- FindStat

Identifier

Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000439: Dyck paths ⟶ ℤ (values match St000025The number of initial rises of a Dyck path.)

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1051 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8

[[1,2,3,4,5,6,7,8]] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2

[[1,3,4,5,6,7,8],[2]] => [[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3

[[1,2,4,5,6,7,8],[3]] => [[1,3],[2],[4],[5],[6],[7],[8]] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2

[[1,2,3,5,6,7,8],[4]] => [[1,4],[2],[3],[5],[6],[7],[8]] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2

[[1,2,3,4,6,7,8],[5]] => [[1,5],[2],[3],[4],[6],[7],[8]] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2

[[1,2,3,4,5,7,8],[6]] => [[1,6],[2],[3],[4],[5],[7],[8]] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2

[[1,2,3,4,5,6,8],[7]] => [[1,7],[2],[3],[4],[5],[6],[8]] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[[1,2,3,4,5,6,7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2

[[1,3,5,6,7,8],[2,4]] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 3

[[1,2,5,6,7,8],[3,4]] => [[1,3],[2,4],[5],[6],[7],[8]] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2

[[1,3,4,6,7,8],[2,5]] => [[1,2],[3,5],[4],[6],[7],[8]] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 3

[[1,2,4,6,7,8],[3,5]] => [[1,3],[2,5],[4],[6],[7],[8]] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2

[[1,2,3,6,7,8],[4,5]] => [[1,4],[2,5],[3],[6],[7],[8]] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2

[[1,3,4,5,7,8],[2,6]] => [[1,2],[3,6],[4],[5],[7],[8]] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[[1,2,4,5,7,8],[3,6]] => [[1,3],[2,6],[4],[5],[7],[8]] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2

[[1,2,3,5,7,8],[4,6]] => [[1,4],[2,6],[3],[5],[7],[8]] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[[1,2,3,4,7,8],[5,6]] => [[1,5],[2,6],[3],[4],[7],[8]] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2

[[1,3,4,5,6,8],[2,7]] => [[1,2],[3,7],[4],[5],[6],[8]] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3

[[1,2,4,5,6,8],[3,7]] => [[1,3],[2,7],[4],[5],[6],[8]] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[[1,2,3,5,6,8],[4,7]] => [[1,4],[2,7],[3],[5],[6],[8]] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[[1,2,3,4,6,8],[5,7]] => [[1,5],[2,7],[3],[4],[6],[8]] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,4,5,8],[6,7]] => [[1,6],[2,7],[3],[4],[5],[8]] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2

[[1,3,4,5,6,7],[2,8]] => [[1,2],[3,8],[4],[5],[6],[7]] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3

[[1,2,4,5,6,7],[3,8]] => [[1,3],[2,8],[4],[5],[6],[7]] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2

[[1,2,3,5,6,7],[4,8]] => [[1,4],[2,8],[3],[5],[6],[7]] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2

[[1,2,3,4,6,7],[5,8]] => [[1,5],[2,8],[3],[4],[6],[7]] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,2,3,4,5,7],[6,8]] => [[1,6],[2,8],[3],[4],[5],[7]] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,4,5,6],[7,8]] => [[1,7],[2,8],[3],[4],[5],[6]] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[[1,4,5,6,7,8],[2],[3]] => [[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4

[[1,3,5,6,7,8],[2],[4]] => [[1,2,4],[3],[5],[6],[7],[8]] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 3

[[1,2,5,6,7,8],[3],[4]] => [[1,3,4],[2],[5],[6],[7],[8]] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2

[[1,3,4,6,7,8],[2],[5]] => [[1,2,5],[3],[4],[6],[7],[8]] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 3

[[1,2,4,6,7,8],[3],[5]] => [[1,3,5],[2],[4],[6],[7],[8]] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2

[[1,2,3,6,7,8],[4],[5]] => [[1,4,5],[2],[3],[6],[7],[8]] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2

[[1,3,4,5,7,8],[2],[6]] => [[1,2,6],[3],[4],[5],[7],[8]] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[[1,2,4,5,7,8],[3],[6]] => [[1,3,6],[2],[4],[5],[7],[8]] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2

[[1,2,3,5,7,8],[4],[6]] => [[1,4,6],[2],[3],[5],[7],[8]] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[[1,2,3,4,7,8],[5],[6]] => [[1,5,6],[2],[3],[4],[7],[8]] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2

[[1,3,4,5,6,8],[2],[7]] => [[1,2,7],[3],[4],[5],[6],[8]] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3

[[1,2,4,5,6,8],[3],[7]] => [[1,3,7],[2],[4],[5],[6],[8]] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[[1,2,3,5,6,8],[4],[7]] => [[1,4,7],[2],[3],[5],[6],[8]] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[[1,2,3,4,6,8],[5],[7]] => [[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,4,5,8],[6],[7]] => [[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[[1,3,4,5,6,7],[2],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3

[[1,2,4,5,6,7],[3],[8]] => [[1,3,8],[2],[4],[5],[6],[7]] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2

[[1,2,3,5,6,7],[4],[8]] => [[1,4,8],[2],[3],[5],[6],[7]] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2

[[1,2,3,4,6,7],[5],[8]] => [[1,5,8],[2],[3],[4],[6],[7]] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,2,3,4,5,7],[6],[8]] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,4,5,6],[7],[8]] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2

[[1,3,5,7,8],[2,4,6]] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[[1,2,5,7,8],[3,4,6]] => [[1,3],[2,4],[5,6],[7],[8]] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2

[[1,3,4,7,8],[2,5,6]] => [[1,2],[3,5],[4,6],[7],[8]] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 3

[[1,2,4,7,8],[3,5,6]] => [[1,3],[2,5],[4,6],[7],[8]] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2

[[1,2,3,7,8],[4,5,6]] => [[1,4],[2,5],[3,6],[7],[8]] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[[1,3,5,6,8],[2,4,7]] => [[1,2],[3,4],[5,7],[6],[8]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,5,6,8],[3,4,7]] => [[1,3],[2,4],[5,7],[6],[8]] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[[1,3,4,6,8],[2,5,7]] => [[1,2],[3,5],[4,7],[6],[8]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4,6,8],[3,5,7]] => [[1,3],[2,5],[4,7],[6],[8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,6,8],[4,5,7]] => [[1,4],[2,5],[3,7],[6],[8]] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,4,5,8],[2,6,7]] => [[1,2],[3,6],[4,7],[5],[8]] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[[1,2,4,5,8],[3,6,7]] => [[1,3],[2,6],[4,7],[5],[8]] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2

[[1,2,3,5,8],[4,6,7]] => [[1,4],[2,6],[3,7],[5],[8]] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[[1,2,3,4,8],[5,6,7]] => [[1,5],[2,6],[3,7],[4],[8]] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,3,5,6,7],[2,4,8]] => [[1,2],[3,4],[5,8],[6],[7]] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[[1,2,5,6,7],[3,4,8]] => [[1,3],[2,4],[5,8],[6],[7]] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2

[[1,3,4,6,7],[2,5,8]] => [[1,2],[3,5],[4,8],[6],[7]] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[[1,2,4,6,7],[3,5,8]] => [[1,3],[2,5],[4,8],[6],[7]] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,2,3,6,7],[4,5,8]] => [[1,4],[2,5],[3,8],[6],[7]] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2

[[1,3,4,5,7],[2,6,8]] => [[1,2],[3,6],[4,8],[5],[7]] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[[1,2,4,5,7],[3,6,8]] => [[1,3],[2,6],[4,8],[5],[7]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,5,7],[4,6,8]] => [[1,4],[2,6],[3,8],[5],[7]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,4,7],[5,6,8]] => [[1,5],[2,6],[3,8],[4],[7]] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,3,4,5,6],[2,7,8]] => [[1,2],[3,7],[4,8],[5],[6]] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3

[[1,2,4,5,6],[3,7,8]] => [[1,3],[2,7],[4,8],[5],[6]] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[[1,2,3,5,6],[4,7,8]] => [[1,4],[2,7],[3,8],[5],[6]] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[[1,2,3,4,6],[5,7,8]] => [[1,5],[2,7],[3,8],[4],[6]] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,4,5],[6,7,8]] => [[1,6],[2,7],[3,8],[4],[5]] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,3,6,7,8],[2,5],[4]] => [[1,2,4],[3,5],[6],[7],[8]] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 3

[[1,2,6,7,8],[3,5],[4]] => [[1,3,4],[2,5],[6],[7],[8]] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2

[[1,3,6,7,8],[2,4],[5]] => [[1,2,5],[3,4],[6],[7],[8]] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3

[[1,2,6,7,8],[3,4],[5]] => [[1,3,5],[2,4],[6],[7],[8]] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2

[[1,3,5,7,8],[2,6],[4]] => [[1,2,4],[3,6],[5],[7],[8]] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[[1,2,5,7,8],[3,6],[4]] => [[1,3,4],[2,6],[5],[7],[8]] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2

[[1,3,4,7,8],[2,6],[5]] => [[1,2,5],[3,6],[4],[7],[8]] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 3

[[1,2,4,7,8],[3,6],[5]] => [[1,3,5],[2,6],[4],[7],[8]] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2

