Identifier
-
Mp00128:
Set partitions
—to composition⟶
Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
St000161: Binary trees ⟶ ℤ
Values
{{1}} => [1] => [1,0] => [.,.] => 0
{{1,2}} => [2] => [1,1,0,0] => [[.,.],.] => 0
{{1},{2}} => [1,1] => [1,0,1,0] => [.,[.,.]] => 1
{{1,2,3}} => [3] => [1,1,1,0,0,0] => [[[.,.],.],.] => 0
{{1,2},{3}} => [2,1] => [1,1,0,0,1,0] => [[.,.],[.,.]] => 1
{{1,3},{2}} => [2,1] => [1,1,0,0,1,0] => [[.,.],[.,.]] => 1
{{1},{2,3}} => [1,2] => [1,0,1,1,0,0] => [.,[[.,.],.]] => 2
{{1},{2},{3}} => [1,1,1] => [1,0,1,0,1,0] => [.,[.,[.,.]]] => 3
{{1,2,3,4}} => [4] => [1,1,1,1,0,0,0,0] => [[[[.,.],.],.],.] => 0
{{1,2,3},{4}} => [3,1] => [1,1,1,0,0,0,1,0] => [[[.,.],.],[.,.]] => 1
{{1,2,4},{3}} => [3,1] => [1,1,1,0,0,0,1,0] => [[[.,.],.],[.,.]] => 1
{{1,2},{3,4}} => [2,2] => [1,1,0,0,1,1,0,0] => [[.,.],[[.,.],.]] => 2
{{1,2},{3},{4}} => [2,1,1] => [1,1,0,0,1,0,1,0] => [[.,.],[.,[.,.]]] => 3
{{1,3,4},{2}} => [3,1] => [1,1,1,0,0,0,1,0] => [[[.,.],.],[.,.]] => 1
{{1,3},{2,4}} => [2,2] => [1,1,0,0,1,1,0,0] => [[.,.],[[.,.],.]] => 2
{{1,3},{2},{4}} => [2,1,1] => [1,1,0,0,1,0,1,0] => [[.,.],[.,[.,.]]] => 3
{{1,4},{2,3}} => [2,2] => [1,1,0,0,1,1,0,0] => [[.,.],[[.,.],.]] => 2
{{1},{2,3,4}} => [1,3] => [1,0,1,1,1,0,0,0] => [.,[[[.,.],.],.]] => 3
{{1},{2,3},{4}} => [1,2,1] => [1,0,1,1,0,0,1,0] => [.,[[.,.],[.,.]]] => 4
{{1,4},{2},{3}} => [2,1,1] => [1,1,0,0,1,0,1,0] => [[.,.],[.,[.,.]]] => 3
{{1},{2,4},{3}} => [1,2,1] => [1,0,1,1,0,0,1,0] => [.,[[.,.],[.,.]]] => 4
{{1},{2},{3,4}} => [1,1,2] => [1,0,1,0,1,1,0,0] => [.,[.,[[.,.],.]]] => 5
{{1},{2},{3},{4}} => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [.,[.,[.,[.,.]]]] => 6
{{1,2,3,4,5}} => [5] => [1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],.] => 0
{{1,2,3,4},{5}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,.]] => 1
{{1,2,3,5},{4}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,.]] => 1
{{1,2,3},{4,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,.],.]] => 2
{{1,2,3},{4},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,.]]] => 3
{{1,2,4,5},{3}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,.]] => 1
{{1,2,4},{3,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,.],.]] => 2
{{1,2,4},{3},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,.]]] => 3
{{1,2,5},{3,4}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,.],.]] => 2
{{1,2},{3,4,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],.]] => 3
{{1,2},{3,4},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => 4
{{1,2,5},{3},{4}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,.]]] => 3
{{1,2},{3,5},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => 4
{{1,2},{3},{4,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => 5
{{1,2},{3},{4},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,.]]]] => 6
{{1,3,4,5},{2}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,.]] => 1
{{1,3,4},{2,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,.],.]] => 2
{{1,3,4},{2},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,.]]] => 3
{{1,3,5},{2,4}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,.],.]] => 2
{{1,3},{2,4,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],.]] => 3
{{1,3},{2,4},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => 4
{{1,3,5},{2},{4}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,.]]] => 3
{{1,3},{2,5},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => 4
{{1,3},{2},{4,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => 5
{{1,3},{2},{4},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,.]]]] => 6
{{1,4,5},{2,3}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,.],.]] => 2
{{1,4},{2,3,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],.]] => 3
{{1,4},{2,3},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => 4
{{1,5},{2,3,4}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],.]] => 3
{{1},{2,3,4,5}} => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],.]] => 4
{{1},{2,3,4},{5}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[.,.]]] => 5
{{1,5},{2,3},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => 4
{{1},{2,3,5},{4}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[.,.]]] => 5
{{1},{2,3},{4,5}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],.]]] => 6
{{1},{2,3},{4},{5}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[.,[.,.]]]] => 7
{{1,4,5},{2},{3}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,.]]] => 3
{{1,4},{2,5},{3}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => 4
{{1,4},{2},{3,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => 5
{{1,4},{2},{3},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,.]]]] => 6
{{1,5},{2,4},{3}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => 4
{{1},{2,4,5},{3}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[.,.]]] => 5
{{1},{2,4},{3,5}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],.]]] => 6
{{1},{2,4},{3},{5}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[.,[.,.]]]] => 7
{{1,5},{2},{3,4}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => 5
{{1},{2,5},{3,4}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],.]]] => 6
{{1},{2},{3,4,5}} => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => 7
{{1},{2},{3,4},{5}} => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,.],[.,.]]]] => 8
{{1,5},{2},{3},{4}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,.]]]] => 6
{{1},{2,5},{3},{4}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[.,[.,.]]]] => 7
{{1},{2},{3,5},{4}} => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,.],[.,.]]]] => 8
{{1},{2},{3},{4,5}} => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],.]]]] => 9
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => 10
{{1,2,3,4,5,6}} => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[.,.],.],.],.],.],.] => 0
{{1,2,3,4,5},{6}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,.]] => 1
{{1,2,3,4,6},{5}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,.]] => 1
{{1,2,3,4},{5,6}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 2
{{1,2,3,4},{5},{6}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => 3
{{1,2,3,5,6},{4}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,.]] => 1
{{1,2,3,5},{4,6}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 2
{{1,2,3,5},{4},{6}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => 3
{{1,2,3,6},{4,5}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 2
{{1,2,3},{4,5,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
{{1,2,3},{4,5},{6}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,2,3,6},{4},{5}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => 3
{{1,2,3},{4,6},{5}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,2,3},{4},{5,6}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 5
{{1,2,3},{4},{5},{6}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => 6
{{1,2,4,5,6},{3}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,.]] => 1
{{1,2,4,5},{3,6}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 2
{{1,2,4,5},{3},{6}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => 3
{{1,2,4,6},{3,5}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 2
{{1,2,4},{3,5,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
