- FindStat

Identifier

Mp00080: Set partitions —to permutation⟶ Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
St000204: Binary trees ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1155 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{1,4,6,7},{2,5},{3}} => [4,5,3,6,2,7,1] => [7,1,6,2,5,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2

{{1,4,6},{2,5,7},{3}} => [4,5,3,6,7,1,2] => [2,7,1,5,3,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2

{{1,4,6},{2,5},{3,7}} => [4,5,7,6,2,1,3] => [3,7,6,2,1,4,5] => [[[.,[[.,.],.]],.],[.,[.,.]]] => 2

{{1,4,6},{2,5},{3},{7}} => [4,5,3,6,2,1,7] => [6,2,1,5,3,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 1

{{1,4,7},{2,5,6},{3}} => [4,5,3,7,6,2,1] => [7,6,2,1,5,3,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

{{1,4},{2,5,6,7},{3}} => [4,5,3,1,6,7,2] => [7,2,5,3,1,4,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 2

{{1,4},{2,5,6},{3,7}} => [4,5,7,1,6,2,3] => [3,6,2,7,1,4,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2

{{1,4},{2,5,6},{3},{7}} => [4,5,3,1,6,2,7] => [6,2,5,3,1,4,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 2

{{1,4,7},{2,5},{3,6}} => [4,5,6,7,2,3,1] => [3,1,7,2,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1

{{1,4},{2,5,7},{3,6}} => [4,5,6,1,7,3,2] => [7,3,2,6,1,4,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 1

{{1,4},{2,5},{3,6,7}} => [4,5,6,1,2,7,3] => [2,7,3,6,1,4,5] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3

{{1,4},{2,5},{3,6},{7}} => [4,5,6,1,2,3,7] => [2,3,6,1,4,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2

{{1,4,7},{2,5},{3},{6}} => [4,5,3,7,2,6,1] => [6,1,7,2,5,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2

{{1,4},{2,5,7},{3},{6}} => [4,5,3,1,7,6,2] => [7,6,2,5,3,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => 2

{{1,4},{2,5},{3,7},{6}} => [4,5,7,1,2,6,3] => [2,6,3,7,1,4,5] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3

{{1,4},{2,5},{3},{6,7}} => [4,5,3,1,2,7,6] => [2,5,3,1,4,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => 3

{{1,4},{2,5},{3},{6},{7}} => [4,5,3,1,2,6,7] => [2,5,3,1,4,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2

{{1,4,6,7},{2},{3,5}} => [4,2,5,6,3,7,1] => [7,1,6,3,4,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 3

{{1,4,6},{2,7},{3,5}} => [4,7,5,6,3,1,2] => [2,6,3,1,4,7,5] => [[.,[[.,.],.]],[.,[[.,.],.]]] => 3

{{1,4,6},{2},{3,5,7}} => [4,2,5,6,7,1,3] => [3,7,1,4,2,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2

{{1,4,6},{2},{3,5},{7}} => [4,2,5,6,3,1,7] => [6,3,1,4,2,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 1

{{1,4,7},{2,6},{3,5}} => [4,6,5,7,3,2,1] => [7,3,2,1,4,6,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => 1

{{1,4},{2,6,7},{3,5}} => [4,6,5,1,3,7,2] => [7,2,3,6,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => 3

{{1,4},{2,6},{3,5,7}} => [4,6,5,1,7,2,3] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => 3

{{1,4},{2,6},{3,5},{7}} => [4,6,5,1,3,2,7] => [3,2,6,5,1,4,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 2

{{1,4,7},{2},{3,5,6}} => [4,2,5,7,6,3,1] => [7,6,3,1,4,2,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

{{1,4},{2,7},{3,5,6}} => [4,7,5,1,6,3,2] => [6,3,2,7,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => 2

{{1,4},{2},{3,5,6,7}} => [4,2,5,1,6,7,3] => [7,3,5,1,4,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 2

{{1,4},{2},{3,5,6},{7}} => [4,2,5,1,6,3,7] => [6,3,5,1,4,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 2

{{1,4,7},{2},{3,5},{6}} => [4,2,5,7,3,6,1] => [6,1,7,3,4,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 3

{{1,4},{2,7},{3,5},{6}} => [4,7,5,1,3,6,2] => [6,2,3,7,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => 3

{{1,4},{2},{3,5,7},{6}} => [4,2,5,1,7,6,3] => [7,6,3,5,1,4,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => 2

{{1,4},{2},{3,5},{6,7}} => [4,2,5,1,3,7,6] => [3,5,1,4,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3

{{1,4},{2},{3,5},{6},{7}} => [4,2,5,1,3,6,7] => [3,5,1,4,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2

{{1,4,6,7},{2},{3},{5}} => [4,2,3,6,5,7,1] => [7,1,3,4,2,6,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3

{{1,4,6},{2,7},{3},{5}} => [4,7,3,6,5,1,2] => [2,6,5,1,7,3,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => 3

{{1,4,6},{2},{3,7},{5}} => [4,2,7,6,5,1,3] => [3,7,6,5,1,4,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => 4

{{1,4,6},{2},{3},{5,7}} => [4,2,3,6,7,1,5] => [5,7,1,3,4,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3

{{1,4,6},{2},{3},{5},{7}} => [4,2,3,6,5,1,7] => [6,5,1,3,4,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2