[[1,2,3,7,8],[4,6],[5]] => [[1,4,5],[2,6],[3],[7],[8]] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2

[[1,3,5,7,8],[2,4],[6]] => [[1,2,6],[3,4],[5],[7],[8]] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[[1,2,5,7,8],[3,4],[6]] => [[1,3,6],[2,4],[5],[7],[8]] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2

[[1,3,4,7,8],[2,5],[6]] => [[1,2,6],[3,5],[4],[7],[8]] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[[1,2,4,7,8],[3,5],[6]] => [[1,3,6],[2,5],[4],[7],[8]] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2

[[1,2,3,7,8],[4,5],[6]] => [[1,4,6],[2,5],[3],[7],[8]] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[[1,3,5,6,8],[2,7],[4]] => [[1,2,4],[3,7],[5],[6],[8]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,5,6,8],[3,7],[4]] => [[1,3,4],[2,7],[5],[6],[8]] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,4,6,8],[2,7],[5]] => [[1,2,5],[3,7],[4],[6],[8]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4,6,8],[3,7],[5]] => [[1,3,5],[2,7],[4],[6],[8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,6,8],[4,7],[5]] => [[1,4,5],[2,7],[3],[6],[8]] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[[1,3,4,5,8],[2,7],[6]] => [[1,2,6],[3,7],[4],[5],[8]] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[[1,2,4,5,8],[3,7],[6]] => [[1,3,6],[2,7],[4],[5],[8]] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2

[[1,2,3,5,8],[4,7],[6]] => [[1,4,6],[2,7],[3],[5],[8]] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[[1,2,3,4,8],[5,7],[6]] => [[1,5,6],[2,7],[3],[4],[8]] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2

[[1,3,5,6,8],[2,4],[7]] => [[1,2,7],[3,4],[5],[6],[8]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,5,6,8],[3,4],[7]] => [[1,3,7],[2,4],[5],[6],[8]] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[[1,3,4,6,8],[2,5],[7]] => [[1,2,7],[3,5],[4],[6],[8]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4,6,8],[3,5],[7]] => [[1,3,7],[2,5],[4],[6],[8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,6,8],[4,5],[7]] => [[1,4,7],[2,5],[3],[6],[8]] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,4,5,8],[2,6],[7]] => [[1,2,7],[3,6],[4],[5],[8]] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3

[[1,2,4,5,8],[3,6],[7]] => [[1,3,7],[2,6],[4],[5],[8]] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[[1,2,3,5,8],[4,6],[7]] => [[1,4,7],[2,6],[3],[5],[8]] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[[1,2,3,4,8],[5,6],[7]] => [[1,5,7],[2,6],[3],[4],[8]] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,4,5,6,7],[2,8],[3]] => [[1,2,3],[4,8],[5],[6],[7]] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 4

[[1,3,5,6,7],[2,8],[4]] => [[1,2,4],[3,8],[5],[6],[7]] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[[1,2,5,6,7],[3,8],[4]] => [[1,3,4],[2,8],[5],[6],[7]] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2

[[1,3,4,6,7],[2,8],[5]] => [[1,2,5],[3,8],[4],[6],[7]] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[[1,2,4,6,7],[3,8],[5]] => [[1,3,5],[2,8],[4],[6],[7]] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,2,3,6,7],[4,8],[5]] => [[1,4,5],[2,8],[3],[6],[7]] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[[1,3,4,5,7],[2,8],[6]] => [[1,2,6],[3,8],[4],[5],[7]] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[[1,2,4,5,7],[3,8],[6]] => [[1,3,6],[2,8],[4],[5],[7]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,5,7],[4,8],[6]] => [[1,4,6],[2,8],[3],[5],[7]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,4,7],[5,8],[6]] => [[1,5,6],[2,8],[3],[4],[7]] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,3,4,5,6],[2,8],[7]] => [[1,2,7],[3,8],[4],[5],[6]] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3

[[1,2,4,5,6],[3,8],[7]] => [[1,3,7],[2,8],[4],[5],[6]] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[[1,2,3,5,6],[4,8],[7]] => [[1,4,7],[2,8],[3],[5],[6]] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[[1,2,3,4,6],[5,8],[7]] => [[1,5,7],[2,8],[3],[4],[6]] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,4,5],[6,8],[7]] => [[1,6,7],[2,8],[3],[4],[5]] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[[1,3,5,6,7],[2,4],[8]] => [[1,2,8],[3,4],[5],[6],[7]] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[[1,2,5,6,7],[3,4],[8]] => [[1,3,8],[2,4],[5],[6],[7]] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2

[[1,3,4,6,7],[2,5],[8]] => [[1,2,8],[3,5],[4],[6],[7]] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[[1,2,4,6,7],[3,5],[8]] => [[1,3,8],[2,5],[4],[6],[7]] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,2,3,6,7],[4,5],[8]] => [[1,4,8],[2,5],[3],[6],[7]] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2

[[1,3,4,5,7],[2,6],[8]] => [[1,2,8],[3,6],[4],[5],[7]] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[[1,2,4,5,7],[3,6],[8]] => [[1,3,8],[2,6],[4],[5],[7]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,5,7],[4,6],[8]] => [[1,4,8],[2,6],[3],[5],[7]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,4,7],[5,6],[8]] => [[1,5,8],[2,6],[3],[4],[7]] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,3,4,5,6],[2,7],[8]] => [[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3

[[1,2,4,5,6],[3,7],[8]] => [[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[[1,2,3,5,6],[4,7],[8]] => [[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[[1,2,3,4,6],[5,7],[8]] => [[1,5,8],[2,7],[3],[4],[6]] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,2,3,4,5],[6,7],[8]] => [[1,6,8],[2,7],[3],[4],[5]] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,3,6,7,8],[2],[4],[5]] => [[1,2,4,5],[3],[6],[7],[8]] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3

[[1,2,6,7,8],[3],[4],[5]] => [[1,3,4,5],[2],[6],[7],[8]] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2

[[1,3,5,7,8],[2],[4],[6]] => [[1,2,4,6],[3],[5],[7],[8]] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[[1,2,5,7,8],[3],[4],[6]] => [[1,3,4,6],[2],[5],[7],[8]] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2

[[1,3,4,7,8],[2],[5],[6]] => [[1,2,5,6],[3],[4],[7],[8]] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[[1,2,4,7,8],[3],[5],[6]] => [[1,3,5,6],[2],[4],[7],[8]] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2

[[1,2,3,7,8],[4],[5],[6]] => [[1,4,5,6],[2],[3],[7],[8]] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2

[[1,3,5,6,8],[2],[4],[7]] => [[1,2,4,7],[3],[5],[6],[8]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,5,6,8],[3],[4],[7]] => [[1,3,4,7],[2],[5],[6],[8]] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,4,6,8],[2],[5],[7]] => [[1,2,5,7],[3],[4],[6],[8]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4,6,8],[3],[5],[7]] => [[1,3,5,7],[2],[4],[6],[8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,6,8],[4],[5],[7]] => [[1,4,5,7],[2],[3],[6],[8]] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[[1,3,4,5,8],[2],[6],[7]] => [[1,2,6,7],[3],[4],[5],[8]] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3

[[1,2,4,5,8],[3],[6],[7]] => [[1,3,6,7],[2],[4],[5],[8]] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[[1,2,3,5,8],[4],[6],[7]] => [[1,4,6,7],[2],[3],[5],[8]] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[[1,2,3,4,8],[5],[6],[7]] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[[1,4,5,6,7],[2],[3],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 4

[[1,3,5,6,7],[2],[4],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[[1,2,5,6,7],[3],[4],[8]] => [[1,3,4,8],[2],[5],[6],[7]] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2

[[1,3,4,6,7],[2],[5],[8]] => [[1,2,5,8],[3],[4],[6],[7]] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[[1,2,4,6,7],[3],[5],[8]] => [[1,3,5,8],[2],[4],[6],[7]] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,2,3,6,7],[4],[5],[8]] => [[1,4,5,8],[2],[3],[6],[7]] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[[1,3,4,5,7],[2],[6],[8]] => [[1,2,6,8],[3],[4],[5],[7]] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[[1,2,4,5,7],[3],[6],[8]] => [[1,3,6,8],[2],[4],[5],[7]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,5,7],[4],[6],[8]] => [[1,4,6,8],[2],[3],[5],[7]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,4,7],[5],[6],[8]] => [[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,3,4,5,6],[2],[7],[8]] => [[1,2,7,8],[3],[4],[5],[6]] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3