{{1,2,4},{3,5},{6}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,2,4,6},{3},{5}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => 3
{{1,2,4},{3,6},{5}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,2,4},{3},{5,6}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 5
{{1,2,4},{3},{5},{6}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => 6
{{1,2,5,6},{3,4}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 2
>>> Load all 796 entries. <<<{{1,2,5},{3,4,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
{{1,2,5},{3,4},{6}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,2,6},{3,4,5}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
{{1,2},{3,4,5,6}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],.]] => 4
{{1,2},{3,4,5},{6}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1,2,6},{3,4},{5}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,2},{3,4,6},{5}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1,2},{3,4},{5,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1,2},{3,4},{5},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1,2,5,6},{3},{4}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => 3
{{1,2,5},{3,6},{4}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,2,5},{3},{4,6}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 5
{{1,2,5},{3},{4},{6}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => 6
{{1,2,6},{3,5},{4}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,2},{3,5,6},{4}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1,2},{3,5},{4,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1,2},{3,5},{4},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1,2,6},{3},{4,5}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 5
{{1,2},{3,6},{4,5}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1,2},{3},{4,5,6}} => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => 7
{{1,2},{3},{4,5},{6}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => 8
{{1,2,6},{3},{4},{5}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => 6
{{1,2},{3,6},{4},{5}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1,2},{3},{4,6},{5}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => 8
{{1,2},{3},{4},{5,6}} => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 9
{{1,2},{3},{4},{5},{6}} => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 10
{{1,3,4,5,6},{2}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,.]] => 1
{{1,3,4,5},{2,6}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 2
{{1,3,4,5},{2},{6}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => 3
{{1,3,4,6},{2,5}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 2
{{1,3,4},{2,5,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
{{1,3,4},{2,5},{6}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,3,4,6},{2},{5}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => 3
{{1,3,4},{2,6},{5}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,3,4},{2},{5,6}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 5
{{1,3,4},{2},{5},{6}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => 6
{{1,3,5,6},{2,4}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 2
{{1,3,5},{2,4,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
{{1,3,5},{2,4},{6}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,3,6},{2,4,5}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
{{1,3},{2,4,5,6}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],.]] => 4
{{1,3},{2,4,5},{6}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1,3,6},{2,4},{5}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,3},{2,4,6},{5}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1,3},{2,4},{5,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1,3},{2,4},{5},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1,3,5,6},{2},{4}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => 3
{{1,3,5},{2,6},{4}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,3,5},{2},{4,6}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 5
{{1,3,5},{2},{4},{6}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => 6
{{1,3,6},{2,5},{4}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,3},{2,5,6},{4}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1,3},{2,5},{4,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1,3},{2,5},{4},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1,3,6},{2},{4,5}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 5
{{1,3},{2,6},{4,5}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1,3},{2},{4,5,6}} => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => 7
{{1,3},{2},{4,5},{6}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => 8
{{1,3,6},{2},{4},{5}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => 6
{{1,3},{2,6},{4},{5}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1,3},{2},{4,6},{5}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => 8
{{1,3},{2},{4},{5,6}} => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 9
{{1,3},{2},{4},{5},{6}} => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 10
{{1,4,5,6},{2,3}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 2
{{1,4,5},{2,3,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
{{1,4,5},{2,3},{6}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,4,6},{2,3,5}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
{{1,4},{2,3,5,6}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],.]] => 4
{{1,4},{2,3,5},{6}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1,4,6},{2,3},{5}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,4},{2,3,6},{5}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1,4},{2,3},{5,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1,4},{2,3},{5},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1,5,6},{2,3,4}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
{{1,5},{2,3,4,6}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],.]] => 4
{{1,5},{2,3,4},{6}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1,6},{2,3,4,5}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],.]] => 4
{{1},{2,3,4,5,6}} => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[[[.,.],.],.],.],.]] => 5
{{1},{2,3,4,5},{6}} => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[[.,.],.],.],[.,.]]] => 6
{{1,6},{2,3,4},{5}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1},{2,3,4,6},{5}} => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[[.,.],.],.],[.,.]]] => 6
{{1},{2,3,4},{5,6}} => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => 7
{{1},{2,3,4},{5},{6}} => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => 8
{{1,5,6},{2,3},{4}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,5},{2,3,6},{4}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1,5},{2,3},{4,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1,5},{2,3},{4},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1,6},{2,3,5},{4}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1},{2,3,5,6},{4}} => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[[.,.],.],.],[.,.]]] => 6
{{1},{2,3,5},{4,6}} => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => 7
{{1},{2,3,5},{4},{6}} => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => 8
