- FindStat

Identifier

Mp00080: Set partitions —to permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
St000026: Dyck paths ⟶ ℤ

Values

{{1}} => [1] => [.,.] => [1,0] => 1

{{1,2}} => [2,1] => [[.,.],.] => [1,1,0,0] => 2

{{1},{2}} => [1,2] => [.,[.,.]] => [1,0,1,0] => 1

{{1,2,3}} => [2,3,1] => [[.,[.,.]],.] => [1,1,0,1,0,0] => 3

{{1,2},{3}} => [2,1,3] => [[.,.],[.,.]] => [1,1,0,0,1,0] => 2

{{1,3},{2}} => [3,2,1] => [[[.,.],.],.] => [1,1,1,0,0,0] => 3

{{1},{2,3}} => [1,3,2] => [.,[[.,.],.]] => [1,0,1,1,0,0] => 1

{{1},{2},{3}} => [1,2,3] => [.,[.,[.,.]]] => [1,0,1,0,1,0] => 1

{{1,2,3,4}} => [2,3,4,1] => [[.,[.,[.,.]]],.] => [1,1,0,1,0,1,0,0] => 4

{{1,2,3},{4}} => [2,3,1,4] => [[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => 3

{{1,2,4},{3}} => [2,4,3,1] => [[.,[[.,.],.]],.] => [1,1,0,1,1,0,0,0] => 4

{{1,2},{3,4}} => [2,1,4,3] => [[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => 2

{{1,2},{3},{4}} => [2,1,3,4] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => 2

{{1,3,4},{2}} => [3,2,4,1] => [[[.,.],[.,.]],.] => [1,1,1,0,0,1,0,0] => 4

{{1,3},{2,4}} => [3,4,1,2] => [[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => 3

{{1,3},{2},{4}} => [3,2,1,4] => [[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0] => 3

{{1,4},{2,3}} => [4,3,2,1] => [[[[.,.],.],.],.] => [1,1,1,1,0,0,0,0] => 4

{{1},{2,3,4}} => [1,3,4,2] => [.,[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0] => 1

{{1},{2,3},{4}} => [1,3,2,4] => [.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => 1

{{1,4},{2},{3}} => [4,2,3,1] => [[[.,.],[.,.]],.] => [1,1,1,0,0,1,0,0] => 4

{{1},{2,4},{3}} => [1,4,3,2] => [.,[[[.,.],.],.]] => [1,0,1,1,1,0,0,0] => 1

{{1},{2},{3,4}} => [1,2,4,3] => [.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => 1

{{1},{2},{3},{4}} => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 1

{{1,2,3,4,5}} => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,0,0] => 5

{{1,2,3,4},{5}} => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 4

{{1,2,3,5},{4}} => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,0,0] => 5

{{1,2,3},{4,5}} => [2,3,1,5,4] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 3

{{1,2,3},{4},{5}} => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 3

{{1,2,4,5},{3}} => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,1,0,0] => 5

{{1,2,4},{3,5}} => [2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 4

{{1,2,4},{3},{5}} => [2,4,3,1,5] => [[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => 4

{{1,2,5},{3,4}} => [2,5,4,3,1] => [[.,[[[.,.],.],.]],.] => [1,1,0,1,1,1,0,0,0,0] => 5

{{1,2},{3,4,5}} => [2,1,4,5,3] => [[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => 2

{{1,2},{3,4},{5}} => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 2

{{1,2,5},{3},{4}} => [2,5,3,4,1] => [[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,1,0,0] => 5

{{1,2},{3,5},{4}} => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => 2

{{1,2},{3},{4,5}} => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => 2

{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 2

{{1,3,4,5},{2}} => [3,2,4,5,1] => [[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => 5

{{1,3,4},{2,5}} => [3,5,4,1,2] => [[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => 4

{{1,3,4},{2},{5}} => [3,2,4,1,5] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 4

{{1,3,5},{2,4}} => [3,4,5,2,1] => [[[.,[.,[.,.]]],.],.] => [1,1,1,0,1,0,1,0,0,0] => 5