[[1,2,4,5,6],[3],[7],[8]] => [[1,3,7,8],[2],[4],[5],[6]] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[[1,2,3,5,6],[4],[7],[8]] => [[1,4,7,8],[2],[3],[5],[6]] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[[1,2,3,4,6],[5],[7],[8]] => [[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,2,3,4,5],[6],[7],[8]] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[[1,3,5,7],[2,4,6,8]] => [[1,2],[3,4],[5,6],[7,8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5,7],[3,4,6,8]] => [[1,3],[2,4],[5,6],[7,8]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4,7],[2,5,6,8]] => [[1,2],[3,5],[4,6],[7,8]] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[[1,2,4,7],[3,5,6,8]] => [[1,3],[2,5],[4,6],[7,8]] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,2,3,7],[4,5,6,8]] => [[1,4],[2,5],[3,6],[7,8]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,5,6],[2,4,7,8]] => [[1,2],[3,4],[5,7],[6,8]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,5,6],[3,4,7,8]] => [[1,3],[2,4],[5,7],[6,8]] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[[1,3,4,6],[2,5,7,8]] => [[1,2],[3,5],[4,7],[6,8]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4,6],[3,5,7,8]] => [[1,3],[2,5],[4,7],[6,8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,6],[4,5,7,8]] => [[1,4],[2,5],[3,7],[6,8]] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,4,5],[2,6,7,8]] => [[1,2],[3,6],[4,7],[5,8]] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[[1,2,4,5],[3,6,7,8]] => [[1,3],[2,6],[4,7],[5,8]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,5],[4,6,7,8]] => [[1,4],[2,6],[3,7],[5,8]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,4],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8]] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,3,6,8],[2,5,7],[4]] => [[1,2,4],[3,5],[6,7],[8]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,6,8],[3,5,7],[4]] => [[1,3,4],[2,5],[6,7],[8]] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,6,8],[2,4,7],[5]] => [[1,2,5],[3,4],[6,7],[8]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2,6,8],[3,4,7],[5]] => [[1,3,5],[2,4],[6,7],[8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,3,5,8],[2,6,7],[4]] => [[1,2,4],[3,6],[5,7],[8]] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[[1,2,5,8],[3,6,7],[4]] => [[1,3,4],[2,6],[5,7],[8]] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2

[[1,3,4,8],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7],[8]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4,8],[3,6,7],[5]] => [[1,3,5],[2,6],[4,7],[8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,8],[4,6,7],[5]] => [[1,4,5],[2,6],[3,7],[8]] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[[1,3,5,8],[2,4,7],[6]] => [[1,2,6],[3,4],[5,7],[8]] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[[1,2,5,8],[3,4,7],[6]] => [[1,3,6],[2,4],[5,7],[8]] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2

[[1,3,4,8],[2,5,7],[6]] => [[1,2,6],[3,5],[4,7],[8]] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[[1,2,4,8],[3,5,7],[6]] => [[1,3,6],[2,5],[4,7],[8]] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2

[[1,2,3,8],[4,5,7],[6]] => [[1,4,6],[2,5],[3,7],[8]] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[[1,3,5,8],[2,4,6],[7]] => [[1,2,7],[3,4],[5,6],[8]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2,5,8],[3,4,6],[7]] => [[1,3,7],[2,4],[5,6],[8]] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[[1,3,4,8],[2,5,6],[7]] => [[1,2,7],[3,5],[4,6],[8]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4,8],[3,5,6],[7]] => [[1,3,7],[2,5],[4,6],[8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,8],[4,5,6],[7]] => [[1,4,7],[2,5],[3,6],[8]] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3,6,7],[2,5,8],[4]] => [[1,2,4],[3,5],[6,8],[7]] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[[1,2,6,7],[3,5,8],[4]] => [[1,3,4],[2,5],[6,8],[7]] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2

[[1,3,6,7],[2,4,8],[5]] => [[1,2,5],[3,4],[6,8],[7]] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[[1,2,6,7],[3,4,8],[5]] => [[1,3,5],[2,4],[6,8],[7]] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,3,5,7],[2,6,8],[4]] => [[1,2,4],[3,6],[5,8],[7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5,7],[3,6,8],[4]] => [[1,3,4],[2,6],[5,8],[7]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4,7],[2,6,8],[5]] => [[1,2,5],[3,6],[4,8],[7]] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[[1,2,4,7],[3,6,8],[5]] => [[1,3,5],[2,6],[4,8],[7]] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,2,3,7],[4,6,8],[5]] => [[1,4,5],[2,6],[3,8],[7]] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[[1,3,5,7],[2,4,8],[6]] => [[1,2,6],[3,4],[5,8],[7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5,7],[3,4,8],[6]] => [[1,3,6],[2,4],[5,8],[7]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4,7],[2,5,8],[6]] => [[1,2,6],[3,5],[4,8],[7]] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[[1,2,4,7],[3,5,8],[6]] => [[1,3,6],[2,5],[4,8],[7]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,2,3,7],[4,5,8],[6]] => [[1,4,6],[2,5],[3,8],[7]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,5,6],[2,7,8],[4]] => [[1,2,4],[3,7],[5,8],[6]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,5,6],[3,7,8],[4]] => [[1,3,4],[2,7],[5,8],[6]] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,4,6],[2,7,8],[5]] => [[1,2,5],[3,7],[4,8],[6]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4,6],[3,7,8],[5]] => [[1,3,5],[2,7],[4,8],[6]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,6],[4,7,8],[5]] => [[1,4,5],[2,7],[3,8],[6]] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[[1,3,4,5],[2,7,8],[6]] => [[1,2,6],[3,7],[4,8],[5]] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[[1,2,4,5],[3,7,8],[6]] => [[1,3,6],[2,7],[4,8],[5]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,5],[4,7,8],[6]] => [[1,4,6],[2,7],[3,8],[5]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,4],[5,7,8],[6]] => [[1,5,6],[2,7],[3,8],[4]] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,3,5,6],[2,4,8],[7]] => [[1,2,7],[3,4],[5,8],[6]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,5,6],[3,4,8],[7]] => [[1,3,7],[2,4],[5,8],[6]] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[[1,3,4,6],[2,5,8],[7]] => [[1,2,7],[3,5],[4,8],[6]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4,6],[3,5,8],[7]] => [[1,3,7],[2,5],[4,8],[6]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,6],[4,5,8],[7]] => [[1,4,7],[2,5],[3,8],[6]] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,4,5],[2,6,8],[7]] => [[1,2,7],[3,6],[4,8],[5]] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3

[[1,2,4,5],[3,6,8],[7]] => [[1,3,7],[2,6],[4,8],[5]] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[[1,2,3,5],[4,6,8],[7]] => [[1,4,7],[2,6],[3,8],[5]] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[[1,2,3,4],[5,6,8],[7]] => [[1,5,7],[2,6],[3,8],[4]] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,3,5,7],[2,4,6],[8]] => [[1,2,8],[3,4],[5,6],[7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5,7],[3,4,6],[8]] => [[1,3,8],[2,4],[5,6],[7]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4,7],[2,5,6],[8]] => [[1,2,8],[3,5],[4,6],[7]] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[[1,2,4,7],[3,5,6],[8]] => [[1,3,8],[2,5],[4,6],[7]] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,2,3,7],[4,5,6],[8]] => [[1,4,8],[2,5],[3,6],[7]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,5,6],[2,4,7],[8]] => [[1,2,8],[3,4],[5,7],[6]] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[[1,2,5,6],[3,4,7],[8]] => [[1,3,8],[2,4],[5,7],[6]] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[[1,3,4,6],[2,5,7],[8]] => [[1,2,8],[3,5],[4,7],[6]] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[[1,2,4,6],[3,5,7],[8]] => [[1,3,8],[2,5],[4,7],[6]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,2,3,6],[4,5,7],[8]] => [[1,4,8],[2,5],[3,7],[6]] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[[1,3,4,5],[2,6,7],[8]] => [[1,2,8],[3,6],[4,7],[5]] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[[1,2,4,5],[3,6,7],[8]] => [[1,3,8],[2,6],[4,7],[5]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,5],[4,6,7],[8]] => [[1,4,8],[2,6],[3,7],[5]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,4],[5,6,7],[8]] => [[1,5,8],[2,6],[3,7],[4]] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,3,7,8],[2,5],[4,6]] => [[1,2,4],[3,5,6],[7],[8]] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[[1,2,7,8],[3,5],[4,6]] => [[1,3,4],[2,5,6],[7],[8]] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2

[[1,3,7,8],[2,4],[5,6]] => [[1,2,5],[3,4,6],[7],[8]] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3

[[1,2,7,8],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7],[8]] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2

[[1,3,6,8],[2,5],[4,7]] => [[1,2,4],[3,5,7],[6],[8]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,6,8],[3,5],[4,7]] => [[1,3,4],[2,5,7],[6],[8]] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,6,8],[2,4],[5,7]] => [[1,2,5],[3,4,7],[6],[8]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2,6,8],[3,4],[5,7]] => [[1,3,5],[2,4,7],[6],[8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,3,5,8],[2,6],[4,7]] => [[1,2,4],[3,6,7],[5],[8]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2,5,8],[3,6],[4,7]] => [[1,3,4],[2,6,7],[5],[8]] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3,4,8],[2,6],[5,7]] => [[1,2,5],[3,6,7],[4],[8]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4,8],[3,6],[5,7]] => [[1,3,5],[2,6,7],[4],[8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,8],[4,6],[5,7]] => [[1,4,5],[2,6,7],[3],[8]] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[[1,3,5,8],[2,4],[6,7]] => [[1,2,6],[3,4,7],[5],[8]] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[[1,2,5,8],[3,4],[6,7]] => [[1,3,6],[2,4,7],[5],[8]] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2

