Identifier
-
Mp00183:
Skew partitions
—inner shape⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
St000719: Perfect matchings ⟶ ℤ
Values
[[2,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[2,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[2,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[2,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[3,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[3,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[2,2,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[3,2,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,3,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[2,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[3,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[2,2,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[2,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[2,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[3,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[3,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[3,3,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,2,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,3,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,2,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,3,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[3,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,3,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,3,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[3,2,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[3,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,3,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[3,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[4,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,4],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[3,3,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[4,3,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,4,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[2,2,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,4,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[3,2,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,3,2],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,4,2],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[2,2,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[3,3,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,4,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[3,2,1,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,3,2,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[4,3,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,4,2,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[3,3,3],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,4,3],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[4,3,3],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,4,3],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[2,2,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,3,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[3,3,2,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,4,3,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[3,2,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,3,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[4,3,2,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,4,3,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[2,2,2,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[3,3,3,2],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[3,3,2,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,4,3,2],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[3,2,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,3,3,2],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[4,3,2,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,4,3,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[2,2,2,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[2,2,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[3,3,2,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
>>> Load all 1133 entries. <<<[[4,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[2,1,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[3,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[3,2,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[4,3,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[6,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[6,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[5,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[6,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[6,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[4,3,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,2,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,3,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,2,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[6,3,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[4,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[5,3,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[5,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[6,3,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[4,2,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[4,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[5,3,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[5,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[6,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[4,4],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[6,4],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[3,3,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,4,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,3,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[6,4,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[3,3,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[3,2,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,3,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,4,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[4,2,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,3,2],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[6,4,2],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[3,3,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[3,3,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[3,2,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,3,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,3,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,4,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[4,2,1,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,3,2,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[5,3,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[6,4,2,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[4,3,3],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[5,4,3],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[5,3,3],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[6,4,3],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[3,2,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,3,3,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,3,2,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[5,4,3,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[4,2,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,3,3,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,3,2,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[6,4,3,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[3,2,2,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[4,3,3,2],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[4,3,2,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[5,4,3,2],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[4,2,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[5,3,3,2],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[5,3,2,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[6,4,3,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[3,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[3,2,2,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[4,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[3,2,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[4,3,2,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[5,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[3,1,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[4,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[5,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[4,2,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[5,3,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[6,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[5,5],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[4,4,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,5,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[5,4,1],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[3,3,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,2],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,5,2],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[4,3,2],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,4,2],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[3,3,1,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,2,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[4,4,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,5,2,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[4,3,1,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,4,2,1],[4,1,1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 6
[[5,4,1,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[3,3,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,4,3],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,5,3],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[4,3,3],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,4,3],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[2,2,2,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[3,3,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,4,3,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[4,4,2,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,5,3,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[3,2,2,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,3,3,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[4,3,2,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,4,3,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[5,4,2,1],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[3,3,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,4,3,2],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[4,4,2,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,5,3,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[4,3,2,2],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[5,4,3,2],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 8