{{1,3},{2,4,5}} => [3,4,1,5,2] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 3

{{1,3},{2,4},{5}} => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 3

{{1,3,5},{2},{4}} => [3,2,5,4,1] => [[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => 5

{{1,3},{2,5},{4}} => [3,5,1,4,2] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 3

{{1,3},{2},{4,5}} => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => 3

{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => 3

{{1,4,5},{2,3}} => [4,3,2,5,1] => [[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => 5

{{1,4},{2,3,5}} => [4,3,5,1,2] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 4

{{1,4},{2,3},{5}} => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0] => 4

{{1,5},{2,3,4}} => [5,3,4,2,1] => [[[[.,.],[.,.]],.],.] => [1,1,1,1,0,0,1,0,0,0] => 5

{{1},{2,3,4,5}} => [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,0,0] => 1

{{1},{2,3,4},{5}} => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => 1

{{1,5},{2,3},{4}} => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => 5

{{1},{2,3,5},{4}} => [1,3,5,4,2] => [.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,0,0] => 1

{{1},{2,3},{4,5}} => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => 1

{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => 1

{{1,4,5},{2},{3}} => [4,2,3,5,1] => [[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => 5

{{1,4},{2,5},{3}} => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0] => 4

{{1,4},{2},{3,5}} => [4,2,5,1,3] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 4

{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 4

{{1,5},{2,4},{3}} => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => [1,1,1,1,1,0,0,0,0,0] => 5

{{1},{2,4,5},{3}} => [1,4,3,5,2] => [.,[[[.,.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => 1

{{1},{2,4},{3,5}} => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => 1

{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0] => 1

{{1,5},{2},{3,4}} => [5,2,4,3,1] => [[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => 5

{{1},{2,5},{3,4}} => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => [1,0,1,1,1,1,0,0,0,0] => 1

{{1},{2},{3,4,5}} => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,0,0] => 1

{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => 1

{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => 5

{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => 1

{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,0,0] => 1

{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => 1

{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1155 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{1,5},{2,4},{3},{6,7}} => [5,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5

{{1,5},{2,4},{3},{6},{7}} => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5

{{1,6,7},{2,4,5},{3}} => [6,4,3,5,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 7

{{1,6},{2,4,5,7},{3}} => [6,4,3,5,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 6

{{1,6},{2,4,5},{3,7}} => [6,4,7,5,2,1,3] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 6

{{1,6},{2,4,5},{3},{7}} => [6,4,3,5,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6

{{1,7},{2,4,5,6},{3}} => [7,4,3,5,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 7

{{1},{2,4,5,6,7},{3}} => [1,4,3,5,6,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1

{{1},{2,4,5,6},{3,7}} => [1,4,7,5,6,2,3] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 1

{{1},{2,4,5,6},{3},{7}} => [1,4,3,5,6,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1

{{1,7},{2,4,5},{3,6}} => [7,4,6,5,2,3,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7

{{1},{2,4,5,7},{3,6}} => [1,4,6,5,7,3,2] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1

{{1},{2,4,5},{3,6,7}} => [1,4,6,5,2,7,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

{{1},{2,4,5},{3,6},{7}} => [1,4,6,5,2,3,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1

{{1,7},{2,4,5},{3},{6}} => [7,4,3,5,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 7

{{1},{2,4,5,7},{3},{6}} => [1,4,3,5,7,6,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

{{1},{2,4,5},{3,7},{6}} => [1,4,7,5,2,6,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

{{1},{2,4,5},{3},{6,7}} => [1,4,3,5,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

{{1},{2,4,5},{3},{6},{7}} => [1,4,3,5,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 1

{{1,6,7},{2,4},{3,5}} => [6,4,5,2,3,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 7

{{1,6},{2,4,7},{3,5}} => [6,4,5,7,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 6

{{1,6},{2,4},{3,5,7}} => [6,4,5,2,7,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 6

{{1,6},{2,4},{3,5},{7}} => [6,4,5,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 6

{{1,7},{2,4,6},{3,5}} => [7,4,5,6,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 7

{{1},{2,4,6,7},{3,5}} => [1,4,5,6,3,7,2] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1