{{1,4,7},{2,6},{3},{5}} => [4,6,3,7,5,2,1] => [7,5,2,1,6,3,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

{{1,4},{2,6,7},{3},{5}} => [4,6,3,1,5,7,2] => [7,2,5,6,3,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => 3

{{1,4},{2,6},{3,7},{5}} => [4,6,7,1,5,2,3] => [3,5,2,7,1,4,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2

{{1,4},{2,6},{3},{5,7}} => [4,6,3,1,7,2,5] => [5,7,2,6,3,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => 3

{{1,4},{2,6},{3},{5},{7}} => [4,6,3,1,5,2,7] => [5,2,6,3,1,4,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 2

{{1,4,7},{2},{3,6},{5}} => [4,2,6,7,5,3,1] => [7,5,3,1,4,2,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

{{1,4},{2,7},{3,6},{5}} => [4,7,6,1,5,3,2] => [5,3,2,7,6,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => 2

{{1,4},{2},{3,6,7},{5}} => [4,2,6,1,5,7,3] => [7,3,5,6,1,4,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => 3

{{1,4},{2},{3,6},{5,7}} => [4,2,6,1,7,3,5] => [5,7,3,6,1,4,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => 3

{{1,4},{2},{3,6},{5},{7}} => [4,2,6,1,5,3,7] => [5,3,6,1,4,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 2

{{1,4,7},{2},{3},{5,6}} => [4,2,3,7,6,5,1] => [7,6,5,1,3,4,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

{{1,4},{2,7},{3},{5,6}} => [4,7,3,1,6,5,2] => [6,5,2,7,3,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => 2

{{1,4},{2},{3,7},{5,6}} => [4,2,7,1,6,5,3] => [6,5,3,7,1,4,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => 2

{{1,4},{2},{3},{5,6,7}} => [4,2,3,1,6,7,5] => [3,1,4,2,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2

{{1,4},{2},{3},{5,6},{7}} => [4,2,3,1,6,5,7] => [3,1,4,2,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2

{{1,4,7},{2},{3},{5},{6}} => [4,2,3,7,5,6,1] => [6,1,3,4,2,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3

{{1,4},{2,7},{3},{5},{6}} => [4,7,3,1,5,6,2] => [6,2,5,7,3,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => 3

{{1,4},{2},{3,7},{5},{6}} => [4,2,7,1,5,6,3] => [6,3,5,7,1,4,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => 3

{{1,4},{2},{3},{5,7},{6}} => [4,2,3,1,7,6,5] => [3,1,4,2,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => 3

{{1,4},{2},{3},{5},{6,7}} => [4,2,3,1,5,7,6] => [3,1,4,2,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2

{{1,4},{2},{3},{5},{6},{7}} => [4,2,3,1,5,6,7] => [3,1,4,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1

{{1,5,6,7},{2,4},{3}} => [5,4,3,2,6,7,1] => [7,1,5,4,3,2,6] => [[.,.],[[[[.,.],.],.],[.,.]]] => 3

{{1,5,6},{2,4,7},{3}} => [5,4,3,7,6,1,2] => [2,7,6,1,5,4,3] => [[.,[[.,.],.]],[[[.,.],.],.]] => 4

{{1,5,6},{2,4},{3,7}} => [5,4,7,2,6,1,3] => [3,6,1,7,2,5,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3

{{1,5,6},{2,4},{3},{7}} => [5,4,3,2,6,1,7] => [6,1,5,4,3,2,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => 3

{{1,5,7},{2,4,6},{3}} => [5,4,3,6,7,2,1] => [7,2,1,5,4,3,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => 2

{{1,5},{2,4,6,7},{3}} => [5,4,3,6,1,7,2] => [7,2,6,1,5,4,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => 3

{{1,5},{2,4,6},{3,7}} => [5,4,7,6,1,2,3] => [2,3,7,6,1,5,4] => [[.,[.,[[.,.],.]]],[[.,.],.]] => 4

{{1,5},{2,4,6},{3},{7}} => [5,4,3,6,1,2,7] => [2,6,1,5,4,3,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => 3

{{1,5,7},{2,4},{3,6}} => [5,4,6,2,7,3,1] => [7,3,1,6,2,5,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => 2

{{1,5},{2,4,7},{3,6}} => [5,4,6,7,1,3,2] => [3,2,7,1,5,4,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 2

{{1,5},{2,4},{3,6,7}} => [5,4,6,2,1,7,3] => [7,3,6,2,1,5,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => 2

{{1,5},{2,4},{3,6},{7}} => [5,4,6,2,1,3,7] => [3,6,2,1,5,4,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => 2

{{1,5,7},{2,4},{3},{6}} => [5,4,3,2,7,6,1] => [7,6,1,5,4,3,2] => [[[.,.],.],[[[[.,.],.],.],.]] => 3

{{1,5},{2,4,7},{3},{6}} => [5,4,3,7,1,6,2] => [6,2,7,1,5,4,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => 3

{{1,5},{2,4},{3,7},{6}} => [5,4,7,2,1,6,3] => [6,3,7,2,1,5,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => 2

{{1,5},{2,4},{3},{6,7}} => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[.,.],.]] => 1

{{1,5},{2,4},{3},{6},{7}} => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => 0

{{1,6,7},{2,4,5},{3}} => [6,4,3,5,2,7,1] => [7,1,5,2,6,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => 3

