],[3,7],[8]] => [[1,2,5,7],[3,6],[4,8]] => 2
[[1,3,6],[2,5],[4,7],[8]] => [[1,2,4,5],[3,7],[6,8]] => 2
[[1,2,6],[3,5],[4,7],[8]] => [[1,2,3,5],[4,7],[6,8]] => 2
[[1,3,6],[2,4],[5,7],[8]] => [[1,2,4,7],[3,5],[6,8]] => 2
[[1,2,6],[3,4],[5,7],[8]] => [[1,2,3,4],[5,7],[6,8]] => 1
[[1,4,5],[2,6],[3,7],[8]] => [[1,2,5,6],[3,7],[4,8]] => 1
[[1,3,5],[2,6],[4,7],[8]] => [[1,2,4,6],[3,7],[5,8]] => 2
[[1,2,5],[3,6],[4,7],[8]] => [[1,2,3,6],[4,7],[5,8]] => 1
[[1,3,4],[2,6],[5,7],[8]] => [[1,2,4,5,6],[3,7],[8]] => 1
[[1,2,4],[3,6],[5,7],[8]] => [[1,2,3,5,6],[4,7],[8]] => 1
[[1,2,3],[4,6],[5,7],[8]] => [[1,2,3,4,6],[5,7],[8]] => 1
[[1,3,5],[2,4],[6,7],[8]] => [[1,2,4,6,7],[3,5],[8]] => 2
[[1,2,5],[3,4],[6,7],[8]] => [[1,2,3,4,7],[5,6],[8]] => 1
[[1,3,4],[2,5],[6,7],[8]] => [[1,2,4,5,7],[3,6],[8]] => 2
[[1,2,4],[3,5],[6,7],[8]] => [[1,2,3,5,7],[4,6],[8]] => 2
[[1,2,3],[4,5],[6,7],[8]] => [[1,2,3,4,5],[6,7],[8]] => 0
[[1,6,8],[2,7],[3],[4],[5]] => [[1,2,7],[3,8],[4],[5],[6]] => 1
[[1,5,8],[2,7],[3],[4],[6]] => [[1,2,6,7],[3],[4],[5],[8]] => 1
[[1,4,8],[2,7],[3],[5],[6]] => [[1,2,5,7],[3],[4],[6],[8]] => 2
[[1,3,8],[2,7],[4],[5],[6]] => [[1,2,4,7],[3],[5],[6],[8]] => 2
[[1,2,8],[3,7],[4],[5],[6]] => [[1,2,3,7],[4],[5],[6],[8]] => 1
[[1,5,8],[2,6],[3],[4],[7]] => [[1,2,6],[3,7],[4],[5],[8]] => 1
[[1,4,8],[2,6],[3],[5],[7]] => [[1,2,5,6],[3],[4],[7],[8]] => 1
[[1,3,8],[2,6],[4],[5],[7]] => [[1,2,4,6],[3],[5],[7],[8]] => 2
[[1,2,8],[3,6],[4],[5],[7]] => [[1,2,3,6],[4],[5],[7],[8]] => 1
[[1,4,8],[2,5],[3],[6],[7]] => [[1,2,5],[3,6],[4],[7],[8]] => 1
[[1,3,8],[2,5],[4],[6],[7]] => [[1,2,4,5],[3],[6],[7],[8]] => 1
[[1,2,8],[3,5],[4],[6],[7]] => [[1,2,3,5],[4],[6],[7],[8]] => 1
[[1,3,8],[2,4],[5],[6],[7]] => [[1,2,4],[3,5],[6],[7],[8]] => 1
[[1,2,8],[3,4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[[1,6,7],[2,8],[3],[4],[5]] => [[1,2,7,8],[3],[4],[5],[6]] => 1
[[1,5,7],[2,8],[3],[4],[6]] => [[1,2,6,8],[3],[4],[5],[7]] => 2
[[1,4,7],[2,8],[3],[5],[6]] => [[1,2,5,8],[3],[4],[6],[7]] => 2
[[1,3,7],[2,8],[4],[5],[6]] => [[1,2,4,8],[3],[5],[6],[7]] => 2
[[1,2,7],[3,8],[4],[5],[6]] => [[1,2,3,8],[4],[5],[6],[7]] => 1
[[1,5,6],[2,8],[3],[4],[7]] => [[1,2,6,7,8],[3],[4],[5]] => 1
[[1,4,6],[2,8],[3],[5],[7]] => [[1,2,5,7,8],[3],[4],[6]] => 2
[[1,3,6],[2,8],[4],[5],[7]] => [[1,2,4,7,8],[3],[5],[6]] => 2
