- FindStat

Identifier

Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
St000211: Set partitions ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 625 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The rank of the set partition.
This is defined as the number of elements in the set partition minus the number of blocks, or, equivalently, the number of arcs in the one-line diagram associated to the set partition.

Map

first fundamental transformation

Description

Return the permutation whose cycles are the subsequences between successive left to right maxima.

Map

to 312-avoiding permutation

Description

Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.

Map

weak exceedance partition

Description

The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.