{{1,6},{2,3},{4,5}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1},{2,3,6},{4,5}} => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => 7
{{1},{2,3},{4,5,6}} => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => 8
{{1},{2,3},{4,5},{6}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => 9
{{1,6},{2,3},{4},{5}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1},{2,3,6},{4},{5}} => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => 8
{{1},{2,3},{4,6},{5}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => 9
{{1},{2,3},{4},{5,6}} => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => 10
{{1},{2,3},{4},{5},{6}} => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => 11
{{1,4,5,6},{2},{3}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => 3
{{1,4,5},{2,6},{3}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,4,5},{2},{3,6}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 5
{{1,4,5},{2},{3},{6}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => 6
{{1,4,6},{2,5},{3}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,4},{2,5,6},{3}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1,4},{2,5},{3,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1,4},{2,5},{3},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1,4,6},{2},{3,5}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 5
{{1,4},{2,6},{3,5}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1,4},{2},{3,5,6}} => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => 7
{{1,4},{2},{3,5},{6}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => 8
{{1,4,6},{2},{3},{5}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => 6
{{1,4},{2,6},{3},{5}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1,4},{2},{3,6},{5}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => 8
{{1,4},{2},{3},{5,6}} => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 9
{{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 10
{{1,5,6},{2,4},{3}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 4
{{1,5},{2,4,6},{3}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1,5},{2,4},{3,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1,5},{2,4},{3},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1,6},{2,4,5},{3}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 5
{{1},{2,4,5,6},{3}} => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[[.,.],.],.],[.,.]]] => 6
{{1},{2,4,5},{3,6}} => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => 7
{{1},{2,4,5},{3},{6}} => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => 8
{{1,6},{2,4},{3,5}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1},{2,4,6},{3,5}} => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => 7
{{1},{2,4},{3,5,6}} => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => 8
{{1},{2,4},{3,5},{6}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => 9
{{1,6},{2,4},{3},{5}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1},{2,4,6},{3},{5}} => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => 8
{{1},{2,4},{3,6},{5}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => 9
{{1},{2,4},{3},{5,6}} => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => 10
{{1},{2,4},{3},{5},{6}} => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => 11
{{1,5,6},{2},{3,4}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 5
{{1,5},{2,6},{3,4}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1,5},{2},{3,4,6}} => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => 7
{{1,5},{2},{3,4},{6}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => 8
{{1,6},{2,5},{3,4}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 6
{{1},{2,5,6},{3,4}} => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => 7
{{1},{2,5},{3,4,6}} => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => 8
{{1},{2,5},{3,4},{6}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => 9
{{1,6},{2},{3,4,5}} => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => 7
{{1},{2,6},{3,4,5}} => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => 8
{{1},{2},{3,4,5,6}} => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => 9
{{1},{2},{3,4,5},{6}} => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[[[.,.],.],[.,.]]]] => 10
{{1,6},{2},{3,4},{5}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => 8
{{1},{2,6},{3,4},{5}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => 9
{{1},{2},{3,4,6},{5}} => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[[[.,.],.],[.,.]]]] => 10
{{1},{2},{3,4},{5,6}} => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => 11
{{1},{2},{3,4},{5},{6}} => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,.]]]]] => 12
{{1,5,6},{2},{3},{4}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => 6
{{1,5},{2,6},{3},{4}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1,5},{2},{3,6},{4}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => 8
{{1,5},{2},{3},{4,6}} => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 9
{{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 10
{{1,6},{2,5},{3},{4}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 7
{{1},{2,5,6},{3},{4}} => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => 8
{{1},{2,5},{3,6},{4}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => 9
{{1},{2,5},{3},{4,6}} => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => 10
{{1},{2,5},{3},{4},{6}} => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => 11
{{1,6},{2},{3,5},{4}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => 8
{{1},{2,6},{3,5},{4}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => 9
{{1},{2},{3,5,6},{4}} => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[[[.,.],.],[.,.]]]] => 10
{{1},{2},{3,5},{4,6}} => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => 11
{{1},{2},{3,5},{4},{6}} => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,.]]]]] => 12
{{1,6},{2},{3},{4,5}} => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 9
{{1},{2,6},{3},{4,5}} => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => 10
{{1},{2},{3,6},{4,5}} => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => 11
{{1},{2},{3},{4,5,6}} => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => 12
{{1},{2},{3},{4,5},{6}} => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[.,.]]]]] => 13
{{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 10
{{1},{2,6},{3},{4},{5}} => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => 11
{{1},{2},{3,6},{4},{5}} => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,.]]]]] => 12
{{1},{2},{3},{4,6},{5}} => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[.,.]]]]] => 13
{{1},{2},{3},{4},{5,6}} => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => 14
{{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
{{1,2,3,4,5,6},{7}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,.]] => 1
{{1,2,3,4,5,7},{6}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,.]] => 1
{{1,2,3,4,5},{6,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,2,3,4,5},{6},{7}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,2,3,4,6,7},{5}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,.]] => 1