[[1,2,6],[3,8],[4],[5],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 1
[[1,4,5],[2,8],[3],[6],[7]] => [[1,2,5,6,8],[3],[4],[7]] => 2
[[1,3,5],[2,8],[4],[6],[7]] => [[1,2,4,6,8],[3],[5],[7]] => 3
[[1,2,5],[3,8],[4],[6],[7]] => [[1,2,3,6,8],[4],[5],[7]] => 2
[[1,3,4],[2,8],[5],[6],[7]] => [[1,2,4,5,8],[3],[6],[7]] => 2
[[1,2,4],[3,8],[5],[6],[7]] => [[1,2,3,5,8],[4],[6],[7]] => 2
[[1,2,3],[4,8],[5],[6],[7]] => [[1,2,3,4,8],[5],[6],[7]] => 1
[[1,5,7],[2,6],[3],[4],[8]] => [[1,2,6,8],[3,7],[4],[5]] => 2
[[1,4,7],[2,6],[3],[5],[8]] => [[1,2,5,6],[3,8],[4],[7]] => 2
[[1,3,7],[2,6],[4],[5],[8]] => [[1,2,4,6],[3,8],[5],[7]] => 3
[[1,2,7],[3,6],[4],[5],[8]] => [[1,2,3,6],[4,8],[5],[7]] => 2
[[1,4,7],[2,5],[3],[6],[8]] => [[1,2,5,8],[3,6],[4],[7]] => 2
[[1,3,7],[2,5],[4],[6],[8]] => [[1,2,4,5],[3,8],[6],[7]] => 2
[[1,2,7],[3,5],[4],[6],[8]] => [[1,2,3,5],[4,8],[6],[7]] => 2
[[1,3,7],[2,4],[5],[6],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 2
[[1,2,7],[3,4],[5],[6],[8]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[[1,5,6],[2,7],[3],[4],[8]] => [[1,2,6,7],[3,8],[4],[5]] => 1
[[1,4,6],[2,7],[3],[5],[8]] => [[1,2,5,7],[3,8],[4],[6]] => 2
[[1,3,6],[2,7],[4],[5],[8]] => [[1,2,4,7],[3,8],[5],[6]] => 2
[[1,2,6],[3,7],[4],[5],[8]] => [[1,2,3,7],[4,8],[5],[6]] => 1
[[1,4,5],[2,7],[3],[6],[8]] => [[1,2,5,6,7],[3],[4],[8]] => 1
[[1,3,5],[2,7],[4],[6],[8]] => [[1,2,4,6,7],[3],[5],[8]] => 2
[[1,2,5],[3,7],[4],[6],[8]] => [[1,2,3,6,7],[4],[5],[8]] => 1
[[1,3,4],[2,7],[5],[6],[8]] => [[1,2,4,5,7],[3],[6],[8]] => 2
[[1,2,4],[3,7],[5],[6],[8]] => [[1,2,3,5,7],[4],[6],[8]] => 2
[[1,2,3],[4,7],[5],[6],[8]] => [[1,2,3,4,7],[5],[6],[8]] => 1
[[1,4,6],[2,5],[3],[7],[8]] => [[1,2,5,7],[3,6],[4],[8]] => 2
[[1,3,6],[2,5],[4],[7],[8]] => [[1,2,4,5],[3,7],[6],[8]] => 2
[[1,2,6],[3,5],[4],[7],[8]] => [[1,2,3,5],[4,7],[6],[8]] => 2
[[1,3,6],[2,4],[5],[7],[8]] => [[1,2,4,7],[3,5],[6],[8]] => 2
[[1,2,6],[3,4],[5],[7],[8]] => [[1,2,3,4],[5,7],[6],[8]] => 1
[[1,4,5],[2,6],[3],[7],[8]] => [[1,2,5,6],[3,7],[4],[8]] => 1
[[1,3,5],[2,6],[4],[7],[8]] => [[1,2,4,6],[3,7],[5],[8]] => 2
[[1,2,5],[3,6],[4],[7],[8]] => [[1,2,3,6],[4,7],[5],[8]] => 1
[[1,3,4],[2,6],[5],[7],[8]] => [[1,2,4,5,6],[3],[7],[8]] => 1
[[1,2,4],[3,6],[5],[7],[8]] => [[1,2,3,5,6],[4],[7],[8]] => 1
[[1,2,3],[4,6],[5],[7],[8]] => [[1,2,3,4,6],[5],[7],[8]] => 1