{{1,6},{2,4,5,7},{3}} => [6,4,3,5,7,1,2] => [2,7,1,5,6,4,3] => [[.,[.,.]],[[[.,[.,.]],.],.]] => 4

{{1,6},{2,4,5},{3,7}} => [6,4,7,5,2,1,3] => [3,7,5,2,1,6,4] => [[[.,[[.,.],.]],.],[[.,.],.]] => 3

{{1,6},{2,4,5},{3},{7}} => [6,4,3,5,2,1,7] => [5,2,1,6,4,3,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => 2

{{1,7},{2,4,5,6},{3}} => [7,4,3,5,6,2,1] => [6,2,1,5,7,4,3] => [[[.,.],.],[[[.,[.,.]],.],.]] => 3

{{1},{2,4,5,6,7},{3}} => [1,4,3,5,6,7,2] => [1,7,2,4,3,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2

{{1},{2,4,5,6},{3,7}} => [1,4,7,5,6,2,3] => [1,3,6,2,4,7,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 3

{{1},{2,4,5,6},{3},{7}} => [1,4,3,5,6,2,7] => [1,6,2,4,3,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2

{{1,7},{2,4,5},{3,6}} => [7,4,6,5,2,3,1] => [3,1,6,5,2,7,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => 3

{{1},{2,4,5,7},{3,6}} => [1,4,6,5,7,3,2] => [1,7,3,2,4,6,5] => [.,[[[.,.],.],[.,[[.,.],.]]]] => 3

{{1},{2,4,5},{3,6,7}} => [1,4,6,5,2,7,3] => [1,7,3,6,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => 4

{{1},{2,4,5},{3,6},{7}} => [1,4,6,5,2,3,7] => [1,3,6,5,2,4,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 3

{{1,7},{2,4,5},{3},{6}} => [7,4,3,5,2,6,1] => [6,1,5,2,7,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => 3

{{1},{2,4,5,7},{3},{6}} => [1,4,3,5,7,6,2] => [1,7,6,2,4,3,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 3

{{1},{2,4,5},{3,7},{6}} => [1,4,7,5,2,6,3] => [1,6,3,7,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => 4

{{1},{2,4,5},{3},{6,7}} => [1,4,3,5,2,7,6] => [1,5,2,4,3,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3

{{1},{2,4,5},{3},{6},{7}} => [1,4,3,5,2,6,7] => [1,5,2,4,3,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2

{{1,6,7},{2,4},{3,5}} => [6,4,5,2,3,7,1] => [7,1,3,5,2,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3

{{1,6},{2,4,7},{3,5}} => [6,4,5,7,3,1,2] => [2,7,3,1,5,6,4] => [[.,[[.,.],.]],[[.,[.,.]],.]] => 4

{{1,6},{2,4},{3,5,7}} => [6,4,5,2,7,1,3] => [3,7,1,5,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3

{{1,6},{2,4},{3,5},{7}} => [6,4,5,2,3,1,7] => [3,1,5,2,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 2

{{1,7},{2,4,6},{3,5}} => [7,4,5,6,3,2,1] => [6,3,2,1,5,7,4] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

{{1},{2,4,6,7},{3,5}} => [1,4,5,6,3,7,2] => [1,7,2,6,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2

{{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => [1,3,7,2,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2

{{1},{2,4,6},{3,5},{7}} => [1,4,5,6,3,2,7] => [1,6,3,2,4,5,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => 2

{{1,7},{2,4},{3,5,6}} => [7,4,5,2,6,3,1] => [6,3,1,5,2,7,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => 2

{{1},{2,4,7},{3,5,6}} => [1,4,5,7,6,3,2] => [1,7,6,3,2,4,5] => [.,[[[[.,.],.],.],[.,[.,.]]]] => 3

{{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => [1,7,3,5,2,4,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => 3

{{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => [1,6,3,5,2,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => 3

{{1,7},{2,4},{3,5},{6}} => [7,4,5,2,3,6,1] => [6,1,3,5,2,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3

{{1},{2,4,7},{3,5},{6}} => [1,4,5,7,3,6,2] => [1,6,2,7,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2

{{1},{2,4},{3,5,7},{6}} => [1,4,5,2,7,6,3] => [1,7,6,3,5,2,4] => [.,[[[[.,.],.],[.,.]],[.,.]]] => 4

{{1},{2,4},{3,5},{6,7}} => [1,4,5,2,3,7,6] => [1,3,5,2,4,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 3

{{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => [1,3,5,2,4,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2

{{1,6,7},{2,4},{3},{5}} => [6,4,3,2,5,7,1] => [7,1,5,6,4,3,2] => [[.,.],[[[[.,[.,.]],.],.],.]] => 4

{{1,6},{2,4,7},{3},{5}} => [6,4,3,7,5,1,2] => [2,7,5,1,6,4,3] => [[.,[[.,.],.]],[[[.,.],.],.]] => 4

{{1,6},{2,4},{3,7},{5}} => [6,4,7,2,5,1,3] => [3,5,1,7,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3

{{1,6},{2,4},{3},{5,7}} => [6,4,3,2,7,1,5] => [5,7,1,6,4,3,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => 4

{{1,6},{2,4},{3},{5},{7}} => [6,4,3,2,5,1,7] => [5,1,6,4,3,2,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => 3