{{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1

{{1},{2,4,6},{3,5},{7}} => [1,4,5,6,3,2,7] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1

{{1,7},{2,4},{3,5,6}} => [7,4,5,2,6,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7

{{1},{2,4,7},{3,5,6}} => [1,4,5,7,6,3,2] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

{{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

{{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1

{{1,7},{2,4},{3,5},{6}} => [7,4,5,2,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 7

{{1},{2,4,7},{3,5},{6}} => [1,4,5,7,3,6,2] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1

{{1},{2,4},{3,5,7},{6}} => [1,4,5,2,7,6,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

{{1},{2,4},{3,5},{6,7}} => [1,4,5,2,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

{{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1

{{1,6,7},{2,4},{3},{5}} => [6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 7

{{1,6},{2,4,7},{3},{5}} => [6,4,3,7,5,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 6

{{1,6},{2,4},{3,7},{5}} => [6,4,7,2,5,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 6

{{1,6},{2,4},{3},{5,7}} => [6,4,3,2,7,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6

{{1,6},{2,4},{3},{5},{7}} => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6

{{1,7},{2,4,6},{3},{5}} => [7,4,3,6,5,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 7

{{1},{2,4,6,7},{3},{5}} => [1,4,3,6,5,7,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

{{1},{2,4,6},{3,7},{5}} => [1,4,7,6,5,2,3] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1

{{1},{2,4,6},{3},{5,7}} => [1,4,3,6,7,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1

{{1},{2,4,6},{3},{5},{7}} => [1,4,3,6,5,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1

{{1,7},{2,4},{3,6},{5}} => [7,4,6,2,5,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7

{{1},{2,4,7},{3,6},{5}} => [1,4,6,7,5,3,2] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

{{1},{2,4},{3,6,7},{5}} => [1,4,6,2,5,7,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

{{1},{2,4},{3,6},{5,7}} => [1,4,6,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1

{{1},{2,4},{3,6},{5},{7}} => [1,4,6,2,5,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1

{{1,7},{2,4},{3},{5,6}} => [7,4,3,2,6,5,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 7

{{1},{2,4,7},{3},{5,6}} => [1,4,3,7,6,5,2] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

{{1},{2,4},{3,7},{5,6}} => [1,4,7,2,6,5,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

{{1},{2,4},{3},{5,6,7}} => [1,4,3,2,6,7,5] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

{{1},{2,4},{3},{5,6},{7}} => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1

{{1,7},{2,4},{3},{5},{6}} => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 7

{{1},{2,4,7},{3},{5},{6}} => [1,4,3,7,5,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

{{1},{2,4},{3,7},{5},{6}} => [1,4,7,2,5,6,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

{{1},{2,4},{3},{5,7},{6}} => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

{{1},{2,4},{3},{5},{6,7}} => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

{{1},{2,4},{3},{5},{6},{7}} => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1

{{1,5,6,7},{2},{3,4}} => [5,2,4,3,6,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 7

{{1,5,6},{2,7},{3,4}} => [5,7,4,3,6,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 6

{{1,5,6},{2},{3,4,7}} => [5,2,4,7,6,1,3] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 6

{{1,5,6},{2},{3,4},{7}} => [5,2,4,3,6,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6

{{1,5,7},{2,6},{3,4}} => [5,6,4,3,7,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 7

{{1,5},{2,6,7},{3,4}} => [5,6,4,3,1,7,2] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 5

{{1,5},{2,6},{3,4,7}} => [5,6,4,7,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

{{1,5},{2,6},{3,4},{7}} => [5,6,4,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 5

{{1,5,7},{2},{3,4,6}} => [5,2,4,6,7,3,1] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 7

{{1,5},{2,7},{3,4,6}} => [5,7,4,6,1,3,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 5

{{1,5},{2},{3,4,6,7}} => [5,2,4,6,1,7,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 5

{{1,5},{2},{3,4,6},{7}} => [5,2,4,6,1,3,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

{{1,5,7},{2},{3,4},{6}} => [5,2,4,3,7,6,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 7