[[1,3,5],[2,4],[6],[7],[8]] => [[1,2,4,6],[3,5],[7],[8]] => 2
[[1,2,5],[3,4],[6],[7],[8]] => [[1,2,3,4],[5,6],[7],[8]] => 0
[[1,3,4],[2,5],[6],[7],[8]] => [[1,2,4,5],[3,6],[7],[8]] => 1
[[1,2,4],[3,5],[6],[7],[8]] => [[1,2,3,5],[4,6],[7],[8]] => 1
[[1,2,3],[4,5],[6],[7],[8]] => [[1,2,3,4,5],[6],[7],[8]] => 0
[[1,7,8],[2],[3],[4],[5],[6]] => [[1,2,8],[3],[4],[5],[6],[7]] => 1
[[1,6,8],[2],[3],[4],[5],[7]] => [[1,2,7],[3],[4],[5],[6],[8]] => 1
[[1,5,8],[2],[3],[4],[6],[7]] => [[1,2,6],[3],[4],[5],[7],[8]] => 1
[[1,4,8],[2],[3],[5],[6],[7]] => [[1,2,5],[3],[4],[6],[7],[8]] => 1
[[1,3,8],[2],[4],[5],[6],[7]] => [[1,2,4],[3],[5],[6],[7],[8]] => 1
[[1,2,8],[3],[4],[5],[6],[7]] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[[1,6,7],[2],[3],[4],[5],[8]] => [[1,2,7,8],[3],[4],[5],[6]] => 1
[[1,5,7],[2],[3],[4],[6],[8]] => [[1,2,6,8],[3],[4],[5],[7]] => 2
[[1,4,7],[2],[3],[5],[6],[8]] => [[1,2,5,8],[3],[4],[6],[7]] => 2
[[1,3,7],[2],[4],[5],[6],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => 2
[[1,2,7],[3],[4],[5],[6],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 1
[[1,5,6],[2],[3],[4],[7],[8]] => [[1,2,6,7],[3],[4],[5],[8]] => 1
[[1,4,6],[2],[3],[5],[7],[8]] => [[1,2,5,7],[3],[4],[6],[8]] => 2
[[1,3,6],[2],[4],[5],[7],[8]] => [[1,2,4,7],[3],[5],[6],[8]] => 2
[[1,2,6],[3],[4],[5],[7],[8]] => [[1,2,3,7],[4],[5],[6],[8]] => 1
[[1,4,5],[2],[3],[6],[7],[8]] => [[1,2,5,6],[3],[4],[7],[8]] => 1
[[1,3,5],[2],[4],[6],[7],[8]] => [[1,2,4,6],[3],[5],[7],[8]] => 2
[[1,2,5],[3],[4],[6],[7],[8]] => [[1,2,3,6],[4],[5],[7],[8]] => 1
[[1,3,4],[2],[5],[6],[7],[8]] => [[1,2,4,5],[3],[6],[7],[8]] => 1
[[1,2,4],[3],[5],[6],[7],[8]] => [[1,2,3,5],[4],[6],[7],[8]] => 1
[[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[[1,5],[2,6],[3,7],[4,8]] => [[1,2,6],[3,7],[4,8],[5]] => 1
[[1,4],[2,6],[3,7],[5,8]] => [[1,2,5,6],[3,7],[4,8]] => 1
[[1,3],[2,6],[4,7],[5,8]] => [[1,2,4,6],[3,7],[5,8]] => 2
[[1,2],[3,6],[4,7],[5,8]] => [[1,2,3,6],[4,7],[5,8]] => 1
[[1,4],[2,5],[3,7],[6,8]] => [[1,2,5,7],[3,6],[4,8]] => 2
[[1,3],[2,5],[4,7],[6,8]] => [[1,2,4,5],[3,7],[6,8]] => 2
[[1,2],[3,5],[4,7],[6,8]] => [[1,2,3,5],[4,7],[6,8]] => 2
[[1,3],[2,4],[5,7],[6,8]] => [[1,2,4,7],[3,5],[6,8]] => 2
[[1,2],[3,4],[5,7],[6,8]] => [[1,2,3,4],[5,7],[6,8]] => 1
[[1,4],[2,5],[3,6],[7,8]] => [[1,2,5,8],[3,6],[4,7]] => 2