[[1,3,4,8],[2,5],[6,7]] => [[1,2,6],[3,5,7],[4],[8]] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[[1,2,4,8],[3,5],[6,7]] => [[1,3,6],[2,5,7],[4],[8]] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2

[[1,2,3,8],[4,5],[6,7]] => [[1,4,6],[2,5,7],[3],[8]] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[[1,3,6,7],[2,5],[4,8]] => [[1,2,4],[3,5,8],[6],[7]] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[[1,2,6,7],[3,5],[4,8]] => [[1,3,4],[2,5,8],[6],[7]] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2

[[1,3,6,7],[2,4],[5,8]] => [[1,2,5],[3,4,8],[6],[7]] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[[1,2,6,7],[3,4],[5,8]] => [[1,3,5],[2,4,8],[6],[7]] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,3,5,7],[2,6],[4,8]] => [[1,2,4],[3,6,8],[5],[7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5,7],[3,6],[4,8]] => [[1,3,4],[2,6,8],[5],[7]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4,7],[2,6],[5,8]] => [[1,2,5],[3,6,8],[4],[7]] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[[1,2,4,7],[3,6],[5,8]] => [[1,3,5],[2,6,8],[4],[7]] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,2,3,7],[4,6],[5,8]] => [[1,4,5],[2,6,8],[3],[7]] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[[1,3,5,7],[2,4],[6,8]] => [[1,2,6],[3,4,8],[5],[7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5,7],[3,4],[6,8]] => [[1,3,6],[2,4,8],[5],[7]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4,7],[2,5],[6,8]] => [[1,2,6],[3,5,8],[4],[7]] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[[1,2,4,7],[3,5],[6,8]] => [[1,3,6],[2,5,8],[4],[7]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,2,3,7],[4,5],[6,8]] => [[1,4,6],[2,5,8],[3],[7]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,5,6],[2,7],[4,8]] => [[1,2,4],[3,7,8],[5],[6]] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[[1,2,5,6],[3,7],[4,8]] => [[1,3,4],[2,7,8],[5],[6]] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[[1,3,4,6],[2,7],[5,8]] => [[1,2,5],[3,7,8],[4],[6]] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[[1,2,4,6],[3,7],[5,8]] => [[1,3,5],[2,7,8],[4],[6]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,2,3,6],[4,7],[5,8]] => [[1,4,5],[2,7,8],[3],[6]] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[[1,3,4,5],[2,7],[6,8]] => [[1,2,6],[3,7,8],[4],[5]] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[[1,2,4,5],[3,7],[6,8]] => [[1,3,6],[2,7,8],[4],[5]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,5],[4,7],[6,8]] => [[1,4,6],[2,7,8],[3],[5]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,4],[5,7],[6,8]] => [[1,5,6],[2,7,8],[3],[4]] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,3,5,6],[2,4],[7,8]] => [[1,2,7],[3,4,8],[5],[6]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,5,6],[3,4],[7,8]] => [[1,3,7],[2,4,8],[5],[6]] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[[1,3,4,6],[2,5],[7,8]] => [[1,2,7],[3,5,8],[4],[6]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4,6],[3,5],[7,8]] => [[1,3,7],[2,5,8],[4],[6]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,6],[4,5],[7,8]] => [[1,4,7],[2,5,8],[3],[6]] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,4,5],[2,6],[7,8]] => [[1,2,7],[3,6,8],[4],[5]] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3

[[1,2,4,5],[3,6],[7,8]] => [[1,3,7],[2,6,8],[4],[5]] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[[1,2,3,5],[4,6],[7,8]] => [[1,4,7],[2,6,8],[3],[5]] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[[1,2,3,4],[5,6],[7,8]] => [[1,5,7],[2,6,8],[3],[4]] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,3,7,8],[2,6],[4],[5]] => [[1,2,4,5],[3,6],[7],[8]] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3

[[1,2,7,8],[3,6],[4],[5]] => [[1,3,4,5],[2,6],[7],[8]] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2

[[1,3,7,8],[2,5],[4],[6]] => [[1,2,4,6],[3,5],[7],[8]] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[[1,2,7,8],[3,5],[4],[6]] => [[1,3,4,6],[2,5],[7],[8]] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2

[[1,3,7,8],[2,4],[5],[6]] => [[1,2,5,6],[3,4],[7],[8]] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[[1,2,7,8],[3,4],[5],[6]] => [[1,3,5,6],[2,4],[7],[8]] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2

[[1,3,6,8],[2,7],[4],[5]] => [[1,2,4,5],[3,7],[6],[8]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2,6,8],[3,7],[4],[5]] => [[1,3,4,5],[2,7],[6],[8]] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[[1,3,5,8],[2,7],[4],[6]] => [[1,2,4,6],[3,7],[5],[8]] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[[1,2,5,8],[3,7],[4],[6]] => [[1,3,4,6],[2,7],[5],[8]] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2

[[1,3,4,8],[2,7],[5],[6]] => [[1,2,5,6],[3,7],[4],[8]] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[[1,2,4,8],[3,7],[5],[6]] => [[1,3,5,6],[2,7],[4],[8]] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2

[[1,2,3,8],[4,7],[5],[6]] => [[1,4,5,6],[2,7],[3],[8]] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2

[[1,3,6,8],[2,5],[4],[7]] => [[1,2,4,7],[3,5],[6],[8]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,6,8],[3,5],[4],[7]] => [[1,3,4,7],[2,5],[6],[8]] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,6,8],[2,4],[5],[7]] => [[1,2,5,7],[3,4],[6],[8]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2,6,8],[3,4],[5],[7]] => [[1,3,5,7],[2,4],[6],[8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,3,5,8],[2,6],[4],[7]] => [[1,2,4,7],[3,6],[5],[8]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2,5,8],[3,6],[4],[7]] => [[1,3,4,7],[2,6],[5],[8]] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3,4,8],[2,6],[5],[7]] => [[1,2,5,7],[3,6],[4],[8]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4,8],[3,6],[5],[7]] => [[1,3,5,7],[2,6],[4],[8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,8],[4,6],[5],[7]] => [[1,4,5,7],[2,6],[3],[8]] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[[1,3,5,8],[2,4],[6],[7]] => [[1,2,6,7],[3,4],[5],[8]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2,5,8],[3,4],[6],[7]] => [[1,3,6,7],[2,4],[5],[8]] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[[1,3,4,8],[2,5],[6],[7]] => [[1,2,6,7],[3,5],[4],[8]] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[[1,2,4,8],[3,5],[6],[7]] => [[1,3,6,7],[2,5],[4],[8]] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[[1,2,3,8],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3],[8]] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3,6,7],[2,8],[4],[5]] => [[1,2,4,5],[3,8],[6],[7]] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[[1,2,6,7],[3,8],[4],[5]] => [[1,3,4,5],[2,8],[6],[7]] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2

[[1,3,5,7],[2,8],[4],[6]] => [[1,2,4,6],[3,8],[5],[7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5,7],[3,8],[4],[6]] => [[1,3,4,6],[2,8],[5],[7]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4,7],[2,8],[5],[6]] => [[1,2,5,6],[3,8],[4],[7]] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[[1,2,4,7],[3,8],[5],[6]] => [[1,3,5,6],[2,8],[4],[7]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,2,3,7],[4,8],[5],[6]] => [[1,4,5,6],[2,8],[3],[7]] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[[1,3,5,6],[2,8],[4],[7]] => [[1,2,4,7],[3,8],[5],[6]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,5,6],[3,8],[4],[7]] => [[1,3,4,7],[2,8],[5],[6]] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,4,6],[2,8],[5],[7]] => [[1,2,5,7],[3,8],[4],[6]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4,6],[3,8],[5],[7]] => [[1,3,5,7],[2,8],[4],[6]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3,6],[4,8],[5],[7]] => [[1,4,5,7],[2,8],[3],[6]] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[[1,3,4,5],[2,8],[6],[7]] => [[1,2,6,7],[3,8],[4],[5]] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3

[[1,2,4,5],[3,8],[6],[7]] => [[1,3,6,7],[2,8],[4],[5]] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[[1,2,3,5],[4,8],[6],[7]] => [[1,4,6,7],[2,8],[3],[5]] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[[1,2,3,4],[5,8],[6],[7]] => [[1,5,6,7],[2,8],[3],[4]] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[[1,3,6,7],[2,5],[4],[8]] => [[1,2,4,8],[3,5],[6],[7]] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[[1,2,6,7],[3,5],[4],[8]] => [[1,3,4,8],[2,5],[6],[7]] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2