[[5,4,2,2],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[2,2,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[3,3,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,4,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[3,3,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,4,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[4,4,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,5,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[3,2,1,1,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,3,2,2,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 6
[[4,3,2,1,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[5,4,3,2,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 9
[[4,3,1,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,4,2,2,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 8
[[5,4,2,1,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[4,4,4],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[5,4,4],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[3,3,3,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,4,4,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[4,4,3,1],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[4,3,3,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,4,4,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[5,4,3,1],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[2,2,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,3,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,4,4,2],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[3,3,2,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,4,3,2],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[3,2,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,3,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,4,4,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[4,3,2,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,4,3,2],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[2,2,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,3,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[3,3,3,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,4,4,2,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[3,3,2,1,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,4,3,2,1],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 8
[[4,4,3,1,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[3,2,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,3,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[4,3,3,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,4,4,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[4,3,2,1,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,4,3,2,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 9
[[5,4,3,1,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[3,3,3,3],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[4,4,3,3],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[4,3,3,3],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[5,4,3,3],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[2,2,2,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[3,3,3,3,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[3,3,3,2,1],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[3,3,2,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,4,3,3,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[4,4,3,2,1],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[3,2,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,3,3,3,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[4,3,3,2,1],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[4,3,2,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,4,3,3,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[5,4,3,2,1],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[3,3,3,2,2],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[3,3,2,2,2],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[4,4,3,2,2],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[3,2,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[4,3,3,2,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[4,3,2,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[5,4,3,2,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[3,3,3,3,2,1],[2,2,2,2,1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 9
[[2,2,2,1,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[3,3,3,2,1,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[4,4,4,3,2,1],[3,3,3,2,1]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 12
[[2,2,1,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,2,2,1,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[4,4,3,3,2,1],[3,3,2,2,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 11
[[3,3,2,1,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,4,3,2,1,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[5,5,4,3,2,1],[4,4,3,2,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 14
[[2,1,1,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,2,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[4,3,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 10
[[3,2,2,1,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,3,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[5,4,4,3,2,1],[4,3,3,2,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 13
[[3,2,1,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[5,4,3,3,2,1],[4,3,2,2,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 12
[[4,3,2,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,4,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[6,5,4,3,2,1],[5,4,3,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 15
[[7,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[6,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[7,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[6,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[6,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[7,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[6,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[7,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,3,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[5,2,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[6,3,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[6,2,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[7,3,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[6,3,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[6,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[7,3,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,2,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[5,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[6,3,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[5,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[6,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[6,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[7,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[4,4],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,4],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[6,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[7,4],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[4,4,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,3,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,4,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,3,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[6,4,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[6,3,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[7,4,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[4,3,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[5,4,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,2,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,3,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[6,4,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,2,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[6,3,2],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[7,4,2],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[4,3,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[4,3,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[5,4,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,2,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,3,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[5,3,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[6,4,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,2,1,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[6,3,2,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[6,3,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[7,4,2,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[5,3,3],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[6,4,3],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[6,3,3],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[7,4,3],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[4,2,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[5,3,3,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[5,3,2,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[6,4,3,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[5,2,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[6,3,3,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[6,3,2,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[7,4,3,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[4,2,2,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[5,3,3,2],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[5,3,2,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[6,4,3,2],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[5,2,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[6,3,3,2],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[6,3,2,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[7,4,3,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[4,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[4,2,2,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[5,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[4,2,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[5,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[5,3,2,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[6,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[4,1,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[5,