[[1,3],[2,5],[4,6],[7,8]] => [[1,2,4,5],[3,6],[7,8]] => 1
[[1,2],[3,5],[4,6],[7,8]] => [[1,2,3,5],[4,6],[7,8]] => 1
[[1,3],[2,4],[5,6],[7,8]] => [[1,2,4,6],[3,5],[7,8]] => 2
[[1,2],[3,4],[5,6],[7,8]] => [[1,2,3,4],[5,6],[7,8]] => 0
[[1,6],[2,7],[3,8],[4],[5]] => [[1,2,7],[3,8],[4],[5],[6]] => 1
[[1,5],[2,7],[3,8],[4],[6]] => [[1,2,6,7],[3,8],[4],[5]] => 1
[[1,4],[2,7],[3,8],[5],[6]] => [[1,2,5,7],[3,8],[4],[6]] => 2
[[1,3],[2,7],[4,8],[5],[6]] => [[1,2,4,7],[3,8],[5],[6]] => 2
[[1,2],[3,7],[4,8],[5],[6]] => [[1,2,3,7],[4,8],[5],[6]] => 1
[[1,5],[2,6],[3,8],[4],[7]] => [[1,2,6,8],[3,7],[4],[5]] => 2
[[1,4],[2,6],[3,8],[5],[7]] => [[1,2,5,6],[3,8],[4],[7]] => 2
[[1,3],[2,6],[4,8],[5],[7]] => [[1,2,4,6],[3,8],[5],[7]] => 3
[[1,2],[3,6],[4,8],[5],[7]] => [[1,2,3,6],[4,8],[5],[7]] => 2
[[1,4],[2,5],[3,8],[6],[7]] => [[1,2,5,8],[3,6],[4],[7]] => 2
[[1,3],[2,5],[4,8],[6],[7]] => [[1,2,4,5],[3,8],[6],[7]] => 2
[[1,2],[3,5],[4,8],[6],[7]] => [[1,2,3,5],[4,8],[6],[7]] => 2
[[1,3],[2,4],[5,8],[6],[7]] => [[1,2,4,8],[3,5],[6],[7]] => 2
[[1,2],[3,4],[5,8],[6],[7]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[[1,5],[2,6],[3,7],[4],[8]] => [[1,2,6],[3,7],[4,8],[5]] => 1
[[1,4],[2,6],[3,7],[5],[8]] => [[1,2,5,6],[3,7],[4],[8]] => 1
[[1,3],[2,6],[4,7],[5],[8]] => [[1,2,4,6],[3,7],[5],[8]] => 2
[[1,2],[3,6],[4,7],[5],[8]] => [[1,2,3,6],[4,7],[5],[8]] => 1
[[1,4],[2,5],[3,7],[6],[8]] => [[1,2,5,7],[3,6],[4],[8]] => 2
[[1,3],[2,5],[4,7],[6],[8]] => [[1,2,4,5],[3,7],[6],[8]] => 2
[[1,2],[3,5],[4,7],[6],[8]] => [[1,2,3,5],[4,7],[6],[8]] => 2
[[1,3],[2,4],[5,7],[6],[8]] => [[1,2,4,7],[3,5],[6],[8]] => 2
[[1,2],[3,4],[5,7],[6],[8]] => [[1,2,3,4],[5,7],[6],[8]] => 1
[[1,4],[2,5],[3,6],[7],[8]] => [[1,2,5],[3,6],[4,7],[8]] => 1
[[1,3],[2,5],[4,6],[7],[8]] => [[1,2,4,5],[3,6],[7],[8]] => 1
[[1,2],[3,5],[4,6],[7],[8]] => [[1,2,3,5],[4,6],[7],[8]] => 1
[[1,3],[2,4],[5,6],[7],[8]] => [[1,2,4,6],[3,5],[7],[8]] => 2
[[1,2],[3,4],[5,6],[7],[8]] => [[1,2,3,4],[5,6],[7],[8]] => 0
[[1,7],[2,8],[3],[4],[5],[6]] => [[1,2,8],[3],[4],[5],[6],[7]] => 1
[[1,6],[2,8],[3],[4],[5],[7]] => [[1,2,7,8],[3],[4],[5],[6]] => 1
[[1,5],[2,8],[3],[4],[6],[7]] => [[1,2,6,8],[3],[4],[5],[7]] => 2
[[1,4],[2,8],[3],[5],[6],[7]] => [[1,2,5,8],[3],[4],[6],[7]] => 2
[[1,3],[2,8],[4],[5],[6],[7]] => [[1,2,4,8],[3],[5],[6],[7]] => 2
