Identifier
-
Mp00083:
Standard tableaux
—shape⟶
Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001007: Dyck paths ⟶ ℤ (values match St000024The number of double up and double down steps of a Dyck path., St000443The number of long tunnels of a Dyck path., St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra., St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra.)
Values
[[1]] => [1] => [1,0] => 1
[[1,2]] => [2] => [1,0,1,0] => 1
[[1],[2]] => [1,1] => [1,1,0,0] => 2
[[1,2,3]] => [3] => [1,0,1,0,1,0] => 1
[[1,3],[2]] => [2,1] => [1,0,1,1,0,0] => 2
[[1,2],[3]] => [2,1] => [1,0,1,1,0,0] => 2
[[1],[2],[3]] => [1,1,1] => [1,1,0,1,0,0] => 2
[[1,2,3,4]] => [4] => [1,0,1,0,1,0,1,0] => 1
[[1,3,4],[2]] => [3,1] => [1,0,1,0,1,1,0,0] => 2
[[1,2,4],[3]] => [3,1] => [1,0,1,0,1,1,0,0] => 2
[[1,2,3],[4]] => [3,1] => [1,0,1,0,1,1,0,0] => 2
[[1,3],[2,4]] => [2,2] => [1,1,1,0,0,0] => 3
[[1,2],[3,4]] => [2,2] => [1,1,1,0,0,0] => 3
[[1,4],[2],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[[1,3],[2],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[[1,2],[3],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[[1],[2],[3],[4]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 2
[[1,2,3,4,5]] => [5] => [1,0,1,0,1,0,1,0,1,0] => 1
[[1,3,4,5],[2]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[[1,2,4,5],[3]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[[1,2,3,5],[4]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[[1,2,3,4],[5]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[[1,3,5],[2,4]] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[[1,2,5],[3,4]] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[[1,3,4],[2,5]] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[[1,2,4],[3,5]] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[[1,2,3],[4,5]] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[[1,4,5],[2],[3]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[[1,3,5],[2],[4]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,5],[3],[4]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[[1,3,4],[2],[5]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,4],[3],[5]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,3],[4],[5]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[[1,4],[2,5],[3]] => [2,2,1] => [1,1,1,0,0,1,0,0] => 3
[[1,3],[2,5],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => 3
[[1,2],[3,5],[4]] => [2,2,1] => [1,1,1,0,0,1,0,0] => 3
[[1,3],[2,4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => 3
[[1,2],[3,4],[5]] => [2,2,1] => [1,1,1,0,0,1,0,0] => 3
[[1,5],[2],[3],[4]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[[1,4],[2],[3],[5]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[[1,3],[2],[4],[5]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[[1,2],[3],[4],[5]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[[1],[2],[3],[4],[5]] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 2
[[1,2,3,4,5,6]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[[1,3,4,5,6],[2]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[1,2,4,5,6],[3]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[1,2,3,5,6],[4]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[1,2,3,4,6],[5]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[1,2,3,4,5],[6]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[1,3,5,6],[2,4]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,5,6],[3,4]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[[1,3,4,6],[2,5]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,4,6],[3,5]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,6],[4,5]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[[1,3,4,5],[2,6]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,4,5],[3,6]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,5],[4,6]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,4],[5,6]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[[1,4,5,6],[2],[3]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,3,5,6],[2],[4]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,5,6],[3],[4]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,3,4,6],[2],[5]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,4,6],[3],[5]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,3,6],[4],[5]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,3,4,5],[2],[6]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,4,5],[3],[6]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,3,5],[4],[6]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,3,4],[5],[6]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,3,5],[2,4,6]] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[[1,2,5],[3,4,6]] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[[1,3,4],[2,5,6]] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[[1,2,4],[3,5,6]] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[[1,2,3],[4,5,6]] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[[1,4,6],[2,5],[3]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,6],[2,5],[4]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,6],[3,5],[4]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,6],[2,4],[5]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,6],[3,4],[5]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,4,5],[2,6],[3]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,5],[2,6],[4]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,5],[3,6],[4]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4],[2,6],[5]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4],[3,6],[5]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3],[4,6],[5]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,5],[2,4],[6]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,5],[3,4],[6]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4],[2,5],[6]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4],[3,5],[6]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3],[4,5],[6]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[1,5,6],[2],[3],[4]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,4,6],[2],[3],[5]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,3,6],[2],[4],[5]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,2,6],[3],[4],[5]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,4,5],[2],[3],[6]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,3,5],[2],[4],[6]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,2,5],[3],[4],[6]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,3,4],[2],[5],[6]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,2,4],[3],[5],[6]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,2,3],[4],[5],[6]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,4],[2,5],[3,6]] => [2,2,2] => [1,1,1,1,0,0,0,0] => 4
[[1,3],[2,5],[4,6]] => [2,2,2] => [1,1,1,1,0,0,0,0] => 4
>>> Load all 1292 entries. <<<[[1,2],[3,5],[4,6]] => [2,2,2] => [1,1,1,1,0,0,0,0] => 4
[[1,3],[2,4],[5,6]] => [2,2,2] => [1,1,1,1,0,0,0,0] => 4
[[1,2],[3,4],[5,6]] => [2,2,2] => [1,1,1,1,0,0,0,0] => 4
[[1,5],[2,6],[3],[4]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[[1,4],[2,6],[3],[5]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[[1,3],[2,6],[4],[5]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[[1,2],[3,6],[4],[5]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[[1,4],[2,5],[3],[6]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[[1,3],[2,5],[4],[6]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[[1,2],[3,5],[4],[6]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[[1,3],[2,4],[5],[6]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[[1,2],[3,4],[5],[6]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[[1,6],[2],[3],[4],[5]] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,5],[2],[3],[4],[6]] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,4],[2],[3],[5],[6]] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,3],[2],[4],[5],[6]] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 2
[[1,2,3,4,5,6,7]] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[[1,3,4,5,6,7],[2]] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[1,2,4,5,6,7],[3]] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[1,2,3,5,6,7],[4]] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[1,2,3,4,6,7],[5]] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[1,2,3,4,5,7],[6]] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[1,2,3,4,5,6],[7]] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[[1,3,5,6,7],[2,4]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,5,6,7],[3,4]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,3,4,6,7],[2,5]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,4,6,7],[3,5]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,6,7],[4,5]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,3,4,5,7],[2,6]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,4,5,7],[3,6]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,5,7],[4,6]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,4,7],[5,6]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,3,4,5,6],[2,7]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,4,5,6],[3,7]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,5,6],[4,7]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,4,6],[5,7]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,4,5],[6,7]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,4,5,6,7],[2],[3]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,3,5,6,7],[2],[4]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,5,6,7],[3],[4]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,3,4,6,7],[2],[5]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,4,6,7],[3],[5]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,3,6,7],[4],[5]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,3,4,5,7],[2],[6]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,4,5,7],[3],[6]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,3,5,7],[4],[6]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,3,4,7],[5],[6]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,3,4,5,6],[2],[7]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,4,5,6],[3],[7]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,3,5,6],[4],[7]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,3,4,6],[5],[7]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,2,3,4,5],[6],[7]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,3,5,7],[2,4,6]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,5,7],[3,4,6]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[1,3,4,7],[2,5,6]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,4,7],[3,5,6]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,7],[4,5,6]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[1,3,5,6],[2,4,7]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,5,6],[3,4,7]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[1,3,4,6],[2,5,7]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,4,6],[3,5,7]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,6],[4,5,7]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[1,3,4,5],[2,6,7]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,4,5],[3,6,7]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,5],[4,6,7]