[[1,3,6,7],[2,4],[5],[8]] => [[1,2,5,8],[3,4],[6],[7]] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[[1,2,6,7],[3,4],[5],[8]] => [[1,3,5,8],[2,4],[6],[7]] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,3,5,7],[2,6],[4],[8]] => [[1,2,4,8],[3,6],[5],[7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5,7],[3,6],[4],[8]] => [[1,3,4,8],[2,6],[5],[7]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4,7],[2,6],[5],[8]] => [[1,2,5,8],[3,6],[4],[7]] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[[1,2,4,7],[3,6],[5],[8]] => [[1,3,5,8],[2,6],[4],[7]] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,2,3,7],[4,6],[5],[8]] => [[1,4,5,8],[2,6],[3],[7]] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[[1,3,5,7],[2,4],[6],[8]] => [[1,2,6,8],[3,4],[5],[7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5,7],[3,4],[6],[8]] => [[1,3,6,8],[2,4],[5],[7]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4,7],[2,5],[6],[8]] => [[1,2,6,8],[3,5],[4],[7]] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[[1,2,4,7],[3,5],[6],[8]] => [[1,3,6,8],[2,5],[4],[7]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,2,3,7],[4,5],[6],[8]] => [[1,4,6,8],[2,5],[3],[7]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,5,6],[2,7],[4],[8]] => [[1,2,4,8],[3,7],[5],[6]] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[[1,2,5,6],[3,7],[4],[8]] => [[1,3,4,8],[2,7],[5],[6]] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[[1,3,4,6],[2,7],[5],[8]] => [[1,2,5,8],[3,7],[4],[6]] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[[1,2,4,6],[3,7],[5],[8]] => [[1,3,5,8],[2,7],[4],[6]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,2,3,6],[4,7],[5],[8]] => [[1,4,5,8],[2,7],[3],[6]] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[[1,3,4,5],[2,7],[6],[8]] => [[1,2,6,8],[3,7],[4],[5]] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[[1,2,4,5],[3,7],[6],[8]] => [[1,3,6,8],[2,7],[4],[5]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,5],[4,7],[6],[8]] => [[1,4,6,8],[2,7],[3],[5]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,4],[5,7],[6],[8]] => [[1,5,6,8],[2,7],[3],[4]] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,3,5,6],[2,4],[7],[8]] => [[1,2,7,8],[3,4],[5],[6]] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[[1,2,5,6],[3,4],[7],[8]] => [[1,3,7,8],[2,4],[5],[6]] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[[1,3,4,6],[2,5],[7],[8]] => [[1,2,7,8],[3,5],[4],[6]] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[[1,2,4,6],[3,5],[7],[8]] => [[1,3,7,8],[2,5],[4],[6]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,2,3,6],[4,5],[7],[8]] => [[1,4,7,8],[2,5],[3],[6]] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[[1,3,4,5],[2,6],[7],[8]] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[[1,2,4,5],[3,6],[7],[8]] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[[1,2,3,5],[4,6],[7],[8]] => [[1,4,7,8],[2,6],[3],[5]] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,3,7,8],[2],[4],[5],[6]] => [[1,2,4,5,6],[3],[7],[8]] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[[1,2,7,8],[3],[4],[5],[6]] => [[1,3,4,5,6],[2],[7],[8]] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2

[[1,3,6,8],[2],[4],[5],[7]] => [[1,2,4,5,7],[3],[6],[8]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2,6,8],[3],[4],[5],[7]] => [[1,3,4,5,7],[2],[6],[8]] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[[1,3,5,8],[2],[4],[6],[7]] => [[1,2,4,6,7],[3],[5],[8]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2,5,8],[3],[4],[6],[7]] => [[1,3,4,6,7],[2],[5],[8]] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3,4,8],[2],[5],[6],[7]] => [[1,2,5,6,7],[3],[4],[8]] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[[1,2,4,8],[3],[5],[6],[7]] => [[1,3,5,6,7],[2],[4],[8]] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[[1,2,3,8],[4],[5],[6],[7]] => [[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[[1,3,6,7],[2],[4],[5],[8]] => [[1,2,4,5,8],[3],[6],[7]] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[[1,2,6,7],[3],[4],[5],[8]] => [[1,3,4,5,8],[2],[6],[7]] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2

[[1,3,5,7],[2],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5,7],[3],[4],[6],[8]] => [[1,3,4,6,8],[2],[5],[7]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4,7],[2],[5],[6],[8]] => [[1,2,5,6,8],[3],[4],[7]] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[[1,2,4,7],[3],[5],[6],[8]] => [[1,3,5,6,8],[2],[4],[7]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,2,3,7],[4],[5],[6],[8]] => [[1,4,5,6,8],[2],[3],[7]] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[[1,3,5,6],[2],[4],[7],[8]] => [[1,2,4,7,8],[3],[5],[6]] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[[1,2,5,6],[3],[4],[7],[8]] => [[1,3,4,7,8],[2],[5],[6]] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[[1,3,4,6],[2],[5],[7],[8]] => [[1,2,5,7,8],[3],[4],[6]] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[[1,2,4,6],[3],[5],[7],[8]] => [[1,3,5,7,8],[2],[4],[6]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,2,3,6],[4],[5],[7],[8]] => [[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[[1,3,4,5],[2],[6],[7],[8]] => [[1,2,6,7,8],[3],[4],[5]] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[[1,2,4,5],[3],[6],[7],[8]] => [[1,3,6,7,8],[2],[4],[5]] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[[1,2,3,5],[4],[6],[7],[8]] => [[1,4,6,7,8],[2],[3],[5]] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[[1,2,3,4],[5],[6],[7],[8]] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[[1,3,7],[2,5,8],[4,6]] => [[1,2,4],[3,5,6],[7,8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,7],[3,5,8],[4,6]] => [[1,3,4],[2,5,6],[7,8]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,7],[2,4,8],[5,6]] => [[1,2,5],[3,4,6],[7,8]] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[[1,2,7],[3,4,8],[5,6]] => [[1,3,5],[2,4,6],[7,8]] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,3,6],[2,5,8],[4,7]] => [[1,2,4],[3,5,7],[6,8]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,6],[3,5,8],[4,7]] => [[1,3,4],[2,5,7],[6,8]] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,6],[2,4,8],[5,7]] => [[1,2,5],[3,4,7],[6,8]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2,6],[3,4,8],[5,7]] => [[1,3,5],[2,4,7],[6,8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,3,5],[2,6,8],[4,7]] => [[1,2,4],[3,6,7],[5,8]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2,5],[3,6,8],[4,7]] => [[1,3,4],[2,6,7],[5,8]] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3,4],[2,6,8],[5,7]] => [[1,2,5],[3,6,7],[4,8]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4],[3,6,8],[5,7]] => [[1,3,5],[2,6,7],[4,8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3],[4,6,8],[5,7]] => [[1,4,5],[2,6,7],[3,8]] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[[1,3,5],[2,4,8],[6,7]] => [[1,2,6],[3,4,7],[5,8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5],[3,4,8],[6,7]] => [[1,3,6],[2,4,7],[5,8]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4],[2,5,8],[6,7]] => [[1,2,6],[3,5,7],[4,8]] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[[1,2,4],[3,5,8],[6,7]] => [[1,3,6],[2,5,7],[4,8]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,2,3],[4,5,8],[6,7]] => [[1,4,6],[2,5,7],[3,8]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,6],[2,5,7],[4,8]] => [[1,2,4],[3,5,8],[6,7]] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[[1,2,6],[3,5,7],[4,8]] => [[1,3,4],[2,5,8],[6,7]] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[[1,3,6],[2,4,7],[5,8]] => [[1,2,5],[3,4,8],[6,7]] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3

[[1,2,6],[3,4,7],[5,8]] => [[1,3,5],[2,4,8],[6,7]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,3,5],[2,6,7],[4,8]] => [[1,2,4],[3,6,8],[5,7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5],[3,6,7],[4,8]] => [[1,3,4],[2,6,8],[5,7]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4],[2,6,7],[5,8]] => [[1,2,5],[3,6,8],[4,7]] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[[1,2,4],[3,6,7],[5,8]] => [[1,3,5],[2,6,8],[4,7]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,2,3],[4,6,7],[5,8]] => [[1,4,5],[2,6,8],[3,7]] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[[1,3,5],[2,4,7],[6,8]] => [[1,2,6],[3,4,8],[5,7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5],[3,4,7],[6,8]] => [[1,3,6],[2,4,8],[5,7]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4],[2,5,7],[6,8]] => [[1,2,6],[3,5,8],[4,7]] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[[1,2,4],[3,5,7],[6,8]] => [[1,3,6],[2,5,8],[4,7]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,2,3],[4,5,7],[6,8]] => [[1,4,6],[2,5,8],[3,7]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,5],[2,4,6],[7,8]] => [[1,2,7],[3,4,8],[5,6]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2,5],[3,4,6],[7,8]] => [[1,3,7],[2,4,8],[5,6]] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[[1,3,4],[2,5,6],[7,8]] => [[1,2,7],[3,5,8],[4,6]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4],[3,5,6],[7,8]] => [[1,3,7],[2,5,8],[4,6]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3],[4,5,6],[7,8]] => [[1,4,7],[2,5,8],[3,6]] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[[1,5,7],[2,6,8],[3],[4]] => [[1,2,3,4],[5,6],[7,8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5

[[1,3,7],[2,6,8],[4],[5]] => [[1,2,4,5],[3,6],[7,8]] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[[1,2,7],[3,6,8],[4],[5]] => [[1,3,4,5],[2,6],[7,8]] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2