[[1,2],[3,8],[4],[5],[6],[7]] => [[1,2,3,8],[4],[5],[6],[7]] => 1
[[1,6],[2,7],[3],[4],[5],[8]] => [[1,2,7],[3,8],[4],[5],[6]] => 1
[[1,5],[2,7],[3],[4],[6],[8]] => [[1,2,6,7],[3],[4],[5],[8]] => 1
[[1,4],[2,7],[3],[5],[6],[8]] => [[1,2,5,7],[3],[4],[6],[8]] => 2
[[1,3],[2,7],[4],[5],[6],[8]] => [[1,2,4,7],[3],[5],[6],[8]] => 2
[[1,2],[3,7],[4],[5],[6],[8]] => [[1,2,3,7],[4],[5],[6],[8]] => 1
[[1,5],[2,6],[3],[4],[7],[8]] => [[1,2,6],[3,7],[4],[5],[8]] => 1
[[1,4],[2,6],[3],[5],[7],[8]] => [[1,2,5,6],[3],[4],[7],[8]] => 1
[[1,3],[2,6],[4],[5],[7],[8]] => [[1,2,4,6],[3],[5],[7],[8]] => 2
[[1,2],[3,6],[4],[5],[7],[8]] => [[1,2,3,6],[4],[5],[7],[8]] => 1
[[1,4],[2,5],[3],[6],[7],[8]] => [[1,2,5],[3,6],[4],[7],[8]] => 1
[[1,3],[2,5],[4],[6],[7],[8]] => [[1,2,4,5],[3],[6],[7],[8]] => 1
[[1,2],[3,5],[4],[6],[7],[8]] => [[1,2,3,5],[4],[6],[7],[8]] => 1
[[1,3],[2,4],[5],[6],[7],[8]] => [[1,2,4],[3,5],[6],[7],[8]] => 1
[[1,2],[3,4],[5],[6],[7],[8]] => [[1,2,3,4],[5],[6],[7],[8]] => 0
[[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
[[1,7],[2],[3],[4],[5],[6],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 1
[[1,6],[2],[3],[4],[5],[7],[8]] => [[1,2,7],[3],[4],[5],[6],[8]] => 1
[[1,5],[2],[3],[4],[6],[7],[8]] => [[1,2,6],[3],[4],[5],[7],[8]] => 1
[[1,4],[2],[3],[5],[6],[7],[8]] => [[1,2,5],[3],[4],[6],[7],[8]] => 1
[[1,3],[2],[4],[5],[6],[7],[8]] => [[1,2,4],[3],[5],[6],[7],[8]] => 1
[[1,2],[3],[4],[5],[6],[7],[8]] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[[1],[2],[3],[4],[5],[6],[7],[8]] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
7,3 11,15 19,49,8 29,133,70 46,331,346,41
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4$
$F_{4} = 7 + 3\ q$
$F_{5} = 11 + 15\ q$
$F_{6} = 19 + 49\ q + 8\ q^{2}$
$F_{7} = 29 + 133\ q + 70\ q^{2}$
$F_{8} = 46 + 331\ q + 346\ q^{2} + 41\ q^{3}$
Description
The number of natural descents of a standard Young tableau.
A natural descent of a standard tableau $T$ is an entry $i$ such that $i+1$ appears in a higher row than $i$ in English notation.
A natural descent of a standard tableau $T$ is an entry $i$ such that $i+1$ appears in a higher row than $i$ in English notation.
Map
catabolism
Description
Remove the first row of the standard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).
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