{{1,5},{2,7},{3,4},{6}} => [5,7,4,3,1,6,2] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 5

{{1,5},{2},{3,4,7},{6}} => [5,2,4,7,1,6,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 5

{{1,5},{2},{3,4},{6,7}} => [5,2,4,3,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 5

{{1,5},{2},{3,4},{6},{7}} => [5,2,4,3,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 5

{{1,6,7},{2,5},{3,4}} => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7

{{1,6},{2,5,7},{3,4}} => [6,5,4,3,7,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6

{{1,6},{2,5},{3,4,7}} => [6,5,4,7,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6

{{1,6},{2,5},{3,4},{7}} => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6

{{1,7},{2,5,6},{3,4}} => [7,5,4,3,6,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7

{{1},{2,5,6,7},{3,4}} => [1,5,4,3,6,7,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1

{{1},{2,5,6},{3,4,7}} => [1,5,4,7,6,2,3] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1

{{1},{2,5,6},{3,4},{7}} => [1,5,4,3,6,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 1

{{1,7},{2,5},{3,4,6}} => [7,5,4,6,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 7

{{1},{2,5,7},{3,4,6}} => [1,5,4,6,7,3,2] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1

{{1},{2,5},{3,4,6,7}} => [1,5,4,6,2,7,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

{{1},{2,5},{3,4,6},{7}} => [1,5,4,6,2,3,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 1

{{1,7},{2,5},{3,4},{6}} => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7

{{1},{2,5,7},{3,4},{6}} => [1,5,4,3,7,6,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

{{1},{2,5},{3,4,7},{6}} => [1,5,4,7,2,6,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

{{1},{2,5},{3,4},{6,7}} => [1,5,4,3,2,7,6] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

{{1},{2,5},{3,4},{6},{7}} => [1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1

{{1,6,7},{2},{3,4,5}} => [6,2,4,5,3,7,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 7

{{1,6},{2,7},{3,4,5}} => [6,7,4,5,3,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 6

{{1,6},{2},{3,4,5,7}} => [6,2,4,5,7,1,3] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6

{{1,6},{2},{3,4,5},{7}} => [6,2,4,5,3,1,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 6

{{1,7},{2,6},{3,4,5}} => [7,6,4,5,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7

{{1},{2,6,7},{3,4,5}} => [1,6,4,5,3,7,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1

{{1},{2,6},{3,4,5,7}} => [1,6,4,5,7,2,3] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1

{{1},{2,6},{3,4,5},{7}} => [1,6,4,5,3,2,7] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 1

{{1,7},{2},{3,4,5,6}} => [7,2,4,5,6,3,1] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 7

{{1},{2,7},{3,4,5,6}} => [1,7,4,5,6,3,2] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1

{{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1

{{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1

{{1,7},{2},{3,4,5},{6}} => [7,2,4,5,3,6,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 7

{{1},{2,7},{3,4,5},{6}} => [1,7,4,5,3,6,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1

{{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1

{{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

{{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1

{{1,6,7},{2},{3,4},{5}} => [6,2,4,3,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 7

{{1,6},{2,7},{3,4},{5}} => [6,7,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 6

{{1,6},{2},{3,4,7},{5}} => [6,2,4,7,5,1,3] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 6

{{1,6},{2},{3,4},{5,7}} => [6,2,4,3,7,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6

{{1,6},{2},{3,4},{5},{7}} => [6,2,4,3,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6

{{1,7},{2,6},{3,4},{5}} => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7

{{1},{2,6,7},{3,4},{5}} => [1,6,4,3,5,7,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1

{{1},{2,6},{3,4,7},{5}} => [1,6,4,7,5,2,3] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1

{{1},{2,6},{3,4},{5,7}} => [1,6,4,3,7,2,5] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 1

{{1},{2,6},{3,4},{5},{7}} => [1,6,4,3,5,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 1

{{1,7},{2},{3,4,6},{5}} => [7,2,4,6,5,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 7

{{1},{2,7},{3,4,6},{5}} => [1,7,4,6,5,3,2] => [.,[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

{{1},{2},{3,4,6,7},{5}} => [1,2,4,6,5,7,3] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1