{{1,7},{2,4,6},{3},{5}} => [7,4,3,6,5,2,1] => [6,5,2,1,7,4,3] => [[[[.,.],.],.],[[[.,.],.],.]] => 2

{{1},{2,4,6,7},{3},{5}} => [1,4,3,6,5,7,2] => [1,7,2,4,3,6,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3

{{1},{2,4,6},{3,7},{5}} => [1,4,7,6,5,2,3] => [1,3,7,6,5,2,4] => [.,[[.,[[[.,.],.],.]],[.,.]]] => 4

{{1},{2,4,6},{3},{5,7}} => [1,4,3,6,7,2,5] => [1,5,7,2,4,3,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3

{{1},{2,4,6},{3},{5},{7}} => [1,4,3,6,5,2,7] => [1,6,5,2,4,3,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 3

{{1,7},{2,4},{3,6},{5}} => [7,4,6,2,5,3,1] => [5,3,1,6,2,7,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => 2

{{1},{2,4,7},{3,6},{5}} => [1,4,6,7,5,3,2] => [1,7,5,3,2,4,6] => [.,[[[[.,.],.],.],[.,[.,.]]]] => 3

{{1},{2,4},{3,6,7},{5}} => [1,4,6,2,5,7,3] => [1,7,3,5,6,2,4] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => 4

{{1},{2,4},{3,6},{5,7}} => [1,4,6,2,7,3,5] => [1,5,7,3,6,2,4] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => 4

{{1},{2,4},{3,6},{5},{7}} => [1,4,6,2,5,3,7] => [1,5,3,6,2,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => 3

{{1,7},{2,4},{3},{5,6}} => [7,4,3,2,6,5,1] => [6,5,1,7,4,3,2] => [[[.,.],.],[[[[.,.],.],.],.]] => 3

{{1},{2,4,7},{3},{5,6}} => [1,4,3,7,6,5,2] => [1,7,6,5,2,4,3] => [.,[[[[.,.],.],.],[[.,.],.]]] => 4

{{1},{2,4},{3,7},{5,6}} => [1,4,7,2,6,5,3] => [1,6,5,3,7,2,4] => [.,[[[[.,.],.],[.,.]],[.,.]]] => 4

{{1},{2,4},{3},{5,6,7}} => [1,4,3,2,6,7,5] => [1,4,3,2,7,5,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 3

{{1},{2,4},{3},{5,6},{7}} => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 3

{{1,7},{2,4},{3},{5},{6}} => [7,4,3,2,5,6,1] => [6,1,5,7,4,3,2] => [[.,.],[[[[.,[.,.]],.],.],.]] => 4

{{1},{2,4,7},{3},{5},{6}} => [1,4,3,7,5,6,2] => [1,6,2,4,3,7,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3

{{1},{2,4},{3,7},{5},{6}} => [1,4,7,2,5,6,3] => [1,6,3,5,7,2,4] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => 4

{{1},{2,4},{3},{5,7},{6}} => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]] => 4

{{1},{2,4},{3},{5},{6,7}} => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => 3

{{1},{2,4},{3},{5},{6},{7}} => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => 2

{{1,5,6,7},{2},{3,4}} => [5,2,4,3,6,7,1] => [7,1,4,3,5,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 3

{{1,5,6},{2,7},{3,4}} => [5,7,4,3,6,1,2] => [2,6,1,7,4,3,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => 3

{{1,5,6},{2},{3,4,7}} => [5,2,4,7,6,1,3] => [3,7,6,1,4,5,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => 4

{{1,5,6},{2},{3,4},{7}} => [5,2,4,3,6,1,7] => [6,1,4,3,5,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 3

{{1,5,7},{2,6},{3,4}} => [5,6,4,3,7,2,1] => [7,2,1,6,4,3,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => 2

{{1,5},{2,6,7},{3,4}} => [5,6,4,3,1,7,2] => [7,2,6,4,3,1,5] => [[[.,.],[[[.,.],.],.]],[.,.]] => 3

{{1,5},{2,6},{3,4,7}} => [5,6,4,7,1,2,3] => [2,3,7,1,6,4,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3

{{1,5},{2,6},{3,4},{7}} => [5,6,4,3,1,2,7] => [2,6,4,3,1,5,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => 3

{{1,5,7},{2},{3,4,6}} => [5,2,4,6,7,3,1] => [7,3,1,4,5,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2

{{1,5},{2,7},{3,4,6}} => [5,7,4,6,1,3,2] => [3,2,6,1,7,4,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 2

{{1,5},{2},{3,4,6,7}} => [5,2,4,6,1,7,3] => [7,3,6,1,4,5,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 3

{{1,5},{2},{3,4,6},{7}} => [5,2,4,6,1,3,7] => [3,6,1,4,5,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3

{{1,5,7},{2},{3,4},{6}} => [5,2,4,3,7,6,1] => [7,6,1,4,3,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => 3

{{1,5},{2,7},{3,4},{6}} => [5,7,4,3,1,6,2] => [6,2,7,4,3,1,5] => [[[.,.],[[[.,.],.],.]],[.,.]] => 3

{{1,5},{2},{3,4,7},{6}} => [5,2,4,7,1,6,3] => [6,3,7,1,4,5,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 3