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,4],[5,6,7]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[1,4,6,7],[2,5],[3]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,6,7],[2,5],[4]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,6,7],[3,5],[4]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,6,7],[2,4],[5]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,6,7],[3,4],[5]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,4,5,7],[2,6],[3]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,5,7],[2,6],[4]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,5,7],[3,6],[4]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,7],[2,6],[5]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,7],[3,6],[5]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,7],[4,6],[5]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,5,7],[2,4],[6]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,5,7],[3,4],[6]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,7],[2,5],[6]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,7],[3,5],[6]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,7],[4,5],[6]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,4,5,6],[2,7],[3]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,5,6],[2,7],[4]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,5,6],[3,7],[4]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,6],[2,7],[5]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,6],[3,7],[5]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,6],[4,7],[5]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,5],[2,7],[6]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,5],[3,7],[6]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,5],[4,7],[6]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,4],[5,7],[6]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,5,6],[2,4],[7]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,5,6],[3,4],[7]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,6],[2,5],[7]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,6],[3,5],[7]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,6],[4,5],[7]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,5],[2,6],[7]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,5],[3,6],[7]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,5],[4,6],[7]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,4],[5,6],[7]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,5,6,7],[2],[3],[4]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,4,6,7],[2],[3],[5]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,3,6,7],[2],[4],[5]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,2,6,7],[3],[4],[5]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,4,5,7],[2],[3],[6]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,3,5,7],[2],[4],[6]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,2,5,7],[3],[4],[6]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,3,4,7],[2],[5],[6]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,2,4,7],[3],[5],[6]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,2,3,7],[4],[5],[6]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,4,5,6],[2],[3],[7]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,3,5,6],[2],[4],[7]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,2,5,6],[3],[4],[7]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,3,4,6],[2],[5],[7]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,2,4,6],[3],[5],[7]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,2,3,6],[4],[5],[7]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,3,4,5],[2],[6],[7]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,2,4,5],[3],[6],[7]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,2,3,5],[4],[6],[7]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[[1,4,6],[2,5,7],[3]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,6],[2,5,7],[4]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,6],[3,5,7],[4]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,6],[2,4,7],[5]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,6],[3,4,7],[5]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,4,5],[2,6,7],[3]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,5],[2,6,7],[4]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,5],[3,6,7],[4]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4],[2,6,7],[5]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4],[3,6,7],[5]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3],[4,6,7],[5]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,5],[2,4,7],[6]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,5],[3,4,7],[6]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4],[2,5,7],[6]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4],[3,5,7],[6]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3],[4,5,7],[6]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,5],[2,4,6],[7]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,5],[3,4,6],[7]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4],[2,5,6],[7]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4],[3,5,6],[7]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3],[4,5,6],[7]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[1,4,7],[2,5],[3,6]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,7],[2,5],[4,6]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,7],[3,5],[4,6]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,7],[2,4],[5,6]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,7],[3,4],[5,6]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,4,6],[2,5],[3,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,6],[2,5],[4,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,6],[3,5],[4,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,6],[2,4],[5,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,6],[3,4],[5,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,4,5],[2,6],[3,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,5],[2,6],[4,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5],[3,6],[4,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4],[2,6],[5,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,4],[3,6],[5,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3],[4,6],[5,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,5],[2,4],[6,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5],[3,4],[6,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4],[2,5],[6,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,4],[3,5],[6,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3],[4,5],[6,7]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,5,7],[2,6],[3],[4]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,7],[2,6],[3],[5]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,7],[2,6],[4],[5]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,7],[3,6],[4],[5]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,7],[2,5],[3],[6]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,7],[2,5],[4],[6]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,7],[3,5],[4],[6]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,7],[2,4],[5],[6]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,7],[3,4],[5],[6]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,5,6],[2,7],[3],[4]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,6],[2,7],[3],[5]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,6],[2,7],[4],[5]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,6],[3,7],[4],[5]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,5],[2,7],[3],[6]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,5],[2,7],[4],[6]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,5],[3,7],[4],[6]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4],[2,7],[5],[6]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4],[3,7],[5],[6]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3],[4,7],[5],[6]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,6],[2,5],[3],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,6],[2,5],[4],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,6],[3,5],[4],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,6],[2,4],[5],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,6],[3,4],[5],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,5],[2,6],[3],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,5],[2,6],[4],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,5],[3,6],[4],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4],[2,6],[5],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4],[3,6],[5],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3],[4,6],[5],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,5],[2,4],[6],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,5],[3,4],[6],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4],[2,5],[6],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4],[3,5],[6],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,6,7],[2],[3],[4],[5]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,5,7],[2],[3],[4],[6]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,4,7],[2],[3],[5],[6]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,3,7],[2],[4],[5],[6]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,2,7],[3],[4],[5],[6]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,5,6],[2],[3],[4],[7]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,4,6],[2],[3],[5],[7]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,3,6],[2],[4],[5],[7]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,2,6],[3],[4],[5],[7]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,4,5],[2],[3],[6],[7]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,3,5],[2],[4],[6],[7]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,2,5],[3],[4],[6],[7]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,3,4],[2],[5],[6],[7]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,2,4],[3],[5],[6],[7]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[1,5],[2,6],[3,7],[4]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[[1,4],[2,6],[3,7],[5]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[[1,3],[2,6],[4,7],[5]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[[1,2],[3,6],[4,7],[5]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[[1,4],[2,5],[3,7],[6]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[[1,3],[2,5],[4,7],[6]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[[1,2],[3,5],[4,7],[6]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[[1,3],[2,4],[5,7],[6]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[[1,2],[3,4],[5,7],[6]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[[1,4],[2,5],[3,6],[7]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[[1,3],[2,5],[4,6],[7]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[[1,2],[3,5],[4,6],[7]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[[1,3],[2,4],[5,6],[7]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[[1,6],[2,7],[3],[4],[5]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,5],[2,7],[3],[4],[6]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4],[2,7],[3],[5],[6]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3],[2,7],[4],