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[6,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[5,2,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[6,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[6,3,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[7,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[5,5],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[6,5],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[4,4,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,5,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,4,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[6,5,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[6,4,1],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[3,3,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,5,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[4,3,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,4,2],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[6,5,2],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[5,3,2],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[6,4,2],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[3,3,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,4,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,5,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[4,3,1,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,4,2,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[5,4,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[6,5,2,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[5,3,1,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[6,4,2,1],[4,1,1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 6
[[6,4,1,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[3,3,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,3],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[5,5,3],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[4,3,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,4,3],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[6,5,3],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[5,3,3],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[6,4,3],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[3,3,3,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[3,3,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,3,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,4,2,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[5,5,3,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[3,2,2,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,3,3,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,3,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,4,3,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,4,2,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[6,5,3,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[4,2,2,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,3,3,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[5,3,2,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[6,4,3,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[6,4,2,1],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[3,3,2,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[4,4,3,2],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[4,4,2,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[5,5,3,2],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[4,3,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[5,4,3,2],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[5,4,2,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[6,5,3,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[5,3,2,2],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[6,4,3,2],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 8
[[6,4,2,2],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[3,3,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[3,3,2,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[4,4,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[3,3,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[4,4,2,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[5,5,3,2,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[3,2,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,3,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[4,3,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[5,4,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[4,3,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,4,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[5,4,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[6,5,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[4,2,1,1,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,3,2,2,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 6
[[5,3,2,1,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[6,4,3,2,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 9
[[5,3,1,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[6,4,2,2,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 8
[[6,4,2,1,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[5,4,4],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[6,4,4],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[4,3,3,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[5,4,4,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[5,4,3,1],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[5,3,3,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[6,4,4,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[6,4,3,1],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[3,2,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,3,3,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[5,4,4,2],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[4,3,2,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[5,4,3,2],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[4,2,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,3,3,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[6,4,4,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[5,3,2,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[6,4,3,2],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[3,2,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,3,3,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[4,3,3,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[5,4,4,2,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[4,3,2,1,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[5,4,3,2,1],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 8
[[5,4,3,1,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[4,2,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,3,3,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[5,3,3,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[6,4,4,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[5,3,2,1,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[6,4,3,2,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 9
[[6,4,3,1,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[4,3,3,3],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[5,4,3,3],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[5,3,3,3],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[6,4,3,3],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[3,2,2,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[4,3,3,3,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[4,3,3,2,1],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[4,3,2,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[5,4,3,3,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[5,4,3,2,1],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[4,2,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[5,3,3,3,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[5,3,3,2,1],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[5,3,2,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[6,4,3,3,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[6,4,3,2,1],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[4,3,3,2,2],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[4,3,2,2,2],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[5,4,3,2,2],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[4,2,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[5,3,3,2,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[5,3,2,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[6,4,3,2,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[3,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[4,3,3,3,2,1],[2,2,2,2,1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 9
[[3,2,2,1,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[4,3,3,2,1,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[5,4,4,3,2,1],[3,3,3,2,1]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 12
[[3,2,1,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,3,2,2,1,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[5,4,3,3,2,1],[3,3,2,2,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 11
[[4,3,2,1,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[5,4,3,2,1,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[6,5,4,3,2,1],[4,4,3,2,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 14
[[3,1,1,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,2,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[5,3,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 10
[[4,2,2,1,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[5,3,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[6,4,4,3,2,1],[4,3,3,2,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 13
[[4,2,1,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,3,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[6,4,3,3,2,1],[4,3,2,2,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 12
[[5,3,2,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[6,4,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[7,5,4,3,2,1],[5,4,3,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 15
[[5,5,1],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[4,4,2],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,5,2],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[5,4,2],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[4,4,1,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,5,2,1],[4,1,1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 6