{{1,5},{2},{3,4},{6,7}} => [5,2,4,3,1,7,6] => [4,3,1,5,2,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => 2

{{1,5},{2},{3,4},{6},{7}} => [5,2,4,3,1,6,7] => [4,3,1,5,2,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 1

{{1,6,7},{2,5},{3,4}} => [6,5,4,3,2,7,1] => [7,1,6,5,4,3,2] => [[.,.],[[[[[.,.],.],.],.],.]] => 4

{{1,6},{2,5,7},{3,4}} => [6,5,4,3,7,1,2] => [2,7,1,6,5,4,3] => [[.,[.,.]],[[[[.,.],.],.],.]] => 4

{{1,6},{2,5},{3,4,7}} => [6,5,4,7,2,1,3] => [3,7,2,1,6,5,4] => [[[.,[.,.]],.],[[[.,.],.],.]] => 3

{{1,6},{2,5},{3,4},{7}} => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => 0

{{1,7},{2,5,6},{3,4}} => [7,5,4,3,6,2,1] => [6,2,1,7,5,4,3] => [[[.,.],.],[[[[.,.],.],.],.]] => 3

{{1},{2,5,6,7},{3,4}} => [1,5,4,3,6,7,2] => [1,7,2,5,4,3,6] => [.,[[.,.],[[[.,.],.],[.,.]]]] => 3

{{1},{2,5,6},{3,4,7}} => [1,5,4,7,6,2,3] => [1,3,7,6,2,5,4] => [.,[[.,[[.,.],.]],[[.,.],.]]] => 4

{{1},{2,5,6},{3,4},{7}} => [1,5,4,3,6,2,7] => [1,6,2,5,4,3,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => 3

{{1,7},{2,5},{3,4,6}} => [7,5,4,6,2,3,1] => [3,1,6,2,7,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => 3

{{1},{2,5,7},{3,4,6}} => [1,5,4,6,7,3,2] => [1,7,3,2,5,4,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 3

{{1},{2,5},{3,4,6,7}} => [1,5,4,6,2,7,3] => [1,7,3,6,2,5,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => 4

{{1},{2,5},{3,4,6},{7}} => [1,5,4,6,2,3,7] => [1,3,6,2,5,4,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3

{{1,7},{2,5},{3,4},{6}} => [7,5,4,3,2,6,1] => [6,1,7,5,4,3,2] => [[.,.],[[[[[.,.],.],.],.],.]] => 4

{{1},{2,5,7},{3,4},{6}} => [1,5,4,3,7,6,2] => [1,7,6,2,5,4,3] => [.,[[[.,.],.],[[[.,.],.],.]]] => 4

{{1},{2,5},{3,4,7},{6}} => [1,5,4,7,2,6,3] => [1,6,3,7,2,5,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => 4

{{1},{2,5},{3,4},{6,7}} => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6] => [.,[[[[.,.],.],.],[[.,.],.]]] => 4

{{1},{2,5},{3,4},{6},{7}} => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => 3

{{1,6,7},{2},{3,4,5}} => [6,2,4,5,3,7,1] => [7,1,5,3,4,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 4

{{1,6},{2,7},{3,4,5}} => [6,7,4,5,3,1,2] => [2,5,3,1,7,4,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => 3

{{1,6},{2},{3,4,5,7}} => [6,2,4,5,7,1,3] => [3,7,1,4,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 4

{{1,6},{2},{3,4,5},{7}} => [6,2,4,5,3,1,7] => [5,3,1,4,6,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2

{{1,7},{2,6},{3,4,5}} => [7,6,4,5,3,2,1] => [5,3,2,1,7,6,4] => [[[[.,.],.],.],[[[.,.],.],.]] => 2

{{1},{2,6,7},{3,4,5}} => [1,6,4,5,3,7,2] => [1,7,2,5,3,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3

{{1},{2,6},{3,4,5,7}} => [1,6,4,5,7,2,3] => [1,3,7,2,5,6,4] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 4

{{1},{2,6},{3,4,5},{7}} => [1,6,4,5,3,2,7] => [1,5,3,2,6,4,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 3

{{1,7},{2},{3,4,5,6}} => [7,2,4,5,6,3,1] => [6,3,1,4,5,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 3

{{1},{2,7},{3,4,5,6}} => [1,7,4,5,6,3,2] => [1,6,3,2,5,7,4] => [.,[[[.,.],.],[[.,[.,.]],.]]] => 4

{{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1

{{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1

{{1,7},{2},{3,4,5},{6}} => [7,2,4,5,3,6,1] => [6,1,5,3,4,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 4

{{1},{2,7},{3,4,5},{6}} => [1,7,4,5,3,6,2] => [1,6,2,5,3,7,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3

{{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => [1,2,7,6,3,4,5] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => 2

{{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2

{{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1

{{1,6,7},{2},{3,4},{5}} => [6,2,4,3,5,7,1] => [7,1,4,3,5,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 4

{{1,6},{2,7},{3,4},{5}} => [6,7,4,3,5,1,2] => [2,5,1,7,4,3,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => 3

{{1,6},{2},{3,4,7},{5}} => [6,2,4,7,5,1,3] => [3,7,5,1,4,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => 4

{{1,6},{2},{3,4},{5,7}} => [6,2,4,3,7,1,5] => [5,7,1,4,3,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => 4