{{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1

{{1},{2},{3,4,6},{5},{7}} => [1,2,4,6,5,3,7] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1

{{1,7},{2},{3,4},{5,6}} => [7,2,4,3,6,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 7

{{1},{2,7},{3,4},{5,6}} => [1,7,4,3,6,5,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

{{1},{2},{3,4,7},{5,6}} => [1,2,4,7,6,5,3] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1

{{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1

{{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1

{{1,7},{2},{3,4},{5},{6}} => [7,2,4,3,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 7

{{1},{2,7},{3,4},{5},{6}} => [1,7,4,3,5,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1

{{1},{2},{3,4,7},{5},{6}} => [1,2,4,7,5,6,3] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1

{{1},{2},{3,4},{5,7},{6}} => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

{{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

{{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1

{{1,5,6,7},{2},{3},{4}} => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 7

{{1,5,6},{2,7},{3},{4}} => [5,7,3,4,6,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 6

{{1,5,6},{2},{3,7},{4}} => [5,2,7,4,6,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6

{{1,5,6},{2},{3},{4,7}} => [5,2,3,7,6,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 6

{{1,5,6},{2},{3},{4},{7}} => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6

{{1,5,7},{2,6},{3},{4}} => [5,6,3,4,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 7

{{1,5},{2,6,7},{3},{4}} => [5,6,3,4,1,7,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 5

{{1,5},{2,6},{3,7},{4}} => [5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5

{{1,5},{2,6},{3},{4,7}} => [5,6,3,7,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

{{1,5},{2,6},{3},{4},{7}} => [5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

{{1,5,7},{2},{3,6},{4}} => [5,2,6,4,7,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7

{{1,5},{2,7},{3,6},{4}} => [5,7,6,4,1,3,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 5

{{1,5},{2},{3,6,7},{4}} => [5,2,6,4,1,7,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 5

{{1,5},{2},{3,6},{4,7}} => [5,2,6,7,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

{{1,5},{2},{3,6},{4},{7}} => [5,2,6,4,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 5

{{1,5,7},{2},{3},{4,6}} => [5,2,3,6,7,4,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 7

{{1,5},{2,7},{3},{4,6}} => [5,7,3,6,1,4,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 5

{{1,5},{2},{3,7},{4,6}} => [5,2,7,6,1,4,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 5

{{1,5},{2},{3},{4,6,7}} => [5,2,3,6,1,7,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 5

{{1,5},{2},{3},{4,6},{7}} => [5,2,3,6,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

{{1,5,7},{2},{3},{4},{6}} => [5,2,3,4,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 7

{{1,5},{2,7},{3},{4},{6}} => [5,7,3,4,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 5

{{1,5},{2},{3,7},{4},{6}} => [5,2,7,4,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 5

{{1,5},{2},{3},{4,7},{6}} => [5,2,3,7,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 5

{{1,5},{2},{3},{4},{6,7}} => [5,2,3,4,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 5

{{1,5},{2},{3},{4},{6},{7}} => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

{{1,6,7},{2,5},{3},{4}} => [6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 7

{{1,6},{2,5,7},{3},{4}} => [6,5,3,4,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 6

{{1,6},{2,5},{3,7},{4}} => [6,5,7,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6

{{1,6},{2,5},{3},{4,7}} => [6,5,3,7,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6

{{1,6},{2,5},{3},{4},{7}} => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6

{{1,7},{2,5,6},{3},{4}} => [7,5,3,4,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 7

{{1},{2,5,6,7},{3},{4}} => [1,5,3,4,6,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1

{{1},{2,5,6},{3,7},{4}} => [1,5,7,4,6,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 1

{{1},{2,5,6},{3},{4,7}} => [1,5,3,7,6,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1

{{1},{2,5,6},{3},{4},{7}} => [1,5,3,4,6,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1

{{1,7},{2,5},{3,6},{4}} => [7,5,6,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 7

{{1},{2,5,7},{3,6},{4}} => [1,5,6,4,7,3,2] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1

{{1},{2,5},{3,6,7},{4}} => [1,5,6,4,2,7,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

{{1},{2,5},{3,6},{4,7}} => [1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1