[5],[6]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2],[3,7],[4],[5],[6]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,5],[2,6],[3],[4],[7]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4],[2,6],[3],[5],[7]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3],[2,6],[4],[5],[7]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2],[3,6],[4],[5],[7]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4],[2,5],[3],[6],[7]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3],[2,5],[4],[6],[7]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2],[3,5],[4],[6],[7]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3],[2,4],[5],[6],[7]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,7],[2],[3],[4],[5],[6]] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[[1,6],[2],[3],[4],[5],[7]] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[[1,5],[2],[3],[4],[6],[7]] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[[1,4],[2],[3],[5],[6],[7]] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[[1,3],[2],[4],[5],[6],[7]] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[[1],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[[1,3,5,6,7,8],[2,4]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,5,6,7,8],[3,4]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,3,4,6,7,8],[2,5]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,4,6,7,8],[3,5]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,6,7,8],[4,5]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,3,4,5,7,8],[2,6]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,4,5,7,8],[3,6]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,5,7,8],[4,6]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,4,7,8],[5,6]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,3,4,5,6,8],[2,7]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,4,5,6,8],[3,7]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,5,6,8],[4,7]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,4,6,8],[5,7]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,4,5,8],[6,7]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,3,4,5,6,7],[2,8]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,4,5,6,7],[3,8]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,5,6,7],[4,8]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,4,6,7],[5,8]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,4,5,7],[6,8]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,2,3,4,5,6],[7,8]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,3,5,7,8],[2,4,6]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,5,7,8],[3,4,6]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,3,4,7,8],[2,5,6]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,4,7,8],[3,5,6]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,7,8],[4,5,6]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,3,5,6,8],[2,4,7]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,5,6,8],[3,4,7]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,3,4,6,8],[2,5,7]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,4,6,8],[3,5,7]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,6,8],[4,5,7]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,3,4,5,8],[2,6,7]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,4,5,8],[3,6,7]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,5,8],[4,6,7]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,4,8],[5,6,7]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,3,5,6,7],[2,4,8]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,5,6,7],[3,4,8]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,3,4,6,7],[2,5,8]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,4,6,7],[3,5,8]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,6,7],[4,5,8]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,3,4,5,7],[2,6,8]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,4,5,7],[3,6,8]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,5,7],[4,6,8]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,4,7],[5,6,8]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,3,4,5,6],[2,7,8]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,4,5,6],[3,7,8]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,5,6],[4,7,8]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,4,6],[5,7,8]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,4,5],[6,7,8]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,4,6,7,8],[2,5],[3]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,6,7,8],[2,5],[4]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,6,7,8],[3,5],[4]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,6,7,8],[2,4],[5]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,6,7,8],[3,4],[5]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,4,5,7,8],[2,6],[3]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,5,7,8],[2,6],[4]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,5,7,8],[3,6],[4]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,7,8],[2,6],[5]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,7,8],[3,6],[5]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,7,8],[4,6],[5]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,5,7,8],[2,4],[6]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,5,7,8],[3,4],[6]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,7,8],[2,5],[6]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,7,8],[3,5],[6]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,7,8],[4,5],[6]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,4,5,6,8],[2,7],[3]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,5,6,8],[2,7],[4]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,5,6,8],[3,7],[4]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,6,8],[2,7],[5]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,6,8],[3,7],[5]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,6,8],[4,7],[5]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,5,8],[2,7],[6]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,5,8],[3,7],[6]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,5,8],[4,7],[6]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,4,8],[5,7],[6]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,5,6,8],[2,4],[7]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,5,6,8],[3,4],[7]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,6,8],[2,5],[7]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,6,8],[3,5],[7]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,6,8],[4,5],[7]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,5,8],[2,6],[7]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,5,8],[3,6],[7]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,5,8],[4,6],[7]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,4,8],[5,6],[7]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,4,5,6,7],[2,8],[3]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,5,6,7],[2,8],[4]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,5,6,7],[3,8],[4]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,6,7],[2,8],[5]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,6,7],[3,8],[5]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,6,7],[4,8],[5]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,5,7],[2,8],[6]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,5,7],[3,8],[6]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,5,7],[4,8],[6]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,4,7],[5,8],[6]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,5,6],[2,8],[7]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,5,6],[3,8],[7]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,5,6],[4,8],[7]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,4,6],[5,8],[7]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,4,5],[6,8],[7]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,5,6,7],[2,4],[8]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,5,6,7],[3,4],[8]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,6,7],[2,5],[8]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,6,7],[3,5],[8]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,6,7],[4,5],[8]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,5,7],[2,6],[8]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,5,7],[3,6],[8]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,5,7],[4,6],[8]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,4,7],[5,6],[8]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,4,5,6],[2,7],[8]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,4,5,6],[3,7],[8]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,5,6],[4,7],[8]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,4,6],[5,7],[8]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,2,3,4,5],[6,7],[8]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[1,3,5,7],[2,4,6,8]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,2,5,7],[3,4,6,8]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,3,4,7],[2,5,6,8]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,2,4,7],[3,5,6,8]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,2,3,7],[4,5,6,8]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,3,5,6],[2,4,7,8]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,2,5,6],[3,4,7,8]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,3,4,6],[2,5,7,8]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,2,4,6],[3,5,7,8]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,2,3,6],[4,5,7,8]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5],[2,6,7,8]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5],[3,6,7,8]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5],[4,6,7,8]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4],[5,6,7,8]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,4,6,8],[2,5,7],[3]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,6,8],[2,5,7],[4]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,6,8],[3,5,7],[4]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,6,8],[2,4,7],[5]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,6,8],[3,4,7],[5]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,4,5,8],[2,6,7],[3]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,5,8],[2,6,7],[4]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,5,8],[3,6,7],[4]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4,8],[2,6,7],[5]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,8],[3,6,7],[5]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,8],[4,6,7],[5]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,5,8],[2,4,7],[6]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,5,8],[3,4,7],[6]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4,8],[2,5,7],[6]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,8],[3,5,7],[6]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,8],[4,5,7],[6]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,5,8],[2,4,6],[7]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,5,8],[3,4,6],[7]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4,8],[2,5,6],[7]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,8],[3,5,6],[7]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,8],[4,5,6],[7]