{{1,6},{2},{3,4},{5},{7}} => [6,2,4,3,5,1,7] => [5,1,4,3,6,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 3

{{1,7},{2,6},{3,4},{5}} => [7,6,4,3,5,2,1] => [5,2,1,7,6,4,3] => [[[.,.],.],[[[[.,.],.],.],.]] => 3

{{1},{2,6,7},{3,4},{5}} => [1,6,4,3,5,7,2] => [1,7,2,5,6,4,3] => [.,[[.,.],[[[.,[.,.]],.],.]]] => 4

{{1},{2,6},{3,4,7},{5}} => [1,6,4,7,5,2,3] => [1,3,7,5,2,6,4] => [.,[[.,[[.,.],.]],[[.,.],.]]] => 4

{{1},{2,6},{3,4},{5,7}} => [1,6,4,3,7,2,5] => [1,5,7,2,6,4,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => 4

{{1},{2,6},{3,4},{5},{7}} => [1,6,4,3,5,2,7] => [1,5,2,6,4,3,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => 3

{{1,7},{2},{3,4,6},{5}} => [7,2,4,6,5,3,1] => [6,5,3,1,4,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

{{1},{2,7},{3,4,6},{5}} => [1,7,4,6,5,3,2] => [1,6,5,3,2,7,4] => [.,[[[[.,.],.],.],[[.,.],.]]] => 4

{{1},{2},{3,4,6,7},{5}} => [1,2,4,6,5,7,3] => [1,2,7,3,4,6,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2

{{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => [1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2

{{1},{2},{3,4,6},{5},{7}} => [1,2,4,6,5,3,7] => [1,2,6,5,3,4,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => 2

{{1,7},{2},{3,4},{5,6}} => [7,2,4,3,6,5,1] => [6,5,1,4,3,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => 3

{{1},{2,7},{3,4},{5,6}} => [1,7,4,3,6,5,2] => [1,6,5,2,7,4,3] => [.,[[[.,.],.],[[[.,.],.],.]]] => 4

{{1},{2},{3,4,7},{5,6}} => [1,2,4,7,6,5,3] => [1,2,7,6,5,3,4] => [.,[.,[[[[.,.],.],.],[.,.]]]] => 3

{{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2

{{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2

{{1,7},{2},{3,4},{5},{6}} => [7,2,4,3,5,6,1] => [6,1,4,3,5,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 4

{{1},{2,7},{3,4},{5},{6}} => [1,7,4,3,5,6,2] => [1,6,2,5,7,4,3] => [.,[[.,.],[[[.,[.,.]],.],.]]] => 4

{{1},{2},{3,4,7},{5},{6}} => [1,2,4,7,5,6,3] => [1,2,6,3,4,7,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2

{{1},{2},{3,4},{5,7},{6}} => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]] => 3

{{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2

{{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1

{{1,5,6,7},{2},{3},{4}} => [5,2,3,4,6,7,1] => [7,1,3,4,5,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3

{{1,5,6},{2,7},{3},{4}} => [5,7,3,4,6,1,2] => [2,6,1,4,7,3,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3

{{1,5,6},{2},{3,7},{4}} => [5,2,7,4,6,1,3] => [3,6,1,7,4,5,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => 4

{{1,5,6},{2},{3},{4,7}} => [5,2,3,7,6,1,4] => [4,7,6,1,3,5,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => 4

{{1,5,6},{2},{3},{4},{7}} => [5,2,3,4,6,1,7] => [6,1,3,4,5,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3

{{1,5,7},{2,6},{3},{4}} => [5,6,3,4,7,2,1] => [7,2,1,4,6,3,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2

{{1,5},{2,6,7},{3},{4}} => [5,6,3,4,1,7,2] => [7,2,4,1,6,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 2

{{1,5},{2,6},{3,7},{4}} => [5,6,7,4,1,2,3] => [2,3,7,4,1,5,6] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 3

{{1,5},{2,6},{3},{4,7}} => [5,6,3,7,1,2,4] => [2,4,7,1,6,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3

{{1,5},{2,6},{3},{4},{7}} => [5,6,3,4,1,2,7] => [2,4,1,6,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2

{{1,5,7},{2},{3,6},{4}} => [5,2,6,4,7,3,1] => [7,3,1,6,4,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => 3

{{1,5},{2,7},{3,6},{4}} => [5,7,6,4,1,3,2] => [3,2,7,6,4,1,5] => [[[.,.],[[[.,.],.],.]],[.,.]] => 3

{{1,5},{2},{3,6,7},{4}} => [5,2,6,4,1,7,3] => [7,3,6,4,1,5,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => 3

{{1,5},{2},{3,6},{4,7}} => [5,2,6,7,1,3,4] => [3,4,7,1,5,2,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3

{{1,5},{2},{3,6},{4},{7}} => [5,2,6,4,1,3,7] => [3,6,4,1,5,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => 3

{{1,5,7},{2},{3},{4,6}} => [5,2,3,6,7,4,1] => [7,4,1,3,5,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2

{{1,5},{2,7},{3},{4,6}} => [5,7,3,6,1,4,2] => [4,2,6,1,7,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 2

{{1,5},{2},{3,7},{4,6}} => [5,2,7,6,1,4,3] => [4,3,7,6,1,5,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => 3

{{1,5},{2},{3},{4,6,7}} => [5,2,3,6,1,7,4] => [7,4,6,1,3,5,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 3