{{1},{2,5},{3,6},{4},{7}} => [1,5,6,4,2,3,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1

{{1,7},{2,5},{3},{4,6}} => [7,5,3,6,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 7

{{1},{2,5,7},{3},{4,6}} => [1,5,3,6,7,4,2] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

{{1},{2,5},{3,7},{4,6}} => [1,5,7,6,2,4,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

{{1},{2,5},{3},{4,6,7}} => [1,5,3,6,2,7,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

{{1},{2,5},{3},{4,6},{7}} => [1,5,3,6,2,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 1

{{1,7},{2,5},{3},{4},{6}} => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 7

{{1},{2,5,7},{3},{4},{6}} => [1,5,3,4,7,6,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

{{1},{2,5},{3,7},{4},{6}} => [1,5,7,4,2,6,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

{{1},{2,5},{3},{4,7},{6}} => [1,5,3,7,2,6,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

{{1},{2,5},{3},{4},{6,7}} => [1,5,3,4,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

{{1},{2,5},{3},{4},{6},{7}} => [1,5,3,4,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 1

{{1,6,7},{2},{3,5},{4}} => [6,2,5,4,3,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7

{{1,6},{2,7},{3,5},{4}} => [6,7,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6

{{1,6},{2},{3,5,7},{4}} => [6,2,5,4,7,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6

{{1,6},{2},{3,5},{4,7}} => [6,2,5,7,3,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 6

{{1,6},{2},{3,5},{4},{7}} => [6,2,5,4,3,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 6

{{1,7},{2,6},{3,5},{4}} => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7

{{1},{2,6,7},{3,5},{4}} => [1,6,5,4,3,7,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1

{{1},{2,6},{3,5,7},{4}} => [1,6,5,4,7,2,3] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 1

{{1},{2,6},{3,5},{4,7}} => [1,6,5,7,3,2,4] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 1

{{1},{2,6},{3,5},{4},{7}} => [1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1

{{1,7},{2},{3,5,6},{4}} => [7,2,5,4,6,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7

{{1},{2,7},{3,5,6},{4}} => [1,7,5,4,6,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1

{{1},{2},{3,5,6,7},{4}} => [1,2,5,4,6,7,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1

{{1},{2},{3,5,6},{4,7}} => [1,2,5,7,6,3,4] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1

{{1},{2},{3,5,6},{4},{7}} => [1,2,5,4,6,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 1

{{1,7},{2},{3,5},{4,6}} => [7,2,5,6,3,4,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 7

{{1},{2,7},{3,5},{4,6}} => [1,7,5,6,3,4,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1

{{1},{2},{3,5,7},{4,6}} => [1,2,5,6,7,4,3] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1

{{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

{{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1

{{1,7},{2},{3,5},{4},{6}} => [7,2,5,4,3,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7

{{1},{2,7},{3,5},{4},{6}} => [1,7,5,4,3,6,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1

{{1},{2},{3,5,7},{4},{6}} => [1,2,5,4,7,6,3] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

{{1},{2},{3,5},{4,7},{6}} => [1,2,5,7,3,6,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

{{1},{2},{3,5},{4},{6,7}} => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

{{1},{2},{3,5},{4},{6},{7}} => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1

{{1,6,7},{2},{3},{4,5}} => [6,2,3,5,4,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 7

{{1,6},{2,7},{3},{4,5}} => [6,7,3,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 6

{{1,6},{2},{3,7},{4,5}} => [6,2,7,5,4,1,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 6

{{1,6},{2},{3},{4,5,7}} => [6,2,3,5,7,1,4] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6

{{1,6},{2},{3},{4,5},{7}} => [6,2,3,5,4,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 6

{{1,7},{2,6},{3},{4,5}} => [7,6,3,5,4,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 7

{{1},{2,6,7},{3},{4,5}} => [1,6,3,5,4,7,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

{{1},{2,6},{3,7},{4,5}} => [1,6,7,5,4,2,3] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1

{{1},{2,6},{3},{4,5,7}} => [1,6,3,5,7,2,4] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1

{{1},{2,6},{3},{4,5},{7}} => [1,6,3,5,4,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1