[[5,5,1,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[5,4,1,1],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[3,3,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,3],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,5,3],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[4,3,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,4,3],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[3,3,2,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,3,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[4,4,2,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,5,3,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[5,5,2,1],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[4,3,2,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,4,3,1],[4,1,1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 6
[[5,4,2,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[4,4,2,2],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[5,5,3,2],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 8
[[5,5,2,2],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[5,4,2,2],[4,1,1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 6
[[3,3,1,1,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,2,2,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 6
[[4,4,2,1,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[5,5,3,2,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 9
[[4,4,1,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,5,2,2,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 8
[[5,5,2,1,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[4,3,1,1,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,4,2,2,1],[4,1,1,1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 7
[[5,4,2,1,1],[4,1,1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 6
[[5,4,1,1,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[4,4,4],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,5,4],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[5,4,4],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[3,3,3,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,4,4,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[4,4,3,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,5,4,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[5,5,3,1],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[4,3,3,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,4,4,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[5,4,3,1],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[2,2,2,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,4,4,2],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[3,3,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,4,3,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,5,4,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[4,4,2,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,5,3,2],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[3,2,2,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,3,3,2],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[5,4,4,2],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 8
[[4,3,2,2],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,4,3,2],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[5,4,2,2],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[2,2,2,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[3,3,3,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,4,4,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[3,3,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,4,3,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[4,4,3,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,5,4,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[4,4,2,1,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,5,3,2,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 9
[[5,5,3,1,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[3,2,2,1,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,3,3,2,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 6
[[4,3,3,1,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[5,4,4,2,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 9
[[4,3,2,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,4,3,2,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 8
[[5,4,3,1,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[5,4,2,1,1],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[4,4,3,3],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[5,5,3,3],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[5,4,3,3],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 8
[[3,3,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,4,3,3,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[4,4,3,2,1],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[4,4,2,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,5,3,3,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[5,5,3,2,1],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[4,3,2,2,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[5,4,3,3,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 9
[[5,4,3,2,1],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 8
[[5,4,2,2,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[4,4,3,2,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[4,4,2,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[5,5,3,2,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[4,3,2,2,2],[3,1,1,1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 6
[[5,4,3,2,2],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 9
[[5,4,2,2,2],[4,2,1,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 8
[[2,2,1,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[4,4,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 10
[[3,3,2,1,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,4,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[5,5,4,3,2,1],[4,3,3,2,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 13
[[3,3,1,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,4,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[5,5,3,3,2,1],[4,3,2,2,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 12
[[4,4,2,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,5,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[6,6,4,3,2,1],[5,4,3,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 15
[[3,2,1,1,1,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,3,2,2,1,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 6
[[5,4,3,3,2,1],[4,2,2,2,1]] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => 11
[[4,3,2,1,1,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[5,4,3,2,1,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 9
[[6,5,4,3,2,1],[5,3,3,2,1]] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => 14
[[4,3,1,1,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,4,2,2,1,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 8
[[6,5,3,3,2,1],[5,3,2,2,1]] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => 13
[[5,4,2,1,1,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[4,4,4,1],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[5,4,4,1],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[3,3,3,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,4,4,2],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[4,4,3,2],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[4,3,3,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,4,4,2],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[5,4,3,2],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[3,3,3,1,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,4,4,2,1],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 8
[[4,4,4,1,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[4,4,3,1,1],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[4,3,3,1,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,4,4,2,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 9
[[5,4,4,1,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[5,4,3,1,1],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[3,3,3,3],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,4,4,3],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[4,4,3,3],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[4,3,3,3],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,4,4,3],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[5,4,3,3],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[2,2,2,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,3,3,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[3,3,3,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,4,4,3,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[4,4,4,2,1],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[3,3,2,2,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,4,3,3,1],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 8
[[4,4,3,2,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[3,2,2,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,3,3,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[4,3,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,4,4,3,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[5,4,4,2,1],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[4,3,2,2,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,4,3,3,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 9
[[5,4,3,2,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[4,4,4,2,2],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[4,4,3,2,2],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 8
[[4,3,3,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[5,4,4,2,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[5,4,3,2,2],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 9
[[2,2,2,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,3,2,1,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[4,4,4,3,2,1],[3,3,2,2,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 11
[[3,3,3,1,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,4,4,2,1,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[5,5,5,3,2,1],[4,4,3,2,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 14
[[3,3,2,1,1,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,4,3,2,1,1],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 8
[[5,5,4,3,2,1],[4,4,2,2,1]] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => 13
[[4,4,3,1,1,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[3,2,2,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,3,2,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[5,4,4,3,2,1],[4,3,2,2,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 12
[[4,3,3,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,4,4,2,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[6,5,5,3,2,1],[5,4,3,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 15