{{1,5},{2},{3},{4,6},{7}} => [5,2,3,6,1,4,7] => [4,6,1,3,5,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3

{{1,5,7},{2},{3},{4},{6}} => [5,2,3,4,7,6,1] => [7,6,1,3,4,5,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 3

{{1,5},{2,7},{3},{4},{6}} => [5,7,3,4,1,6,2] => [6,2,4,1,7,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 2

{{1,5},{2},{3,7},{4},{6}} => [5,2,7,4,1,6,3] => [6,3,7,4,1,5,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => 3

{{1,5},{2},{3},{4,7},{6}} => [5,2,3,7,1,6,4] => [6,4,7,1,3,5,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 3

{{1,5},{2},{3},{4},{6,7}} => [5,2,3,4,1,7,6] => [4,1,3,5,2,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3

{{1,5},{2},{3},{4},{6},{7}} => [5,2,3,4,1,6,7] => [4,1,3,5,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2

{{1,6,7},{2,5},{3},{4}} => [6,5,3,4,2,7,1] => [7,1,4,2,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => 3

{{1,6},{2,5,7},{3},{4}} => [6,5,3,4,7,1,2] => [2,7,1,4,6,5,3] => [[.,[.,.]],[[.,[[.,.],.]],.]] => 4

{{1,6},{2,5},{3,7},{4}} => [6,5,7,4,2,1,3] => [3,7,4,2,1,6,5] => [[[.,[[.,.],.]],.],[[.,.],.]] => 3

{{1,6},{2,5},{3},{4,7}} => [6,5,3,7,2,1,4] => [4,7,2,1,6,5,3] => [[[.,[.,.]],.],[[[.,.],.],.]] => 3

{{1,6},{2,5},{3},{4},{7}} => [6,5,3,4,2,1,7] => [4,2,1,6,5,3,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => 2

{{1,7},{2,5,6},{3},{4}} => [7,5,3,4,6,2,1] => [6,2,1,4,7,5,3] => [[[.,.],.],[[.,[[.,.],.]],.]] => 3

{{1},{2,5,6,7},{3},{4}} => [1,5,3,4,6,7,2] => [1,7,2,4,5,3,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3

{{1},{2,5,6},{3,7},{4}} => [1,5,7,4,6,2,3] => [1,3,6,2,7,4,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3

{{1},{2,5,6},{3},{4,7}} => [1,5,3,7,6,2,4] => [1,4,7,6,2,5,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => 4

{{1},{2,5,6},{3},{4},{7}} => [1,5,3,4,6,2,7] => [1,6,2,4,5,3,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3

{{1,7},{2,5},{3,6},{4}} => [7,5,6,4,2,3,1] => [3,1,6,4,2,7,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => 3

{{1},{2,5,7},{3,6},{4}} => [1,5,6,4,7,3,2] => [1,7,3,2,6,4,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 3

{{1},{2,5},{3,6,7},{4}} => [1,5,6,4,2,7,3] => [1,7,3,6,4,2,5] => [.,[[[.,.],[[.,.],.]],[.,.]]] => 4

{{1},{2,5},{3,6},{4,7}} => [1,5,6,7,2,3,4] => [1,3,4,7,2,5,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 3

{{1},{2,5},{3,6},{4},{7}} => [1,5,6,4,2,3,7] => [1,3,6,4,2,5,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 3

{{1,7},{2,5},{3},{4,6}} => [7,5,3,6,2,4,1] => [4,1,6,2,7,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => 3

{{1},{2,5,7},{3},{4,6}} => [1,5,3,6,7,4,2] => [1,7,4,2,5,3,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 3

{{1},{2,5},{3,7},{4,6}} => [1,5,7,6,2,4,3] => [1,4,3,7,6,2,5] => [.,[[[.,.],[[.,.],.]],[.,.]]] => 4

{{1},{2,5},{3},{4,6,7}} => [1,5,3,6,2,7,4] => [1,7,4,6,2,5,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => 4

{{1},{2,5},{3},{4,6},{7}} => [1,5,3,6,2,4,7] => [1,4,6,2,5,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3

{{1,7},{2,5},{3},{4},{6}} => [7,5,3,4,2,6,1] => [6,1,4,2,7,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => 3

{{1},{2,5,7},{3},{4},{6}} => [1,5,3,4,7,6,2] => [1,7,6,2,4,5,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => 4

{{1},{2,5},{3,7},{4},{6}} => [1,5,7,4,2,6,3] => [1,6,3,7,4,2,5] => [.,[[[.,.],[[.,.],.]],[.,.]]] => 4

{{1},{2,5},{3},{4,7},{6}} => [1,5,3,7,2,6,4] => [1,6,4,7,2,5,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => 4

{{1},{2,5},{3},{4},{6,7}} => [1,5,3,4,2,7,6] => [1,4,2,5,3,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3

{{1},{2,5},{3},{4},{6},{7}} => [1,5,3,4,2,6,7] => [1,4,2,5,3,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2

{{1,6,7},{2},{3,5},{4}} => [6,2,5,4,3,7,1] => [7,1,5,4,3,6,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => 4

{{1,6},{2,7},{3,5},{4}} => [6,7,5,4,3,1,2] => [2,7,5,4,3,1,6] => [[.,[[[[.,.],.],.],.]],[.,.]] => 4