{{1,2,3,4,6},{5,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,2,3,4,6},{5},{7}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,2,3,4,7},{5,6}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,2,3,4,7},{5},{6}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,2,3,5,6,7},{4}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,.]] => 1
{{1,2,3,5,6},{4,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,2,3,5,6},{4},{7}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,2,3,5,7},{4,6}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,2,3,5,7},{4},{6}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,2,3,6,7},{4,5}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,2,3,6,7},{4},{5}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,2,4,5,6,7},{3}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,.]] => 1
{{1,2,4,5,6},{3,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,2,4,5,6},{3},{7}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,2,4,5,7},{3,6}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,2,4,5,7},{3},{6}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,2,4,6,7},{3,5}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,2,4,6,7},{3},{5}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,2,5,6,7},{3,4}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,2},{3,4,5,6,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => 5
{{1,2},{3,4},{5},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,2,5,6,7},{3},{4}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,2},{3,5},{4},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,2},{3},{4,5},{6,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,2},{3},{4,5},{6},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,2},{3,6},{4},{5},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,2},{3},{4,6},{5,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,2},{3},{4,6},{5},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,2},{3},{4,7},{5,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,2},{3},{4},{5,6,7}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => 12
{{1,2},{3},{4},{5,6},{7}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 13
{{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,2},{3},{4,7},{5},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,2},{3},{4},{5,7},{6}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 13
{{1,2},{3},{4},{5},{6,7}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 14
{{1,2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 15
{{1,3,4,5,6,7},{2}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,.]] => 1
{{1,3,4,5,6},{2,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,3,4,5,6},{2},{7}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,3,4,5,7},{2,6}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,3,4,5,7},{2},{6}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,3,4,6,7},{2,5}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,3,4,6,7},{2},{5}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,3,5,6,7},{2,4}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,3},{2,4,5,6,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => 5
{{1,3},{2,4},{5},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,3,5,6,7},{2},{4}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,3},{2,5},{4},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,3},{2},{4,5},{6,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,3},{2},{4,5},{6},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,3},{2},{4,6},{5,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,3},{2},{4,6},{5},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,3},{2},{4,7},{5,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,3},{2},{4},{5,6,7}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => 12
{{1,3},{2},{4},{5,6},{7}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 13
{{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,3},{2},{4,7},{5},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,3},{2},{4},{5,7},{6}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 13
{{1,3},{2},{4},{5},{6,7}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 14
{{1,3},{2},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 15
{{1,4,5,6,7},{2,3}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
{{1,4},{2,3,5,6,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => 5
{{1,4},{2,3},{5},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,5},{2,3,4,6,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => 5
{{1,6},{2,3,4,5,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => 5
{{1,7},{2,3,4,5,6}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => 5
{{1},{2,3,4,5,6,7}} => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => 6
{{1},{2,3,4,5,6},{7}} => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => 7
{{1},{2,3,4,5,7},{6}} => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => 7
{{1},{2,3,4,6,7},{5}} => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => 7
{{1,5},{2,3},{4},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1},{2,3,5,6,7},{4}} => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => 7
{{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,4,5,6,7},{2},{3}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 3
{{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,4},{2},{3,5},{6,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,4},{2},{3,5},{6},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,4},{2},{3,6},{5,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,4},{2},{3,6},{5},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,4},{2},{3,7},{5,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,4},{2},{3},{5,6,7}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => 12
{{1,4},{2},{3},{5,6},{7}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 13
{{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,4},{2},{3},{5,7},{6}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 13
{{1,4},{2},{3},{5},{6,7}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 14
{{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 15
{{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1},{2,4,5,6,7},{3}} => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => 7
{{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,5},{2},{3,4},{6,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,5},{2},{3,4},{6},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,6},{2},{3,4},{5,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,6},{2},{3,4},{5},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,7},{2},{3,4},{5,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => 12
{{1,5},{2},{3},{4,6},{7}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 13
{{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 13
{{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 14
{{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 15
{{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => 12
{{1,6},{2},{3},{4,5},{7}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 13
{{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 11
{{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => 12
{{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 13
{{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 13
{{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 14