[[4,3,2,1,1,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,4,3,2,1,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 9
[[6,5,4,3,2,1],[5,4,2,2,1]] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => 14
[[5,4,3,1,1,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[3,3,3,3,1],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[4,4,3,3,1],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[4,3,3,3,1],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[5,4,3,3,1],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[2,2,2,2,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[3,3,3,2,2],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[3,3,2,2,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,4,3,3,2],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[4,4,3,2,2],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[3,2,2,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,3,3,3,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[4,3,3,2,2],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[4,3,2,2,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,4,3,3,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[5,4,3,2,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[3,3,3,3,1,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[4,4,4,4,2,1],[3,3,3,2,1]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 12
[[3,3,3,2,1,1],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[3,3,2,2,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,4,3,3,1,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[5,5,4,4,2,1],[4,4,3,2,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 14
[[4,4,3,2,1,1],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[3,2,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,3,3,3,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[5,4,4,4,2,1],[4,3,3,2,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 13
[[4,3,3,2,1,1],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[4,3,2,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,4,3,3,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[6,5,4,4,2,1],[5,4,3,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 15
[[5,4,3,2,1,1],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[3,3,3,3,3,1],[2,2,2,2,1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 9
[[3,3,3,2,2,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[4,4,4,3,3,1],[3,3,3,2,1]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 12
[[3,3,2,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[4,4,3,3,3,1],[3,3,2,2,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 11
[[4,4,3,2,2,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[5,5,4,3,3,1],[4,4,3,2,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 14
[[3,2,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[4,3,3,3,3,1],[3,2,2,2,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 10
[[4,3,3,2,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[5,4,4,3,3,1],[4,3,3,2,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 13
[[4,3,2,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[5,4,3,3,3,1],[4,3,2,2,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 12
[[5,4,3,2,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[6,5,4,3,3,1],[5,4,3,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 15
[[3,3,3,3,2,2],[2,2,2,2,1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 9
[[4,4,4,3,2,2],[3,3,3,2,1]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 12
[[4,4,3,3,2,2],[3,3,2,2,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 11
[[5,5,4,3,2,2],[4,4,3,2,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 14
[[4,3,3,3,2,2],[3,2,2,2,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 10
[[5,4,4,3,2,2],[4,3,3,2,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 13
[[5,4,3,3,2,2],[4,3,2,2,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 12
[[6,5,4,3,2,2],[5,4,3,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 15
[[2,2,2,2,1,1,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 9
[[2,2,2,1,1,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[3,3,3,2,1,1,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[4,4,4,3,2,1,1],[3,3,3,2,1]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 12
[[2,2,1,1,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,2,2,1,1,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[4,4,3,3,2,1,1],[3,3,2,2,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 11
[[3,3,2,1,1,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,4,3,2,1,1,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[5,5,4,3,2,1,1],[4,4,3,2,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 14
[[2,1,1,1,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,2,2,2,1,1,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[4,3,3,3,2,1,1],[3,2,2,2,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 10
[[3,2,2,1,1,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,3,3,2,1,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[5,4,4,3,2,1,1],[4,3,3,2,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 13
[[3,2,1,1,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,2,2,1,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[5,4,3,3,2,1,1],[4,3,2,2,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 12
[[4,3,2,1,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,4,3,2,1,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[6,5,4,3,2,1,1],[5,4,3,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 15
[[2,2,1,1,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[2,2,2,1,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,2,1,1,1,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[3,2,2,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,2,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,1,1,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[2,2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,3,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,4,2,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[4,3,3,1,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,4,3,1,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,3,1,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[4,3,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,4,2,2,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[4,3,3,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,4,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,3,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,4,4,2,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[5,4,2,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[4,3,3,3,1],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[4,4,3,3,1],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[5,3,3,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,4,4,3,1],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[5,4,3,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,5,3,1],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[5,4,4,1],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[5,5,4,1],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[6,4,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 6
[[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[5,3,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 8
[[5,4,2,2],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 9
[[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[5,3,3,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[5,4,3,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,5,3,2],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[5,4,4,2],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[5,5,4,2],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[6,4,2],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[6,5,2],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[5,3,3,3],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[5,4,3,3],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[5,5,3,3],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 8
[[5,4,4,3],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[5,5,4,3],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[6,4,3],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[6,5,3],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[6,4,4],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[6,5,4],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[7,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[3,3,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,2,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[2,2,2,2,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[3,3,3,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[4,4,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,4],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[5,5],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[3,3,3,3],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,3,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,3,3],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[4,4,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,4],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,4],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,5],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[3,3,3,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[2,2,2,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,2,2,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,2,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[3,3,2,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[2,2,2,2,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[3,3,3,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,3],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,3,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[4,4,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[3,3,3,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[4,4,4],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,4],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[3,3,3,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,3,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4,1],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,4,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,3,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[6,6],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[5,5,5],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 7