[[1,3,7],[2,5,8],[4],[6]] => [[1,2,4,6],[3,5],[7,8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,7],[3,5,8],[4],[6]] => [[1,3,4,6],[2,5],[7,8]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,7],[2,4,8],[5],[6]] => [[1,2,5,6],[3,4],[7,8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3

[[1,2,7],[3,4,8],[5],[6]] => [[1,3,5,6],[2,4],[7,8]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,3,6],[2,7,8],[4],[5]] => [[1,2,4,5],[3,7],[6,8]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2,6],[3,7,8],[4],[5]] => [[1,3,4,5],[2,7],[6,8]] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[[1,3,5],[2,7,8],[4],[6]] => [[1,2,4,6],[3,7],[5,8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5],[3,7,8],[4],[6]] => [[1,3,4,6],[2,7],[5,8]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4],[2,7,8],[5],[6]] => [[1,2,5,6],[3,7],[4,8]] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[[1,2,4],[3,7,8],[5],[6]] => [[1,3,5,6],[2,7],[4,8]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,2,3],[4,7,8],[5],[6]] => [[1,4,5,6],[2,7],[3,8]] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[[1,3,6],[2,5,8],[4],[7]] => [[1,2,4,7],[3,5],[6,8]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,6],[3,5,8],[4],[7]] => [[1,3,4,7],[2,5],[6,8]] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,6],[2,4,8],[5],[7]] => [[1,2,5,7],[3,4],[6,8]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2,6],[3,4,8],[5],[7]] => [[1,3,5,7],[2,4],[6,8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,3,5],[2,6,8],[4],[7]] => [[1,2,4,7],[3,6],[5,8]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2,5],[3,6,8],[4],[7]] => [[1,3,4,7],[2,6],[5,8]] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3,4],[2,6,8],[5],[7]] => [[1,2,5,7],[3,6],[4,8]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4],[3,6,8],[5],[7]] => [[1,3,5,7],[2,6],[4,8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3],[4,6,8],[5],[7]] => [[1,4,5,7],[2,6],[3,8]] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[[1,3,5],[2,4,8],[6],[7]] => [[1,2,6,7],[3,4],[5,8]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2,5],[3,4,8],[6],[7]] => [[1,3,6,7],[2,4],[5,8]] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[[1,3,4],[2,5,8],[6],[7]] => [[1,2,6,7],[3,5],[4,8]] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[[1,2,4],[3,5,8],[6],[7]] => [[1,3,6,7],[2,5],[4,8]] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[[1,2,3],[4,5,8],[6],[7]] => [[1,4,6,7],[2,5],[3,8]] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3,6],[2,5,7],[4],[8]] => [[1,2,4,8],[3,5],[6,7]] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[[1,2,6],[3,5,7],[4],[8]] => [[1,3,4,8],[2,5],[6,7]] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[[1,3,6],[2,4,7],[5],[8]] => [[1,2,5,8],[3,4],[6,7]] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3

[[1,2,6],[3,4,7],[5],[8]] => [[1,3,5,8],[2,4],[6,7]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,3,5],[2,6,7],[4],[8]] => [[1,2,4,8],[3,6],[5,7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5],[3,6,7],[4],[8]] => [[1,3,4,8],[2,6],[5,7]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4],[2,6,7],[5],[8]] => [[1,2,5,8],[3,6],[4,7]] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[[1,2,4],[3,6,7],[5],[8]] => [[1,3,5,8],[2,6],[4,7]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,2,3],[4,6,7],[5],[8]] => [[1,4,5,8],[2,6],[3,7]] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[[1,3,5],[2,4,7],[6],[8]] => [[1,2,6,8],[3,4],[5,7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5],[3,4,7],[6],[8]] => [[1,3,6,8],[2,4],[5,7]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4],[2,5,7],[6],[8]] => [[1,2,6,8],[3,5],[4,7]] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[[1,2,4],[3,5,7],[6],[8]] => [[1,3,6,8],[2,5],[4,7]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,2,3],[4,5,7],[6],[8]] => [[1,4,6,8],[2,5],[3,7]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,5],[2,4,6],[7],[8]] => [[1,2,7,8],[3,4],[5,6]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3

[[1,2,5],[3,4,6],[7],[8]] => [[1,3,7,8],[2,4],[5,6]] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[[1,3,4],[2,5,6],[7],[8]] => [[1,2,7,8],[3,5],[4,6]] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[[1,2,4],[3,5,6],[7],[8]] => [[1,3,7,8],[2,5],[4,6]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,2,3],[4,5,6],[7],[8]] => [[1,4,7,8],[2,5],[3,6]] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[[1,3,8],[2,6],[4,7],[5]] => [[1,2,4,5],[3,6,7],[8]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2,8],[3,6],[4,7],[5]] => [[1,3,4,5],[2,6,7],[8]] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[[1,3,8],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7],[8]] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[[1,2,8],[3,5],[4,7],[6]] => [[1,3,4,6],[2,5,7],[8]] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2

[[1,3,8],[2,4],[5,7],[6]] => [[1,2,5,6],[3,4,7],[8]] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[[1,2,8],[3,4],[5,7],[6]] => [[1,3,5,6],[2,4,7],[8]] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2

[[1,4,8],[2,5],[3,6],[7]] => [[1,2,3,7],[4,5,6],[8]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4

[[1,3,8],[2,5],[4,6],[7]] => [[1,2,4,7],[3,5,6],[8]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2,8],[3,5],[4,6],[7]] => [[1,3,4,7],[2,5,6],[8]] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3,8],[2,4],[5,6],[7]] => [[1,2,5,7],[3,4,6],[8]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2,8],[3,4],[5,6],[7]] => [[1,3,5,7],[2,4,6],[8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,5,7],[2,6],[3,8],[4]] => [[1,2,3,4],[5,6,8],[7]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5

[[1,3,7],[2,6],[4,8],[5]] => [[1,2,4,5],[3,6,8],[7]] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[[1,2,7],[3,6],[4,8],[5]] => [[1,3,4,5],[2,6,8],[7]] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2

[[1,3,7],[2,5],[4,8],[6]] => [[1,2,4,6],[3,5,8],[7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,7],[3,5],[4,8],[6]] => [[1,3,4,6],[2,5,8],[7]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,7],[2,4],[5,8],[6]] => [[1,2,5,6],[3,4,8],[7]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3

[[1,2,7],[3,4],[5,8],[6]] => [[1,3,5,6],[2,4,8],[7]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,3,6],[2,7],[4,8],[5]] => [[1,2,4,5],[3,7,8],[6]] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3

[[1,2,6],[3,7],[4,8],[5]] => [[1,3,4,5],[2,7,8],[6]] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2

[[1,3,5],[2,7],[4,8],[6]] => [[1,2,4,6],[3,7,8],[5]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5],[3,7],[4,8],[6]] => [[1,3,4,6],[2,7,8],[5]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4],[2,7],[5,8],[6]] => [[1,2,5,6],[3,7,8],[4]] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[[1,2,4],[3,7],[5,8],[6]] => [[1,3,5,6],[2,7,8],[4]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,2,3],[4,7],[5,8],[6]] => [[1,4,5,6],[2,7,8],[3]] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[[1,3,6],[2,5],[4,8],[7]] => [[1,2,4,7],[3,5,8],[6]] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[[1,2,6],[3,5],[4,8],[7]] => [[1,3,4,7],[2,5,8],[6]] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[[1,3,6],[2,4],[5,8],[7]] => [[1,2,5,7],[3,4,8],[6]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2,6],[3,4],[5,8],[7]] => [[1,3,5,7],[2,4,8],[6]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,3,5],[2,6],[4,8],[7]] => [[1,2,4,7],[3,6,8],[5]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2,5],[3,6],[4,8],[7]] => [[1,3,4,7],[2,6,8],[5]] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3,4],[2,6],[5,8],[7]] => [[1,2,5,7],[3,6,8],[4]] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[[1,2,4],[3,6],[5,8],[7]] => [[1,3,5,7],[2,6,8],[4]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,2,3],[4,6],[5,8],[7]] => [[1,4,5,7],[2,6,8],[3]] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[[1,3,5],[2,4],[6,8],[7]] => [[1,2,6,7],[3,4,8],[5]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2,5],[3,4],[6,8],[7]] => [[1,3,6,7],[2,4,8],[5]] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[[1,3,4],[2,5],[6,8],[7]] => [[1,2,6,7],[3,5,8],[4]] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[[1,2,4],[3,5],[6,8],[7]] => [[1,3,6,7],[2,5,8],[4]] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[[1,2,3],[4,5],[6,8],[7]] => [[1,4,6,7],[2,5,8],[3]] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3,7],[2,5],[4,6],[8]] => [[1,2,4,8],[3,5,6],[7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,7],[3,5],[4,6],[8]] => [[1,3,4,8],[2,5,6],[7]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,7],[2,4],[5,6],[8]] => [[1,2,5,8],[3,4,6],[7]] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[[1,2,7],[3,4],[5,6],[8]] => [[1,3,5,8],[2,4,6],[7]] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[[1,3,6],[2,5],[4,7],[8]] => [[1,2,4,8],[3,5,7],[6]] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[[1,2,6],[3,5],[4,7],[8]] => [[1,3,4,8],[2,5,7],[6]] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[[1,3,6],[2,4],[5,7],[8]] => [[1,2,5,8],[3,4,7],[6]] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3