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,4,6,7],[2,5,8],[3]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,6,7],[2,5,8],[4]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,6,7],[3,5,8],[4]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,6,7],[2,4,8],[5]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,6,7],[3,4,8],[5]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,4,5,7],[2,6,8],[3]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,5,7],[2,6,8],[4]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,5,7],[3,6,8],[4]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4,7],[2,6,8],[5]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,7],[3,6,8],[5]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,7],[4,6,8],[5]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,5,7],[2,4,8],[6]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,5,7],[3,4,8],[6]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4,7],[2,5,8],[6]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,7],[3,5,8],[6]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,7],[4,5,8],[6]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,4,5,6],[2,7,8],[3]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,5,6],[2,7,8],[4]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,5,6],[3,7,8],[4]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4,6],[2,7,8],[5]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,6],[3,7,8],[5]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,6],[4,7,8],[5]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4,5],[2,7,8],[6]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,5],[3,7,8],[6]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,5],[4,7,8],[6]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,4],[5,7,8],[6]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,5,6],[2,4,8],[7]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,5,6],[3,4,8],[7]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4,6],[2,5,8],[7]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,6],[3,5,8],[7]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,6],[4,5,8],[7]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4,5],[2,6,8],[7]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,5],[3,6,8],[7]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,5],[4,6,8],[7]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,4],[5,6,8],[7]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,5,7],[2,4,6],[8]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,5,7],[3,4,6],[8]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4,7],[2,5,6],[8]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,7],[3,5,6],[8]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,7],[4,5,6],[8]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,5,6],[2,4,7],[8]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,5,6],[3,4,7],[8]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4,6],[2,5,7],[8]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,6],[3,5,7],[8]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,6],[4,5,7],[8]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,3,4,5],[2,6,7],[8]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,5],[3,6,7],[8]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,5],[4,6,7],[8]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,4],[5,6,7],[8]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,4,7,8],[2,5],[3,6]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,7,8],[2,5],[4,6]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,7,8],[3,5],[4,6]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,7,8],[2,4],[5,6]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,7,8],[3,4],[5,6]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,4,6,8],[2,5],[3,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,6,8],[2,5],[4,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,6,8],[3,5],[4,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,6,8],[2,4],[5,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,6,8],[3,4],[5,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,4,5,8],[2,6],[3,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,5,8],[2,6],[4,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,8],[3,6],[4,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4,8],[2,6],[5,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,4,8],[3,6],[5,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,8],[4,6],[5,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,5,8],[2,4],[6,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,8],[3,4],[6,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4,8],[2,5],[6,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,4,8],[3,5],[6,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,8],[4,5],[6,7]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,4,6,7],[2,5],[3,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,6,7],[2,5],[4,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,6,7],[3,5],[4,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,6,7],[2,4],[5,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,6,7],[3,4],[5,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,4,5,7],[2,6],[3,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,5,7],[2,6],[4,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,7],[3,6],[4,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4,7],[2,6],[5,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,4,7],[3,6],[5,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,7],[4,6],[5,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,5,7],[2,4],[6,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,7],[3,4],[6,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4,7],[2,5],[6,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,4,7],[3,5],[6,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,7],[4,5],[6,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,4,5,6],[2,7],[3,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,5,6],[2,7],[4,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,6],[3,7],[4,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4,6],[2,7],[5,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,4,6],[3,7],[5,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,6],[4,7],[5,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4,5],[2,7],[6,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,4,5],[3,7],[6,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,5],[4,7],[6,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,4],[5,7],[6,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,5,6],[2,4],[7,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,6],[3,4],[7,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4,6],[2,5],[7,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,4,6],[3,5],[7,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,6],[4,5],[7,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4,5],[2,6],[7,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,4,5],[3,6],[7,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,5],[4,6],[7,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,4],[5,6],[7,8]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,5,7,8],[2,6],[3],[4]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,7,8],[2,6],[3],[5]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,7,8],[2,6],[4],[5]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,7,8],[3,6],[4],[5]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,7,8],[2,5],[3],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,7,8],[2,5],[4],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,7,8],[3,5],[4],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,7,8],[2,4],[5],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,7,8],[3,4],[5],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,5,6,8],[2,7],[3],[4]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,6,8],[2,7],[3],[5]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,6,8],[2,7],[4],[5]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,6,8],[3,7],[4],[5]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,5,8],[2,7],[3],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,5,8],[2,7],[4],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,5,8],[3,7],[4],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4,8],[2,7],[5],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4,8],[3,7],[5],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,8],[4,7],[5],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,6,8],[2,5],[3],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,6,8],[2,5],[4],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,6,8],[3,5],[4],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,6,8],[2,4],[5],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,6,8],[3,4],[5],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,5,8],[2,6],[3],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,5,8],[2,6],[4],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,5,8],[3,6],[4],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4,8],[2,6],[5],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4,8],[3,6],[5],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,8],[4,6],[5],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,5,8],[2,4],[6],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,5,8],[3,4],[6],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4,8],[2,5],[6],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4,8],[3,5],[6],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,8],[4,5],[6],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,5,6,7],[2,8],[3],[4]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,6,7],[2,8],[3],[5]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,6,7],[2,8],[4],[5]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,6,7],[3,8],[4],[5]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,5,7],[2,8],[3],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,5,7],[2,8],[4],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,5,7],[3,8],[4],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4,7],[2,8],[5],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4,7],[3,8],[5],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,7],[4,8],[5],[6]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,5,6],[2,8],[3],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,5,6],[2,8],[4],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,5,6],[3,8],[4],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4,6],[2,8],[5],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4,6],[3,8],[5],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,6],[4,8],[5],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4,5],[2,8],[6],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4,5],[3,8],[6],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,5],[4,8],[6],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,4],[5,8],[6],[7]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,6,7],[2,5],[3],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,6,7],[2,5],[4],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,6,7],[3,5],[4],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,6