{{1,7},{2},{3,6},{4,5}} => [7,2,6,5,4,3,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 7

{{1},{2,7},{3,6},{4,5}} => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1

{{1},{2},{3,6,7},{4,5}} => [1,2,6,5,4,7,3] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1

{{1},{2},{3,6},{4,5,7}} => [1,2,6,5,7,3,4] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 1

{{1},{2},{3,6},{4,5},{7}} => [1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1

{{1,7},{2},{3},{4,5,6}} => [7,2,3,5,6,4,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 7

{{1},{2,7},{3},{4,5,6}} => [1,7,3,5,6,4,2] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

{{1},{2},{3,7},{4,5,6}} => [1,2,7,5,6,4,3] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1

{{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1

{{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1

{{1,7},{2},{3},{4,5},{6}} => [7,2,3,5,4,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 7

{{1},{2,7},{3},{4,5},{6}} => [1,7,3,5,4,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

{{1},{2},{3,7},{4,5},{6}} => [1,2,7,5,4,6,3] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1

{{1},{2},{3},{4,5,7},{6}} => [1,2,3,5,7,6,4] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1

{{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

{{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1

{{1,6,7},{2},{3},{4},{5}} => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 7

{{1,6},{2,7},{3},{4},{5}} => [6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 6

{{1,6},{2},{3,7},{4},{5}} => [6,2,7,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6

{{1,6},{2},{3},{4,7},{5}} => [6,2,3,7,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 6

{{1,6},{2},{3},{4},{5,7}} => [6,2,3,4,7,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6

{{1,6},{2},{3},{4},{5},{7}} => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6

{{1,7},{2,6},{3},{4},{5}} => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 7

{{1},{2,6,7},{3},{4},{5}} => [1,6,3,4,5,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1

{{1},{2,6},{3,7},{4},{5}} => [1,6,7,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 1

{{1},{2,6},{3},{4,7},{5}} => [1,6,3,7,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1

{{1},{2,6},{3},{4},{5,7}} => [1,6,3,4,7,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1

{{1},{2,6},{3},{4},{5},{7}} => [1,6,3,4,5,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1

{{1,7},{2},{3,6},{4},{5}} => [7,2,6,4,5,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7

{{1},{2,7},{3,6},{4},{5}} => [1,7,6,4,5,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1

{{1},{2},{3,6,7},{4},{5}} => [1,2,6,4,5,7,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1

{{1},{2},{3,6},{4,7},{5}} => [1,2,6,7,5,3,4] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1

{{1},{2},{3,6},{4},{5,7}} => [1,2,6,4,7,3,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 1

{{1},{2},{3,6},{4},{5},{7}} => [1,2,6,4,5,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 1

{{1,7},{2},{3},{4,6},{5}} => [7,2,3,6,5,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7

{{1},{2,7},{3},{4,6},{5}} => [1,7,3,6,5,4,2] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

{{1},{2},{3,7},{4,6},{5}} => [1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1

{{1},{2},{3},{4,6,7},{5}} => [1,2,3,6,5,7,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1

{{1},{2},{3},{4,6},{5,7}} => [1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1

{{1},{2},{3},{4,6},{5},{7}} => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1

{{1,7},{2},{3},{4},{5,6}} => [7,2,3,4,6,5,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 7

{{1},{2,7},{3},{4},{5,6}} => [1,7,3,4,6,5,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

{{1},{2},{3,7},{4},{5,6}} => [1,2,7,4,6,5,3] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

{{1},{2},{3},{4,7},{5,6}} => [1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1

{{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1

{{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1

{{1,7},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 7

{{1},{2,7},{3},{4},{5},{6}} => [1,7,3,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1

{{1},{2},{3,7},{4},{5},{6}} => [1,2,7,4,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1

{{1},{2},{3},{4,7},{5},{6}} => [1,2,3,7,5,6,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1

{{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1

{{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1

{{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1

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Description

The position of the first return of a Dyck path.

Map

to Dyck path: up step, left tree, down step, right tree

Description

Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:

a leaf is associated to the empty Dyck Word
a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.

Map

to increasing tree

Description

Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.

Map

to permutation

Description

Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.