[[6,5],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,5,5],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[6,6],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[4,4,4,4],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[6,4],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,5,4],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[4,4,4,4],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[5,4,4],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,4,4,4],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[5,5,4],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[5,5,5],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[6,5],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,5,5],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[6,6],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,5,5],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[3,3,3,3,3],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 7
[[6,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,5,3],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,4,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,4,4,3],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[5,5,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[3,3,3,3,3],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[5,3,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,3,3],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[3,3,3,3,3],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[[4,3,3,3],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[3,3,3,3,3],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[4,4,3,3],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[5,4,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,4,3],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[5,5,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,4,3],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[4,4,4,4],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[6,4],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,5,4],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[4,4,4,4],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,4,4],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,4,4,4],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[5,5,4],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,5,5],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[6,5],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,5,5],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[6,6],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,5,5],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,4,4,4],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 5
[[5,4,4],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,4,4],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[5,5,4],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,4,4],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[5,5,5],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[5,5,2],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,4,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,4,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[5,5,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,3,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,3,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,3,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,3,3,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[4,4,3,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[5,4,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,5,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[2,2,2,2,2,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[4,4,2,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,3,2,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,2,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[2,2,2,2,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,2,2,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,2,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,3,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,3,3,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,3,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,3,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4,2],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[4,4,4,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,4,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,3,2],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[3,3,3,3,2],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,3,3],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 6
[[5,5,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,4,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,4,3],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[5,5,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[3,3,3,3,3],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 5
[[5,3,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,3,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[3,3,3,3,3],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 4
[[4,3,3,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[3,3,3,3,3],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[4,4,3,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,4,3],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,4,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,5,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,4,4],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 6
[[5,5,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[4,4,4,4],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 5
[[5,4,4],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,4,4],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[5,5,4],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[5,5,5],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[5,5,5],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,5,5],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,4,4],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,4,4],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4,4],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[5,5,4],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4,4],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[5,5,5],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,3,3],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 4
[[4,3,3,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,3,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[4,4,3,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[3,3,3,3,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 3
[[4,3,3,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,3,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[4,4,3,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[4,4,4,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,4,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[3,3,3,3,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[3,3,3,3,3],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[4,4,4,4],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,4,4],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[5,5,5,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[4,4,4,4,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[7,7],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[5,5,5,5],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 9
[[5,5,5,5],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[6,6,6],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 6
[[5,5,5,5],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 8
[[5,5,5,5],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[3,3,3,3,3,3],[2,2,2,2,1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 9
[[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 9
[[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 8
[[5,5,5,5],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 8
[[5,5,5,5],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[5,5,5,5],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 7
[[5,5,5,5],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[4,4,4,4,4],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 8
[[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 7
[[2,2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[3,3,3,3,3,3],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 6
[[4,4,4,4,4],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 8
[[4,4,4,4,4],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 7
[[4,4,4,4,4],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 7
[[4,4,4,4,4],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 6
[[5,5,5,5],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[3,3,3,3,3,3],[2]] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[4,4,4,4,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,5,5,4],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[4,4,4,4,4],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 4
[[5,5,5,5],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[4,4,4,4,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 10
[[5,5,5,5,5],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[5,5,5,5,5,5],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[4,4,4,4,4,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[5,5,5,5,4],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[5,5,5,5,5],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5
[[5,5,5,5,1],[1]] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 1
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Description
The number of alignments in a perfect matching.
An alignment is a pair of edges $(i,j)$, $(k,l)$ such that $i < j < k < l$.
Since any two edges in a perfect matching are either nesting (St000041The number of nestings of a perfect matching.), crossing (St000042The number of crossings of a perfect matching.) or form an alignment, the sum of these numbers in a perfect matching with $n$ edges is $\binom{n}{2}$.
An alignment is a pair of edges $(i,j)$, $(k,l)$ such that $i < j < k < l$.
Since any two edges in a perfect matching are either nesting (St000041The number of nestings of a perfect matching.), crossing (St000042The number of crossings of a perfect matching.) or form an alignment, the sum of these numbers in a perfect matching with $n$ edges is $\binom{n}{2}$.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
inner shape
Description
The inner shape of a skew partition.
Map
to tunnel matching
Description
Sends a Dyck path of semilength n to the noncrossing perfect matching given by matching an up-step with the corresponding down-step.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.
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