,7],[2,4],[5],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,6,7],[3,4],[5],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,5,7],[2,6],[3],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,5,7],[2,6],[4],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,5,7],[3,6],[4],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4,7],[2,6],[5],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4,7],[3,6],[5],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,7],[4,6],[5],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,5,7],[2,4],[6],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,5,7],[3,4],[6],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4,7],[2,5],[6],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4,7],[3,5],[6],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,7],[4,5],[6],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,5,6],[2,7],[3],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,5,6],[2,7],[4],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,5,6],[3,7],[4],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4,6],[2,7],[5],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4,6],[3,7],[5],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,6],[4,7],[5],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4,5],[2,7],[6],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4,5],[3,7],[6],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,5],[4,7],[6],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,4],[5,7],[6],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,5,6],[2,4],[7],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,5,6],[3,4],[7],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4,6],[2,5],[7],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4,6],[3,5],[7],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,6],[4,5],[7],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,3,4,5],[2,6],[7],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,4,5],[3,6],[7],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,5],[4,6],[7],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,4,7],[2,5,8],[3,6]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,7],[2,5,8],[4,6]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,7],[3,5,8],[4,6]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,7],[2,4,8],[5,6]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,7],[3,4,8],[5,6]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,4,6],[2,5,8],[3,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,6],[2,5,8],[4,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,6],[3,5,8],[4,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,6],[2,4,8],[5,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,6],[3,4,8],[5,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,4,5],[2,6,8],[3,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,5],[2,6,8],[4,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,5],[3,6,8],[4,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,4],[2,6,8],[5,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,4],[3,6,8],[5,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,3],[4,6,8],[5,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,5],[2,4,8],[6,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,5],[3,4,8],[6,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,4],[2,5,8],[6,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,4],[3,5,8],[6,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,3],[4,5,8],[6,7]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,4,6],[2,5,7],[3,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,6],[2,5,7],[4,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,6],[3,5,7],[4,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,6],[2,4,7],[5,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,6],[3,4,7],[5,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,4,5],[2,6,7],[3,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,5],[2,6,7],[4,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,5],[3,6,7],[4,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,4],[2,6,7],[5,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,4],[3,6,7],[5,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,3],[4,6,7],[5,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,5],[2,4,7],[6,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,5],[3,4,7],[6,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,4],[2,5,7],[6,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,4],[3,5,7],[6,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,3],[4,5,7],[6,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,5],[2,4,6],[7,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,5],[3,4,6],[7,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,3,4],[2,5,6],[7,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,4],[3,5,6],[7,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,3],[4,5,6],[7,8]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 4
[[1,5,7],[2,6,8],[3],[4]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,4,7],[2,6,8],[3],[5]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,7],[2,6,8],[4],[5]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,7],[3,6,8],[4],[5]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,4,7],[2,5,8],[3],[6]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,7],[2,5,8],[4],[6]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,7],[3,5,8],[4],[6]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,7],[2,4,8],[5],[6]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,7],[3,4,8],[5],[6]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,5,6],[2,7,8],[3],[4]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,4,6],[2,7,8],[3],[5]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,6],[2,7,8],[4],[5]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,6],[3,7,8],[4],[5]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,4,5],[2,7,8],[3],[6]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,5],[2,7,8],[4],[6]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,5],[3,7,8],[4],[6]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,4],[2,7,8],[5],[6]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,4],[3,7,8],[5],[6]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,3],[4,7,8],[5],[6]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,4,6],[2,5,8],[3],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,6],[2,5,8],[4],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,6],[3,5,8],[4],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,6],[2,4,8],[5],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,6],[3,4,8],[5],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,4,5],[2,6,8],[3],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,5],[2,6,8],[4],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,5],[3,6,8],[4],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,4],[2,6,8],[5],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,4],[3,6,8],[5],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,3],[4,6,8],[5],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,5],[2,4,8],[6],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,5],[3,4,8],[6],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,4],[2,5,8],[6],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,4],[3,5,8],[6],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,3],[4,5,8],[6],[7]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,4,6],[2,5,7],[3],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,6],[2,5,7],[4],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,6],[3,5,7],[4],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,6],[2,4,7],[5],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,6],[3,4,7],[5],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,4,5],[2,6,7],[3],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,5],[2,6,7],[4],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,5],[3,6,7],[4],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,4],[2,6,7],[5],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,4],[3,6,7],[5],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,3],[4,6,7],[5],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,5],[2,4,7],[6],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,5],[3,4,7],[6],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,4],[2,5,7],[6],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,4],[3,5,7],[6],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,3],[4,5,7],[6],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,5],[2,4,6],[7],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,5],[3,4,6],[7],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,4],[2,5,6],[7],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,4],[3,5,6],[7],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,5,8],[2,6],[3,7],[4]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,4,8],[2,6],[3,7],[5]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,8],[2,6],[4,7],[5]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,8],[3,6],[4,7],[5]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,4,8],[2,5],[3,7],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,8],[2,5],[4,7],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,8],[3,5],[4,7],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,8],[2,4],[5,7],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,8],[3,4],[5,7],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,4,8],[2,5],[3,6],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,8],[2,5],[4,6],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,8],[3,5],[4,6],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,8],[2,4],[5,6],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,8],[3,4],[5,6],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,5,7],[2,6],[3,8],[4]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,4,7],[2,6],[3,8],[5]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,7],[2,6],[4,8],[5]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,7],[3,6],[4,8],[5]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,4,7],[2,5],[3,8],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,7],[2,5],[4,8],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,7],[3,5],[4,8],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,7],[2,4],[5,8],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,7],[3,4],[5,8],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,5,6],[2,7],[3,8],[4]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,4,6],[2,7],[3,8],[5]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,6],[2,7],[4,8],[5]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,6],[3,7],[4,8],[5]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,4,5],[2,7],[3,8],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,5],[2,7],[4,8],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,5],[3,7],[4,8],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,4],[2,7],[5,8],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,4],[3,7],[5,8],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,3],[4,7],[5,8],[6]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,4,6],[2,5],[3,