{{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 15
{{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 11
{{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 12
{{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 13
{{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 14
{{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 15
{{1,2},{3,4},{5,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,4},{5,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,3},{5,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,3},{4,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,3},{4,5},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,3},{4,5},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,4},{3,5},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,4},{3,5},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,4},{3,5},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,4},{3,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,5},{3,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,5},{4,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,2},{3,5},{4,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,2},{3,6},{4,5},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,6},{4,5},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,6},{3,5},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,6},{3,4},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,5},{3,4},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,5},{3,4},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,6},{3,4},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,6},{3,4},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,7},{3,4},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,7},{3,4},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,7},{3,5},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,7},{4,5},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,2},{3,7},{4,5},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,2},{3,8},{4,5},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,8},{4,5},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,8},{3,5},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,8},{3,4},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,8},{3,4},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,8},{3,4},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,7},{3,5},{4,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,8},{3,5},{4,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,8},{3,6},{4,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,8},{3,6},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,8},{4,6},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,2},{3,8},{4,6},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,2},{3,7},{4,6},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,7},{4,6},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,7},{3,6},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,7},{3,6},{4,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,7},{3,5},{4,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,6},{3,5},{4,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,6},{3,5},{4,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,5},{3,6},{4,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,5},{3,6},{4,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,5},{3,7},{4,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,2},{3,6},{4,7},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,2},{3,5},{4,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,5},{4,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,4},{3,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,4},{3,7},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,4},{3,6},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,4},{3,6},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,3},{4,6},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,3},{4,6},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,3},{4,7},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,3},{4,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,3},{5,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,4},{5,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,2},{3,4},{5,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,2},{3,4},{5,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,4},{5,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,3},{5,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,3},{4,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,3},{4,8},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,3},{4,8},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,4},{3,8},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,4},{3,8},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,4},{3,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,5},{3,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,5},{4,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,2},{3,5},{4,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,2},{3,6},{4,8},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,6},{4,8},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,6},{3,8},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,6},{3,8},{4,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,5},{3,8},{4,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,5},{3,8},{4,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,5},{3,7},{4,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,6},{3,7},{4,5}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,6},{3,8},{4,5}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,7},{3,8},{4,5}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,7},{3,8},{4,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,7},{3,8},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,7},{4,8},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,2},{3,7},{4,8},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,2},{3,8},{4,7},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,3},{2,8},{4,7},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,8},{3,7},{4,5}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,7},{2,8},{3,6},{4,5}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 12
{{1,6},{2,7},{3,8},{4,9},{5,10}} => [2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => 20
{{1},{2,3,4,5,6,7,8}} => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => 7
{{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 21
{{1,2},{3},{4},{5},{6},{7,8}} => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 20
{{1,2},{3},{4},{5},{6,7},{8}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 19
{{1,2},{3},{4},{5},{6,8},{7}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 19
{{1,2},{3},{4},{5},{6,7,8}} => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 18
{{1,2},{3},{4},{5,6},{7},{8}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 18
{{1,2},{3},{4},{5,8},{6},{7}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 18
{{1,2},{3,4},{5,6,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,2},{3,6,7,8},{4,5}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,2},{3,4,5,6},{7,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,2},{3,8},{4,5,6,7}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,2},{3,4,5,8},{6,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,2},{3,4,5,6,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => 6