[[1,2,6],[3,4],[5,7],[8]] => [[1,3,5,8],[2,4,7],[6]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,3,5],[2,6],[4,7],[8]] => [[1,2,4,8],[3,6,7],[5]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3

[[1,2,5],[3,6],[4,7],[8]] => [[1,3,4,8],[2,6,7],[5]] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2

[[1,3,4],[2,6],[5,7],[8]] => [[1,2,5,8],[3,6,7],[4]] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[[1,2,4],[3,6],[5,7],[8]] => [[1,3,5,8],[2,6,7],[4]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,2,3],[4,6],[5,7],[8]] => [[1,4,5,8],[2,6,7],[3]] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[[1,3,5],[2,4],[6,7],[8]] => [[1,2,6,8],[3,4,7],[5]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5],[3,4],[6,7],[8]] => [[1,3,6,8],[2,4,7],[5]] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4],[2,5],[6,7],[8]] => [[1,2,6,8],[3,5,7],[4]] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[[1,2,4],[3,5],[6,7],[8]] => [[1,3,6,8],[2,5,7],[4]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,2,3],[4,5],[6,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,8],[2,7],[4],[5],[6]] => [[1,2,4,5,6],[3,7],[8]] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[[1,2,8],[3,7],[4],[5],[6]] => [[1,3,4,5,6],[2,7],[8]] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2

[[1,3,8],[2,6],[4],[5],[7]] => [[1,2,4,5,7],[3,6],[8]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2,8],[3,6],[4],[5],[7]] => [[1,3,4,5,7],[2,6],[8]] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[[1,4,8],[2,5],[3],[6],[7]] => [[1,2,3,6,7],[4,5],[8]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4

[[1,3,8],[2,5],[4],[6],[7]] => [[1,2,4,6,7],[3,5],[8]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2,8],[3,5],[4],[6],[7]] => [[1,3,4,6,7],[2,5],[8]] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3,8],[2,4],[5],[6],[7]] => [[1,2,5,6,7],[3,4],[8]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[[1,2,8],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4],[8]] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[[1,5,7],[2,8],[3],[4],[6]] => [[1,2,3,4,6],[5,8],[7]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5

[[1,3,7],[2,8],[4],[5],[6]] => [[1,2,4,5,6],[3,8],[7]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3

[[1,2,7],[3,8],[4],[5],[6]] => [[1,3,4,5,6],[2,8],[7]] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2

[[1,3,6],[2,8],[4],[5],[7]] => [[1,2,4,5,7],[3,8],[6]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2,6],[3,8],[4],[5],[7]] => [[1,3,4,5,7],[2,8],[6]] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[[1,3,5],[2,8],[4],[6],[7]] => [[1,2,4,6,7],[3,8],[5]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2,5],[3,8],[4],[6],[7]] => [[1,3,4,6,7],[2,8],[5]] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3,4],[2,8],[5],[6],[7]] => [[1,2,5,6,7],[3,8],[4]] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[[1,2,4],[3,8],[5],[6],[7]] => [[1,3,5,6,7],[2,8],[4]] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[[1,2,3],[4,8],[5],[6],[7]] => [[1,4,5,6,7],[2,8],[3]] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[[1,5,7],[2,6],[3],[4],[8]] => [[1,2,3,4,8],[5,6],[7]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5

[[1,3,7],[2,6],[4],[5],[8]] => [[1,2,4,5,8],[3,6],[7]] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[[1,2,7],[3,6],[4],[5],[8]] => [[1,3,4,5,8],[2,6],[7]] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2

[[1,3,7],[2,5],[4],[6],[8]] => [[1,2,4,6,8],[3,5],[7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,7],[3,5],[4],[6],[8]] => [[1,3,4,6,8],[2,5],[7]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,7],[2,4],[5],[6],[8]] => [[1,2,5,6,8],[3,4],[7]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3

[[1,2,7],[3,4],[5],[6],[8]] => [[1,3,5,6,8],[2,4],[7]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,3,6],[2,7],[4],[5],[8]] => [[1,2,4,5,8],[3,7],[6]] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3

[[1,2,6],[3,7],[4],[5],[8]] => [[1,3,4,5,8],[2,7],[6]] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2

[[1,3,5],[2,7],[4],[6],[8]] => [[1,2,4,6,8],[3,7],[5]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2,5],[3,7],[4],[6],[8]] => [[1,3,4,6,8],[2,7],[5]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3,4],[2,7],[5],[6],[8]] => [[1,2,5,6,8],[3,7],[4]] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[[1,2,4],[3,7],[5],[6],[8]] => [[1,3,5,6,8],[2,7],[4]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,2,3],[4,7],[5],[6],[8]] => [[1,4,5,6,8],[2,7],[3]] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[[1,3,6],[2,5],[4],[7],[8]] => [[1,2,4,7,8],[3,5],[6]] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[[1,2,6],[3,5],[4],[7],[8]] => [[1,3,4,7,8],[2,5],[6]] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[[1,3,6],[2,4],[5],[7],[8]] => [[1,2,5,7,8],[3,4],[6]] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3

[[1,2,6],[3,4],[5],[7],[8]] => [[1,3,5,7,8],[2,4],[6]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,3,5],[2,6],[4],[7],[8]] => [[1,2,4,7,8],[3,6],[5]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3

[[1,2,5],[3,6],[4],[7],[8]] => [[1,3,4,7,8],[2,6],[5]] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2

[[1,3,4],[2,6],[5],[7],[8]] => [[1,2,5,7,8],[3,6],[4]] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[[1,2,4],[3,6],[5],[7],[8]] => [[1,3,5,7,8],[2,6],[4]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,2,3],[4,6],[5],[7],[8]] => [[1,4,5,7,8],[2,6],[3]] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[[1,3,5],[2,4],[6],[7],[8]] => [[1,2,6,7,8],[3,4],[5]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3

[[1,2,5],[3,4],[6],[7],[8]] => [[1,3,6,7,8],[2,4],[5]] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[[1,3,4],[2,5],[6],[7],[8]] => [[1,2,6,7,8],[3,5],[4]] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[[1,2,4],[3,5],[6],[7],[8]] => [[1,3,6,7,8],[2,5],[4]] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2

[[1,2,3],[4,5],[6],[7],[8]] => [[1,4,6,7,8],[2,5],[3]] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[[1,4,8],[2],[3],[5],[6],[7]] => [[1,2,3,5,6,7],[4],[8]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4

[[1,3,8],[2],[4],[5],[6],[7]] => [[1,2,4,5,6,7],[3],[8]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[[1,2,8],[3],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2],[8]] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[[1,5,7],[2],[3],[4],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5

[[1,3,7],[2],[4],[5],[6],[8]] => [[1,2,4,5,6,8],[3],[7]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3

[[1,2,7],[3],[4],[5],[6],[8]] => [[1,3,4,5,6,8],[2],[7]] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2

[[1,3,6],[2],[4],[5],[7],[8]] => [[1,2,4,5,7,8],[3],[6]] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3

[[1,2,6],[3],[4],[5],[7],[8]] => [[1,3,4,5,7,8],[2],[6]] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2

[[1,3,5],[2],[4],[6],[7],[8]] => [[1,2,4,6,7,8],[3],[5]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3

[[1,2,5],[3],[4],[6],[7],[8]] => [[1,3,4,6,7,8],[2],[5]] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2

[[1,3,4],[2],[5],[6],[7],[8]] => [[1,2,5,6,7,8],[3],[4]] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[[1,2,4],[3],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2],[4]] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2

[[1,2,3],[4],[5],[6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[[1,5],[2,6],[3,7],[4,8]] => [[1,2,3,4],[5,6,7,8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 5

[[1,3],[2,6],[4,7],[5,8]] => [[1,2,4,5],[3,6,7,8]] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3

[[1,2],[3,6],[4,7],[5,8]] => [[1,3,4,5],[2,6,7,8]] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2

[[1,3],[2,5],[4,7],[6,8]] => [[1,2,4,6],[3,5,7,8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2],[3,5],[4,7],[6,8]] => [[1,3,4,6],[2,5,7,8]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3],[2,4],[5,7],[6,8]] => [[1,2,5,6],[3,4,7,8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3

[[1,2],[3,4],[5,7],[6,8]] => [[1,3,5,6],[2,4,7,8]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,4],[2,5],[3,6],[7,8]] => [[1,2,3,7],[4,5,6,8]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4

[[1,3],[2,5],[4,6],[7,8]] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2],[3,5],[4,6],[7,8]] => [[1,3,4,7],[2,5,6,8]] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3],[2,4],[5,6],[7,8]] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2],[3,4],[5,6],[7,8]] => [[1,3,5,7],[2,4,6,8]] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[[1,5],[2,7],[3,8],[4],[6]] => [[1,2,3,4,6],[5,7,8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5

[[1,3],[2,7],[4,8],[5],[6]] => [[1,2,4,5,6],[3,7,8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3

[[1,2],[3,7],[4,8],[5],[6]] => [[1,3,4,5,6],[2,7,8]] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2