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,6],[2,5],[4,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,6],[3,5],[4,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,6],[2,4],[5,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,6],[3,4],[5,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,4,5],[2,6],[3,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,5],[2,6],[4,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,5],[3,6],[4,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,4],[2,6],[5,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,4],[3,6],[5,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,3],[4,6],[5,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,5],[2,4],[6,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,5],[3,4],[6,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,4],[2,5],[6,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,4],[3,5],[6,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,3],[4,5],[6,8],[7]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,4,7],[2,5],[3,6],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,7],[2,5],[4,6],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,7],[3,5],[4,6],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,7],[2,4],[5,6],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,7],[3,4],[5,6],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,4,6],[2,5],[3,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,6],[2,5],[4,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,6],[3,5],[4,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,6],[2,4],[5,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,6],[3,4],[5,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,4,5],[2,6],[3,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,5],[2,6],[4,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,5],[3,6],[4,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,4],[2,6],[5,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,4],[3,6],[5,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,3],[4,6],[5,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,5],[2,4],[6,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,5],[3,4],[6,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,4],[2,5],[6,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,4],[3,5],[6,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,6,8],[2,7],[3],[4],[5]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,5,8],[2,7],[3],[4],[6]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4,8],[2,7],[3],[5],[6]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,8],[2,7],[4],[5],[6]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,8],[3,7],[4],[5],[6]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,5,8],[2,6],[3],[4],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4,8],[2,6],[3],[5],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,8],[2,6],[4],[5],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,8],[3,6],[4],[5],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4,8],[2,5],[3],[6],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,8],[2,5],[4],[6],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,8],[3,5],[4],[6],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,8],[2,4],[5],[6],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,8],[3,4],[5],[6],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,6,7],[2,8],[3],[4],[5]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,5,7],[2,8],[3],[4],[6]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4,7],[2,8],[3],[5],[6]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,7],[2,8],[4],[5],[6]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,7],[3,8],[4],[5],[6]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,5,6],[2,8],[3],[4],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4,6],[2,8],[3],[5],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,6],[2,8],[4],[5],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,6],[3,8],[4],[5],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4,5],[2,8],[3],[6],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,5],[2,8],[4],[6],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,5],[3,8],[4],[6],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,4],[2,8],[5],[6],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,4],[3,8],[5],[6],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,3],[4,8],[5],[6],[7]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,5,7],[2,6],[3],[4],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4,7],[2,6],[3],[5],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,7],[2,6],[4],[5],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,7],[3,6],[4],[5],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4,7],[2,5],[3],[6],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,7],[2,5],[4],[6],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,7],[3,5],[4],[6],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,7],[2,4],[5],[6],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,7],[3,4],[5],[6],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,5,6],[2,7],[3],[4],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4,6],[2,7],[3],[5],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,6],[2,7],[4],[5],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,6],[3,7],[4],[5],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4,5],[2,7],[3],[6],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,5],[2,7],[4],[6],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,5],[3,7],[4],[6],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,4],[2,7],[5],[6],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,4],[3,7],[5],[6],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,3],[4,7],[5],[6],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4,6],[2,5],[3],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,6],[2,5],[4],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,6],[3,5],[4],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,6],[2,4],[5],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,6],[3,4],[5],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,4,5],[2,6],[3],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,5],[2,6],[4],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,5],[3,6],[4],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,4],[2,6],[5],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,4],[3,6],[5],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,3],[4,6],[5],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,5],[2,4],[6],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,5],[3,4],[6],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,3,4],[2,5],[6],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,4],[3,5],[6],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[1,5],[2,6],[3,7],[4,8]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 4
[[1,4],[2,6],[3,7],[5,8]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 4
[[1,3],[2,6],[4,7],[5,8]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 4
[[1,2],[3,6],[4,7],[5,8]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 4
[[1,4],[2,5],[3,7],[6,8]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 4
[[1,3],[2,5],[4,7],[6,8]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 4
[[1,2],[3,5],[4,7],[6,8]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 4
[[1,3],[2,4],[5,7],[6,8]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 4
[[1,2],[3,4],[5,7],[6,8]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 4
[[1,4],[2,5],[3,6],[7,8]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 4
[[1,3],[2,5],[4,6],[7,8]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 4
[[1,2],[3,5],[4,6],[7,8]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 4
[[1,3],[2,4],[5,6],[7,8]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 4
[[1,2],[3,4],[5,6],[7,8]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 4
[[1,6],[2,7],[3,8],[4],[5]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,5],[2,7],[3,8],[4],[6]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,4],[2,7],[3,8],[5],[6]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,3],[2,7],[4,8],[5],[6]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,2],[3,7],[4,8],[5],[6]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,5],[2,6],[3,8],[4],[7]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,4],[2,6],[3,8],[5],[7]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,3],[2,6],[4,8],[5],[7]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,2],[3,6],[4,8],[5],[7]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,4],[2,5],[3,8],[6],[7]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,3],[2,5],[4,8],[6],[7]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,2],[3,5],[4,8],[6],[7]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,3],[2,4],[5,8],[6],[7]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,2],[3,4],[5,8],[6],[7]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,5],[2,6],[3,7],[4],[8]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,4],[2,6],[3,7],[5],[8]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,3],[2,6],[4,7],[5],[8]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,2],[3,6],[4,7],[5],[8]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,4],[2,5],[3,7],[6],[8]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,3],[2,5],[4,7],[6],[8]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,2],[3,5],[4,7],[6],[8]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,3],[2,4],[5,7],[6],[8]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,2],[3,4],[5,7],[6],[8]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,4],[2,5],[3,6],[7],[8]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,3],[2,5],[4,6],[7],[8]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,2],[3,5],[4,6],[7],[8]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,3],[2,4],[5,6],[7],[8]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,7],[2,8],[3],[4],[5],[6]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,6],[2,8],[3],[4],[5],[7]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,5],[2,8],[3],[4],[6],[7]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,4],[2,8],[3],[5],[6],[7]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,3],[2,8],[4],[5],[6],[7]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,2],[3,8],[4],[5],[6],[7]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,6],[2,7],[3],[4],[5],[8]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,5],[2,7],[3],[4],[6],[8]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,4],[2,7],[3],[5],[6],[8]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,3],[2,7],[4],[5],[6],[8]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,2],[3,7],[4],[5],[6],[8]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,5],[2,6],[3],[4],[7],[8]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,4],[2,6],[3],[5],[7],[8]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,3],[2,6],[4],[5],[7],[8]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,2],[3,6],[4],[5],[7],[8]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,4],[2,5],[3],[6],[7],[8]