{{1,3},{2},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 21
{{1,3},{2},{4},{5},{6},{7,8}} => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 20
{{1,3},{2},{4},{5},{6,8},{7}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 19
{{1,3},{2},{4},{5},{6,7,8}} => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 18
{{1,4},{2},{3},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 21
{{1,4},{2},{3},{5},{6,8},{7}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 19
{{1,4},{2},{3},{5},{6,7,8}} => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 18
{{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 18
{{1,5},{2},{3},{4},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 21
{{1,5},{2},{3},{4},{6},{7,8}} => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 20
{{1,5},{2},{3},{4},{6,7,8}} => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 18
{{1,6},{2},{3},{4},{5},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 21
{{1,6},{2},{3},{4},{5},{7,8}} => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 20
{{1,7},{2},{3},{4},{5},{6},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 21
{{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 21
{{1,8},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 20
{{1,7},{2},{3},{4},{5,6},{8}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 19
{{1,8},{2},{3},{4},{5,6},{7}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 19
{{1,8},{2},{3},{4},{5,7},{6}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 19
{{1,8},{2},{3},{4},{5,6,7}} => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 18
{{1,6},{2},{3},{4,5},{7},{8}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 18
{{1,8},{2},{3},{4,5},{6},{7}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 18
{{1,7},{2},{3},{4,6},{5},{8}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 18
{{1,3,4,5,6,7,8},{2}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 1
{{1,4},{2,3},{5,6,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,6,7,8},{2,3},{4,5}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,4,5,6},{2,3},{7,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,4,5,8},{2,3},{6,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,4,5,6,7,8},{2,3}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,4,5,6,7,8},{3}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 1
{{1,2,3,4},{5,6},{7,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,3,4},{5,8},{6,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,3,4},{5,6,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,6,7,8},{2,5},{3,4}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,5,6,7,8},{3,4}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,3,5,6,7,8},{4}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 1
{{1,6,7,8},{2,3,4,5}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,2,3,6},{4,5},{7,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,8},{2,3,6,7},{4,5}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,2,3,8},{4,5},{6,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,3,6,7,8},{4,5}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,3,4,6,7,8},{5}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 1
{{1,2,3,4,5,6},{7,8}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,7,8},{3,4,5,6}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,8},{2,3,4,7},{5,6}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,2,3,8},{4,7},{5,6}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,3,4,7,8},{5,6}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,3,4,5,7,8},{6}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 1
{{1,2,3,4,5,6,7},{8}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 1
{{1,8},{2,3,4,5,6,7}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => 6
{{1,2,3,8},{4,5,6,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,2,3,4,5,8},{6,7}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,3,4,5,6,8},{7}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 1
{{1,2,3,4,5,6,7,8}} => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],.] => 0
{{1,3,5,6,7,8},{2,4}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,3,4,6,7,8},{2,5}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,4,6,7,8},{3,5}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,3,4,5,7,8},{2,6}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,4,5,7,8},{3,6}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,3,5,7,8},{4,6}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,3,4,5,6,8},{2,7}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,4,5,6,8},{3,7}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,3,5,6,8},{4,7}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,3,4,6,8},{5,7}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,3,4,5,6,7},{2,8}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,4,5,6,7},{3,8}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,3,5,6,7},{4,8}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,3,4,6,7},{5,8}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,2,3,4,5,7},{6,8}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
{{1,3,5,7},{2,4,6,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,2,5,7},{3,4,6,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,3,4,7},{2,5,6,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,2,4,7},{3,5,6,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,2,3,7},{4,5,6,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,3,5,6},{2,4,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,2,5,6},{3,4,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,3,4,6},{2,5,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,2,4,6},{3,5,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,2,3,6},{4,5,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,3,4,5},{2,6,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,2,4,5},{3,6,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,2,3,5},{4,6,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,4,7,8},{2,5},{3,6}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,7,8},{3,5},{4,6}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,6,8},{3,5},{4,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,3,6,8},{2,4},{5,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,4,5,8},{2,6},{3,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,3,5,8},{2,6},{4,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,5,8},{3,6},{4,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,3,4,8},{2,6},{5,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,3,5,8},{2,4},{6,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,4,8},{3,5},{6,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,3,6,7},{2,4},{5,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,6,7},{3,4},{5,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,4,5,7},{2,6},{3,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,3,5,7},{2,6},{4,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,3,4,7},{2,6},{5,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,3,7},{4,6},{5,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,5,7},{3,4},{6,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,3,4,7},{2,5},{6,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,5,6},{3,7},{4,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,3,4,6},{2,7},{5,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,4,6},{3,7},{5,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,3,6},{4,7},{5,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,4,5},{3,7},{6,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,3,5},{4,7},{6,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,3,4},{5,7},{6,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,3,5,6},{2,4},{7,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,3,4,6},{2,5},{7,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,4,6},{3,5},{7,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,4,5},{3,6},{7,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,3,5},{4,6},{7,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,9},{2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 28