[[1,3],[2,6],[4,8],[5],[7]] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[[1,2],[3,6],[4,8],[5],[7]] => [[1,3,4,5,7],[2,6,8]] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[[1,4],[2,5],[3,8],[6],[7]] => [[1,2,3,6,7],[4,5,8]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4

[[1,3],[2,5],[4,8],[6],[7]] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[[1,2],[3,5],[4,8],[6],[7]] => [[1,3,4,6,7],[2,5,8]] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[[1,3],[2,4],[5,8],[6],[7]] => [[1,2,5,6,7],[3,4,8]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[[1,2],[3,4],[5,8],[6],[7]] => [[1,3,5,6,7],[2,4,8]] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[[1,5],[2,6],[3,7],[4],[8]] => [[1,2,3,4,8],[5,6,7]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 5

[[1,3],[2,6],[4,7],[5],[8]] => [[1,2,4,5,8],[3,6,7]] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3

[[1,2],[3,6],[4,7],[5],[8]] => [[1,3,4,5,8],[2,6,7]] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2

[[1,3],[2,5],[4,7],[6],[8]] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3

[[1,2],[3,5],[4,7],[6],[8]] => [[1,3,4,6,8],[2,5,7]] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2

[[1,3],[2,4],[5,7],[6],[8]] => [[1,2,5,6,8],[3,4,7]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3

[[1,2],[3,4],[5,7],[6],[8]] => [[1,3,5,6,8],[2,4,7]] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2

[[1,3],[2,5],[4,6],[7],[8]] => [[1,2,4,7,8],[3,5,6]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3

[[1,2],[3,5],[4,6],[7],[8]] => [[1,3,4,7,8],[2,5,6]] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2

[[1,3],[2,4],[5,6],[7],[8]] => [[1,2,5,7,8],[3,4,6]] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3

[[1,2],[3,4],[5,6],[7],[8]] => [[1,3,5,7,8],[2,4,6]] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2

[[1,7],[2,8],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7,8]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 7

[[1,4],[2,8],[3],[5],[6],[7]] => [[1,2,3,5,6,7],[4,8]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4

[[1,3],[2,8],[4],[5],[6],[7]] => [[1,2,4,5,6,7],[3,8]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[[1,2],[3,8],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2,8]] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[[1,5],[2,7],[3],[4],[6],[8]] => [[1,2,3,4,6,8],[5,7]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5

[[1,3],[2,7],[4],[5],[6],[8]] => [[1,2,4,5,6,8],[3,7]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3

[[1,2],[3,7],[4],[5],[6],[8]] => [[1,3,4,5,6,8],[2,7]] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2

[[1,5],[2,6],[3],[4],[7],[8]] => [[1,2,3,4,7,8],[5,6]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 5

[[1,3],[2,6],[4],[5],[7],[8]] => [[1,2,4,5,7,8],[3,6]] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3

[[1,2],[3,6],[4],[5],[7],[8]] => [[1,3,4,5,7,8],[2,6]] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2

[[1,3],[2,5],[4],[6],[7],[8]] => [[1,2,4,6,7,8],[3,5]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3

[[1,2],[3,5],[4],[6],[7],[8]] => [[1,3,4,6,7,8],[2,5]] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2

[[1,3],[2,4],[5],[6],[7],[8]] => [[1,2,5,6,7,8],[3,4]] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3

[[1,2],[3,4],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2,4]] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2

[[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7],[8]] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8

[[1,7],[2],[3],[4],[5],[6],[8]] => [[1,2,3,4,5,6,8],[7]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 7

[[1,5],[2],[3],[4],[6],[7],[8]] => [[1,2,3,4,6,7,8],[5]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 5

[[1,3],[2],[4],[5],[6],[7],[8]] => [[1,2,4,5,6,7,8],[3]] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3

[[1,2],[3],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2]] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2

[[1],[2],[3],[4],[5],[6],[7],[8]] => [[1,2,3,4,5,6,7,8]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9

[[1,2,3,4,5,6,7,8],[9]] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2

[[1,2,3,4,5,6],[7,8,9]] => [[1,7],[2,8],[3,9],[4],[5],[6]] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3,4,5,6],[7,8],[9]] => [[1,7,9],[2,8],[3],[4],[5],[6]] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2

[[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2,4]] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,3,4,5,6,7,8,9],[2]] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2

[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [[1,2,3,4,5,6,7,8,9]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10

[[1,2,3,4,5,6,7,8,9],[10]] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2

[[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2

[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,3,4,5,6,7,8,9,10],[2]] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 2

[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,2,3,4,5,6,7,8,9,10]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11

[[1,3,4,5,6,7,8,9],[2]] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3

[[1,4,5,6,7,8,9],[2],[3]] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4

[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [[1,2,3,4,5,6,7,8],[9]] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 9

[[1,3,4,5,6,7,8,9,10],[2]] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3

[[1,4,5,6,7,8,9,10],[2],[3]] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4

[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [[1,2,3,4,5,6,7,8,9],[10]] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 10

[[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => [[1,2,3,4,5,6,7,8],[9,10]] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 9

[[1,2,4],[3,5],[6],[7],[8],[9]] => [[1,3,6,7,8,9],[2,5],[4]] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[[1,2,3,4,5,6,8],[7,9]] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => [[1,2,5,6,7,8,9,10],[3,4]] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3

[[1,2,3,9],[4],[5],[6],[7],[8]] => [[1,4,5,6,7,8],[2],[3],[9]] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[[1,2,9],[3],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2],[9]] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2

[[1,3],[2,9],[4],[5],[6],[7],[8]] => [[1,2,4,5,6,7,8],[3,9]] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3

[[1,2,3,10],[4],[5],[6],[7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3],[10]] => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2

[[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [[1,3,4,5,6,7,8,9],[2],[10]] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2

[[1,8],[2],[3],[4],[5],[6],[7],[9]] => [[1,2,3,4,5,6,7,9],[8]] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 8

[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [[1,2,3,4,5,6,7,8,10],[9]] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 9

[[1,3,4,5,6,7,8],[2,9]] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3

[[1,3,4,5,6,7,8],[2],[9]] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3

[[1,3,4,5,6,7],[2,8,9]] => [[1,2],[3,8],[4,9],[5],[6],[7]] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3

[[1,3,4,5,6,7,8,9],[2,10]] => [[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3

[[1,3,4,5,6,7,8,9],[2],[10]] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3

[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => [[1,2,4,5,6,7,8,9,10],[3]] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3

[[1,2,5,6,7,8],[3,4],[9]] => [[1,3,9],[2,4],[5],[6],[7],[8]] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2

[[1,2,5,6,7,8,9],[3],[4]] => [[1,3,4],[2],[5],[6],[7],[8],[9]] => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 2

[[1,2,8,9],[3],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2],[8],[9]] => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2

[[1,2],[3,8],[4],[5],[6],[7],[9]] => [[1,3,4,5,6,7,9],[2,8]] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 2

[[1,2,9,10],[3],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2],[9],[10]] => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2

[[1,2,4],[3],[5],[6],[7],[8],[9]] => [[1,3,5,6,7,8,9],[2],[4]] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[[1,2,3,4,5,6,8],[7],[9]] => [[1,7,9],[2],[3],[4],[5],[6],[8]] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[[1,2,8],[3,9],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2,9],[8]] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 2

[[1,2,4,5,6,7,8],[3,9]] => [[1,3],[2,9],[4],[5],[6],[7],[8]] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2

[[1,2],[3,9],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2,9]] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2

[[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => [[1,3,4,5,6,7,8,9],[2,10]] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2

[[1,2,3],[4,9],[5],[6],[7],[8]] => [[1,4,5,6,7,8],[2,9],[3]] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[[1,2,3],[4,10],[5],[6],[7],[8],[9]] => [[1,4,5,6,7,8,9],[2,10],[3]] => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2

[[1,3,4,5,6,7,9],[2,8]] => [[1,2],[3,8],[4],[5],[6],[7],[9]] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3

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$F_{1} = q^{2}$

$F_{2} = q^{2} + q^{3}$

$F_{3} = 2\ q^{2} + q^{3} + q^{4}$

$F_{4} = 5\ q^{2} + 3\ q^{3} + q^{4} + q^{5}$

$F_{5} = 13\ q^{2} + 8\ q^{3} + 3\ q^{4} + q^{5} + q^{6}$

$F_{6} = 38\ q^{2} + 24\ q^{3} + 9\ q^{4} + 3\ q^{5} + q^{6} + q^{7}$

$F_{7} = 116\ q^{2} + 74\ q^{3} + 28\ q^{4} + 9\ q^{5} + 3\ q^{6} + q^{7} + q^{8}$

Description

The position of the first down step of a Dyck path.

Map

bounce path

Description

The bounce path determined by an integer composition.

Map

horizontal strip sizes

Description

The composition of horizontal strip sizes.
We associate to a standard Young tableau

$T$ the composition

$(c_1,\dots,c_k)$ , such that

$k$ is minimal and the numbers

$c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in

$T$ for all

$i$ .

Map

conjugate

Description

Sends a standard tableau to its conjugate tableau.