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,3],[2,5],[4],[6],[7],[8]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,2],[3,5],[4],[6],[7],[8]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,3],[2,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[1,3,5,7,9],[2,4,6,8,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,7,8],[2,4,6,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,6,9],[2,4,7,8,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,6,8],[2,4,7,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,6,7],[2,4,8,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,7,9],[2,5,6,8,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,7,8],[2,5,6,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,6,9],[2,5,7,8,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,6,8],[2,5,7,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,6,7],[2,5,8,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,9],[2,6,7,8,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,8],[2,6,7,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,7],[2,6,8,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,6],[2,7,8,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,7,9],[3,4,6,8,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,7,8],[3,4,6,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,6,9],[3,4,7,8,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,6,8],[3,4,7,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,6,7],[3,4,8,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,7,9],[3,5,6,8,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,7,8],[3,5,6,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,6,9],[3,5,7,8,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,6,8],[3,5,7,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,6,7],[3,5,8,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,9],[3,6,7,8,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,8],[3,6,7,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,7],[3,6,8,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,6],[3,7,8,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,7,9],[4,5,6,8,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,7,8],[4,5,6,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,6,9],[4,5,7,8,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,6,8],[4,5,7,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,6,7],[4,5,8,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,9],[4,6,7,8,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,8],[4,6,7,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,7],[4,6,8,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,6],[4,7,8,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,9],[5,6,7,8,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,8],[5,6,7,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,7],[5,6,8,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,6],[5,7,8,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,5],[6,7,8,9,10]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,7,9,11],[2,4,6,8,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,7,9,10],[2,4,6,8,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,7,8,11],[2,4,6,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,7,8,10],[2,4,6,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,7,8,9],[2,4,6,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,6,9,11],[2,4,7,8,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,6,9,10],[2,4,7,8,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,6,8,11],[2,4,7,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,6,8,10],[2,4,7,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,6,8,9],[2,4,7,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,6,7,11],[2,4,8,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,6,7,10],[2,4,8,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,6,7,9],[2,4,8,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,5,6,7,8],[2,4,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,7,9,11],[2,5,6,8,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,7,9,10],[2,5,6,8,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,7,8,11],[2,5,6,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,7,8,10],[2,5,6,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,7,8,9],[2,5,6,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,6,9,11],[2,5,7,8,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,6,9,10],[2,5,7,8,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,6,8,11],[2,5,7,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,6,8,10],[2,5,7,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,6,8,9],[2,5,7,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,6,7,11],[2,5,8,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,6,7,10],[2,5,8,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,6,7,9],[2,5,8,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,6,7,8],[2,5,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,9,11],[2,6,7,8,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,9,10],[2,6,7,8,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,8,11],[2,6,7,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,8,10],[2,6,7,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,8,9],[2,6,7,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,7,11],[2,6,8,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,7,10],[2,6,8,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,7,9],[2,6,8,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,7,8],[2,6,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,6,11],[2,7,8,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,6,10],[2,7,8,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,6,9],[2,7,8,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,6,8],[2,7,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,6,7],[2,8,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,7,9,11],[3,4,6,8,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,7,9,10],[3,4,6,8,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,7,8,11],[3,4,6,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,7,8,10],[3,4,6,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,7,8,9],[3,4,6,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,6,9,11],[3,4,7,8,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,6,9,10],[3,4,7,8,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,6,8,11],[3,4,7,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,6,8,10],[3,4,7,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,6,8,9],[3,4,7,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,6,7,11],[3,4,8,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,6,7,10],[3,4,8,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,6,7,9],[3,4,8,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,5,6,7,8],[3,4,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,7,9,11],[3,5,6,8,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,7,9,10],[3,5,6,8,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,7,8,11],[3,5,6,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,7,8,10],[3,5,6,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,7,8,9],[3,5,6,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,6,9,11],[3,5,7,8,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,6,9,10],[3,5,7,8,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,6,8,11],[3,5,7,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,6,8,10],[3,5,7,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,6,8,9],[3,5,7,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,6,7,11],[3,5,8,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,6,7,10],[3,5,8,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,6,7,9],[3,5,8,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,6,7,8],[3,5,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,9,11],[3,6,7,8,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,9,10],[3,6,7,8,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,8,11],[3,6,7,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,8,10],[3,6,7,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,8,9],[3,6,7,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,7,11],[3,6,8,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,7,10],[3,6,8,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,7,9],[3,6,8,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,7,8],[3,6,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,6,11],[3,7,8,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,6,10],[3,7,8,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,6,9],[3,7,8,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,6,8],[3,7,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5,6,7],[3,8,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,7,9,11],[4,5,6,8,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,7,9,10],[4,5,6,8,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,7,8,11],[4,5,6,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,7,8,10],[4,5,6,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,7,8,9],[4,5,6,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,6,9,11],[4,5,7,8,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,6,9,10],[4,5,7,8,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,6,8,11],[4,5,7,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,6,8,10],[4,5,7,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,6,8,9],[4,5,7,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,6,7,11],[4,5,8,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,6,7,10],[4,5,8,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,6,7,9],[4,5,8,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,6,7,8],[4,5,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,9,11],[4,6,7,8,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,9,10],[4,6,7,8,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,8,11],[4,6,7,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,8,10],[4,6,7,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,8,9],[4,6,7,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,7,11],[4,6,8,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,7,10],[4,6,8,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,7,9],[4,6,8,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,7,8],[4,6,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,6,11],[4,7,8,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,6,10],[4,7,8,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,6,9],[4,7,8,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,6,8],[4,7,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,5,6,7],[4,8,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,9,11],[5,6,7,8,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,9,10],[5,6,7,8,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,8,11],[5,6,7,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,8,10],[5,6,7,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,8,9],[5,6,7,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,7,11],[5,6,8,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,7,10],[5,6,8,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,7,9],[5,6,8,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,7,8],[5,6,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,6,11],[5,7,8,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,6,10],[5,7,8,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,6,9],[5,7,8,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,6,8],[5,7,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,6,7],[5,8,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,5,11],[6,7,8,9,10,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,5,10],[6,7,8,9,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,5,9],[6,7,8,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,5,8],[6,7,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,5,7],[6,8,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,5,6],[7,8,9,10,11,12]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,5,6],[7,8,9]] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,4,5],[6,7,8,9]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,5],[6,7,8],[9]] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,3,4,5],[6,7],[8,9]] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,4],[5,6,7,8],[9]] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 3