{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 36
{{1,2,3,4,5,6,7,8},{9}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 1
{{1},{2,3,4,5,6,7,8,9}} => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => 8
{{1,2,3,4,5,6,7,8,9},{10}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 1
{{1},{2,3,4,5,6,7,8,9,10}} => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => 9
{{1,2,3,4,5,6,7,8,9,10},{11}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 1
{{1},{2,3,4,5,6,7,8,9,10,11}} => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => 10
{{1,3},{2,4,5,6},{7,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,4},{2,3,5,6},{7,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,4},{2,3,5,7},{6,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,3},{2,4,5,7},{6,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,2},{3,4,5,7},{6,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,3},{2,4,5,6,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => 6
{{1,4},{2,3,5,6,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => 6
{{1,5},{2,3,4,6,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => 6
{{1,2},{3,4,6,7},{5,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,3},{2,4,6,7},{5,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,4},{2,3,6,7},{5,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,5},{2,3,6,7},{4,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,3},{2,4},{5,6,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,4},{2,5},{3,6,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,3},{2,5},{4,6,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,2},{3,5},{4,6,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,2},{3,6},{4,5,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,3},{2,6},{4,5,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,4},{2,6},{3,5,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,5},{2,6},{3,4,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,2},{3,5,6,8},{4,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,3},{2,5,6,8},{4,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,4},{2,5,6,8},{3,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,5},{2,4,6,8},{3,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,4,5,8},{2,3,6,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,4,6,7},{2,3,5,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,5,6,7},{2,3,4,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,5},{2,3},{4,6,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,6},{2,4},{3,5,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,6},{2,5},{3,4,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,5,6,8},{2,3,4,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,5},{2},{3},{4,8},{6},{7}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 18
{{1,3},{2,5,7,8},{4,6}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,7},{2,4},{3,5,6,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,4},{2,7},{3,5,6,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,2,3,5},{4,8},{6,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,4,6},{3,8},{5,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,5,6},{3,8},{4,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,3,4,8},{2,5,6,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,3,6,7},{2,4,5,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,5},{2,7},{3,4,6,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 28
{{1,3},{2},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 28
{{1,4},{2},{3},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 28
{{1,5},{2},{3},{4},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 28
{{1,6},{2},{3},{4},{5},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 28
{{1,7},{2},{3},{4},{5},{6},{8},{9}} => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 28
{{1,8},{2},{3},{4},{5},{6},{7},{9}} => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 28
{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 36
{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 36
{{1,4},{2},{3},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 36
{{1,5},{2},{3},{4},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 36
{{1,6},{2},{3},{4},{5},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 36
{{1,7},{2},{3},{4},{5},{6},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 36
{{1,8},{2},{3},{4},{5},{6},{7},{9},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 36
{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 36
{{1,8},{2},{3},{4},{5},{6,7},{9}} => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 26
{{1,9},{2},{3},{4},{5},{6},{7,8}} => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 27
{{1,4,5,7},{2,3,6,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,5},{2,3,6,8},{4,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,7},{2,4,5,8},{3,6}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,6},{2,4,5,8},{3,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,4,5,7},{2,8},{3,6}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,7},{2,5},{3,4,6,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,6},{2,4,5,7},{3,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,3,4,5,6,7,8,9},{2}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 1
{{1,3,4,5,6,7,8,9,10},{2}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 1
{{1,4,5,8},{2,7},{3,6}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,3,4,5,6,7,9},{8}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 1
{{1,2,3,4,5,6,7,8,10},{9}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 1
{{1,2,3,4,5,6,7,8,9,11},{10}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 1
{{1,5,7,8},{2,3,4,6}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,3,6,8},{2,4,5,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,2,6,8},{3,4,5,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,6},{2,3,4,5,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => 6
{{1,5},{2,3,4,8},{6,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,4,7,8},{2,6},{3,5}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,2,3,5,6,7,8,9,10},{4}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 1
{{1,2,3,4,6,7,8,9,10},{5}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 1