[[1,2,3,4],[5,6,7],[8,9]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,3],[4,5,6],[7,8,9]] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 5
[[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 4
[[1,2,3],[4,5,6],[7],[8],[9]] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,3],[4,5],[6,7],[8,9]] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,2],[3,4],[5,6],[7,8],[9]] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 4
[[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4
[[1,2,3,4,5,6],[7,8,9,10]] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,5],[6,7,8,9],[10]] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
[[1,2,3,4,5],[6,7,8],[9,10]] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,3,4],[5,6,7,8],[9,10]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[[1,2,3,4],[5,6,7,8],[9],[10]] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,3,4],[5,6,7],[8,9,10]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[[1,2,3,4],[5,6,7],[8,9],[10]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[[1,2,3,4],[5,6],[7,8],[9,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3],[4,5,6],[7,8,9],[10]] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[[1,2,3],[4,5,6],[7,8],[9,10]] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 4
[[1,2,3],[4,5,6],[7,8],[9],[10]] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 4
[[1,2,3],[4,5],[6,7],[8,9],[10]] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[[1,2],[3,4],[5,6],[7,8],[9,10]] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 4
[[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4
[[1,2,3,7,8,9],[4,5,6]] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,3,4,9],[5,6,7,8]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[1,3,4,8,9],[2,6,7],[5]] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,7,8,9],[3,4],[5,6]] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4,5],[2,7,8,9],[6]] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 3
[[1,2,5,9],[3,4,8],[6,7]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[[1,4,5,9],[2,7,8],[3],[6]] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,3,8,9],[2,5],[4,7],[6]] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,3,6],[2,5,9],[4,8],[7]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 4
[[1,5,6],[2,8,9],[3],[4],[7]] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[[1,2,9],[3,4],[5,6],[7,8]] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,4,9],[2,6],[3,8],[5],[7]] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,3],[2,5],[4,7],[6,9],[8]] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 4
[[1,5],[2,7],[3,9],[4],[6],[8]] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4
[[1,2,3,4,9,10],[5,6,7,8]] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[1,3,4,5,10],[2,7,8,9],[6]] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
[[1,2,5,9,10],[3,4,8],[6,7]] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,5,6],[3,4,9,10],[7,8]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[[1,4,5,6],[2,8,9,10],[3],[7]] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,3,10],[4,5,6],[7,8,9]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[[1,3,6,10],[2,5,9],[4,8],[7]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[[1,2,9,10],[3,4],[5,6],[7,8]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,3,4],[2,6,7],[5,9,10],[8]] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[[1,2,7],[3,4,10],[5,6],[8,9]] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 4
[[1,4,7],[2,6,10],[3,9],[5],[8]] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 4
[[1,3,10],[2,5],[4,7],[6,9],[8]] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[[1,4],[2,6],[3,8],[5,10],[7],[9]] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4
[[1,2,5],[3,6],[4,7],[8],[9]] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,2,6],[3,7],[4,8],[5,9]] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3,6],[4,7],[5,8],[9]] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,4,6],[3,5,7],[8],[9]] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,4,7],[3,5,8],[6,9]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,3,4,7],[5,8],[6,9]] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,5,7],[4,6,8],[9]] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,6,8],[3,5,7,9]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,6,8],[5,7,9]] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,6],[3,7],[4,8],[5,9],[10]] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[[1,2,3,7],[4,8],[5,9],[6,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,4,7],[3,5,8],[6,9],[10]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[[1,2,5,8],[3,6,9],[4,7,10]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[[1,2,3,5,8],[4,6,9],[7,10]] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,4,6,8],[3,5,7,9],[10]] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
[[1,2,3,5,7,9],[4,6,8,10]] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[1,2,3,4,9],[5,6],[7,8]] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,7,9],[3,6,8],[4]] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,6,8,10],[3,5,7,9]] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[1,2,4,5],[3,7],[6,9],[8]] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,3,5,7,9],[4,6,8]] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,4,5],[3,8],[6,9],[7,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,7],[3,8],[4,9],[5],[6]] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,2,6,9],[3,7],[4,8],[5]] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,6,8],[3,7,9],[4],[5]] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,2,5,8],[3,6,9],[4,7]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,5,8,9],[3,6],[4,7]] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[1,2,4,6,8,9],[3,5,7]] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[1,2,7],[3,8],[4,9],[5,10],[6]] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[[1,2,6,10],[3,7],[4,8],[5,9]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,6,9],[3,7,10],[4,8],[5]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[[1,2,5,8,10],[3,6,9],[4,7]] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,5,7,9],[3,6,8,10],[4]] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
[[1,2,3,4],[5,6],[7,9],[8,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3,4],[5,7],[6,8],[9,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3,4],[5,7],[6,9],[8,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3,4],[5,8],[6,9],[7,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3,5],[4,6],[7,8],[9,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3,5],[4,6],[7,9],[8,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3,5],[4,7],[6,8],[9,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3,5],[4,7],[6,9],[8,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3,5],[4,8],[6,9],[7,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3,6],[4,7],[5,8],[9,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3,6],[4,7],[5,9],[8,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3,6],[4,8],[5,9],[7,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,4,6],[3,5],[7,8],[9,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,4,6],[3,5],[7,9],[8,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,4,7],[3,5],[6,8],[9,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,4,7],[3,5],[6,9],[8,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,4,8],[3,5],[6,9],[7,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,4,5],[3,6],[7,8],[9,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,4,5],[3,6],[7,9],[8,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,4,5],[3,7],[6,8],[9,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,4,5],[3,7],[6,9],[8,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,4,6],[3,7],[5,8],[9,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,4,6],[3,7],[5,9],[8,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,4,6],[3,8],[5,9],[7,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,4,7],[3,8],[5,9],[6,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,5,8],[3,6],[4,7],[9,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,5,9],[3,6],[4,7],[8,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,5,7],[3,6],[4,8],[9,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,5,7],[3,6],[4,9],[8,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,5,8],[3,6],[4,9],[7,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,5,6],[3,7],[4,8],[9,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,5,6],[3,7],[4,9],[8,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,5,6],[3,8],[4,9],[7,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,5,7],[3,8],[4,9],[6,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,6,9],[3,7],[4,8],[5,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,6,8],[3,7],[4,9],[5,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,6,7],[3,8],[4,9],[5,10]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[1,2,3,7],[4,8],[5,9],[6]] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[1,2,3,5,8],[4,6,9],[7]] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[1,2,4,8],[3,5,9],[6,10],[7]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[[1,2,3,6,9],[4,7,10],[5,8]] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4
[[1,2,4,6,9],[3,5,7,10],[8]] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
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Generating function
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Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3 1,7,2 1,15,10 1,31,39,5 1,63,133,35
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + 3\ q^{2}$
$F_{4} = q + 7\ q^{2} + 2\ q^{3}$
$F_{5} = q + 15\ q^{2} + 10\ q^{3}$
$F_{6} = q + 31\ q^{2} + 39\ q^{3} + 5\ q^{4}$
$F_{7} = q + 63\ q^{2} + 133\ q^{3} + 35\ q^{4}$
Description
Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path.
Map
shape
Description
Sends a tableau to its shape.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
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