{{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}} => [2,2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => 30
{{1,2},{3},{4},{5},{6},{7},{8,9}} => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 27
{{1,7},{2},{3},{4},{5},{6},{8,9}} => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 27
{{1,3,4,5,6,7,8,9,10,11},{2}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 1
{{1,7},{2,3,4,5,6,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => 6
{{1,2,6,7},{3,4,5,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,6},{2,5,7,8},{3,4}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,2,5,8},{3,4,6,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,4,6,8},{2,3,5,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,5},{2,6,7,8},{3,4}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,2,3,4,5,6,8,9},{7}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 1
{{1,2,3,4,5,7,8,9},{6}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 1
{{1,2,3,4,6,7,8,9},{5}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 1
{{1,2,3,5,6,7,8,9},{4}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 1
{{1,2,4,5,6,7,8,9},{3}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 1
{{1,2,3,4,5,6,7,9,10},{8}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 1
{{1,2,3,4,5,6,8,9,10},{7}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 1
{{1,2,3,4,5,7,8,9,10},{6}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 1
{{1,2,4,5,6,7,8,9,10},{3}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 1
{{1,7},{2},{3},{4},{5},{6,8}} => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 20
{{1,6},{2},{3},{4},{5,8},{7}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 19
{{1,5},{2},{3},{4,6},{7},{8}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 18
{{1,6},{2},{3},{4,7},{5},{8}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 18
{{1,8},{2,3,4,6},{5,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,7},{2,3},{4,5,6,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,7},{2,3,5,6},{4,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,4,7,8},{2,3,5,6}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,5,7,8},{2,4},{3,6}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,5,7,8},{2,3},{4,6}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,5,6,8},{2,3},{4,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,3,5,8},{2,7},{4,6}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,4},{2},{3},{5},{6},{7,9},{8}} => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 26
{{1,3},{2},{4},{5},{6},{7},{8,9}} => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 27
{{1,5,6,7},{2,4},{3,8}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,5},{2,3,4,7},{6,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,3,4,6},{2,8},{5,7}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,3},{2,7},{4,5,6,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,3,4,8},{2,7},{5,6}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,7},{2,3,5,8},{4,6}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,2},{3,5,7,8},{4,6}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,5,7,8},{2,6},{3,4}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,5},{2,3,4,6},{7,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,3,6,7},{2,8},{4,5}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,7},{2,6},{3,4,5,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,2},{3,7},{4,5,6,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 10
{{1,7},{2,5,6,8},{3,4}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,6},{2,4,7,8},{3,5}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,2},{3},{4},{5},{6},{7,9},{8}} => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 26
{{1,3},{2},{4},{5},{6},{7,9},{8}} => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 26
{{1,2},{3},{4},{5},{6},{7},{8},{9,10}} => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => 35
{{1,2},{3,4,6,8},{5,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,2,3,4,5,6,7,8,10,11},{9}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 1
{{1,4},{2,3,6,8},{5,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,3,6,8},{2,7},{4,5}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
{{1,9},{2},{3},{4},{5},{6,7},{8}} => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 26
{{1,9},{2},{3},{4},{5},{6,8},{7}} => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 26
{{1,5},{2},{3},{4},{6},{7},{8,9}} => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 27
{{1,3,5,8},{2,4,6,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 4
{{1,2},{3},{4},{5},{6},{7,8},{9}} => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 26
{{1,6},{2,3,5,8},{4,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 8
{{1,2,5,7},{3,8},{4,6}} => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,2,1,1 1,3,3,4,2,1,1 1,4,6,10,9,7,7,4,2,1,1 1,5,10,20,25,26,29,26,20,14,12,7,4,2,1,1
F1=1
F2=1+q
F3=1+2 q+q2+q3
F4=1+3 q+3 q2+4 q3+2 q4+q5+q6
F5=1+4 q+6 q2+10 q3+9 q4+7 q5+7 q6+4 q7+2 q8+q9+q10
F6=1+5 q+10 q2+20 q3+25 q4+26 q5+29 q6+26 q7+20 q8+14 q9+12 q10+7 q11+4 q12+2 q13+q14+q15
Description
The sum of the sizes of the right subtrees of a binary tree.
This statistic corresponds to St000012The area of a Dyck path. under the Tamari Dyck path-binary tree bijection, and to St000018The number of inversions of a permutation. of the 312-avoiding permutation corresponding to the binary tree.
It is also the sum of all heights j of the coordinates (i,j) of the Dyck path corresponding to the binary tree.
This statistic corresponds to St000012The area of a Dyck path. under the Tamari Dyck path-binary tree bijection, and to St000018The number of inversions of a permutation. of the 312-avoiding permutation corresponding to the binary tree.
It is also the sum of all heights j of the coordinates (i,j) of the Dyck path corresponding to the binary tree.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to composition
Description
The integer composition of block sizes of a set partition.
For a set partition of {1,2,…,n}, this is the integer composition of n obtained by sorting the blocks by their minimal element and then taking the block sizes.
For a set partition of {1,2,…,n}, this is the integer composition of n obtained by sorting the blocks by their minimal element and then taking the block sizes.
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path D of semilength n with n>1 may be uniquely decomposed into 1L0R for Dyck paths L,R of respective semilengths n1,n2 with n1+n2=n−1.
This map sends D to the binary tree T consisting of a root node with a left child according to L and a right child according to R and then recursively proceeds.
The base case of the unique Dyck path of semilength 1 is sent to a single node.
A Dyck path D of semilength n with n>1 may be uniquely decomposed into 1L0R for Dyck paths L,R of respective semilengths n1,n2 with n1+n2=n−1.
This map sends D to the binary tree T consisting of a root node with a left child according to L and a right child according to R and then recursively proceeds.
The base case of the unique Dyck path of semilength 1 is sent to a single node.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!