{{1,6},{2},{3,5,7},{4}} => [6,2,5,4,7,1,3] => [3,7,1,5,4,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => 4

{{1,6},{2},{3,5},{4,7}} => [6,2,5,7,3,1,4] => [4,7,3,1,5,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => 3

{{1,6},{2},{3,5},{4},{7}} => [6,2,5,4,3,1,7] => [5,4,3,1,6,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => 1

{{1,7},{2,6},{3,5},{4}} => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => 0

{{1},{2,6,7},{3,5},{4}} => [1,6,5,4,3,7,2] => [1,7,2,6,5,4,3] => [.,[[.,.],[[[[.,.],.],.],.]]] => 4

{{1},{2,6},{3,5,7},{4}} => [1,6,5,4,7,2,3] => [1,3,7,2,6,5,4] => [.,[[.,[.,.]],[[[.,.],.],.]]] => 4

{{1},{2,6},{3,5},{4,7}} => [1,6,5,7,3,2,4] => [1,4,7,3,2,6,5] => [.,[[[.,[.,.]],.],[[.,.],.]]] => 4

{{1},{2,6},{3,5},{4},{7}} => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]] => 4

{{1,7},{2},{3,5,6},{4}} => [7,2,5,4,6,3,1] => [6,3,1,5,4,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => 3

{{1},{2,7},{3,5,6},{4}} => [1,7,5,4,6,3,2] => [1,6,3,2,7,5,4] => [.,[[[.,.],.],[[[.,.],.],.]]] => 4

{{1},{2},{3,5,6,7},{4}} => [1,2,5,4,6,7,3] => [1,2,7,3,5,4,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2

{{1},{2},{3,5,6},{4,7}} => [1,2,5,7,6,3,4] => [1,2,4,7,6,3,5] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => 3

{{1},{2},{3,5,6},{4},{7}} => [1,2,5,4,6,3,7] => [1,2,6,3,5,4,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2

{{1,7},{2},{3,5},{4,6}} => [7,2,5,6,3,4,1] => [4,1,6,3,5,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 4

{{1},{2,7},{3,5},{4,6}} => [1,7,5,6,3,4,2] => [1,4,2,6,3,7,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3

{{1},{2},{3,5,7},{4,6}} => [1,2,5,6,7,4,3] => [1,2,7,4,3,5,6] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => 2

{{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => [1,2,7,4,6,3,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => 3

{{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => [1,2,4,6,3,5,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2

{{1,7},{2},{3,5},{4},{6}} => [7,2,5,4,3,6,1] => [6,1,5,4,3,7,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => 4

{{1},{2,7},{3,5},{4},{6}} => [1,7,5,4,3,6,2] => [1,6,2,7,5,4,3] => [.,[[.,.],[[[[.,.],.],.],.]]] => 4

{{1},{2},{3,5,7},{4},{6}} => [1,2,5,4,7,6,3] => [1,2,7,6,3,5,4] => [.,[.,[[[.,.],.],[[.,.],.]]]] => 3

{{1},{2},{3,5},{4,7},{6}} => [1,2,5,7,3,6,4] => [1,2,6,4,7,3,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => 3

{{1},{2},{3,5},{4},{6,7}} => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]] => 3

{{1},{2},{3,5},{4},{6},{7}} => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => 2

{{1,6,7},{2},{3},{4,5}} => [6,2,3,5,4,7,1] => [7,1,3,5,4,6,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => 4

{{1,6},{2,7},{3},{4,5}} => [6,7,3,5,4,1,2] => [2,5,4,1,7,3,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => 3

{{1,6},{2},{3,7},{4,5}} => [6,2,7,5,4,1,3] => [3,7,5,4,1,6,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => 4

{{1,6},{2},{3},{4,5,7}} => [6,2,3,5,7,1,4] => [4,7,1,3,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 4

{{1,6},{2},{3},{4,5},{7}} => [6,2,3,5,4,1,7] => [5,4,1,3,6,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2

{{1,7},{2,6},{3},{4,5}} => [7,6,3,5,4,2,1] => [5,4,2,1,7,6,3] => [[[[.,.],.],.],[[[.,.],.],.]] => 2

{{1},{2,6,7},{3},{4,5}} => [1,6,3,5,4,7,2] => [1,7,2,5,4,6,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => 4

{{1},{2,6},{3,7},{4,5}} => [1,6,7,5,4,2,3] => [1,3,7,5,4,2,6] => [.,[[.,[[[.,.],.],.]],[.,.]]] => 4

{{1},{2,6},{3},{4,5,7}} => [1,6,3,5,7,2,4] => [1,4,7,2,5,6,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 4

{{1},{2,6},{3},{4,5},{7}} => [1,6,3,5,4,2,7] => [1,5,4,2,6,3,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 3

{{1,7},{2},{3,6},{4,5}} => [7,2,6,5,4,3,1] => [6,5,4,3,1,7,2] => [[[[[.,.],.],.],.],[[.,.],.]] => 1

{{1},{2,7},{3,6},{4,5}} => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]] => 5

{{1},{2},{3,6,7},{4,5}} => [1,2,6,5,4,7,3] => [1,2,7,3,6,5,4] => [.,[.,[[.,.],[[[.,.],.],.]]]] => 3

{{1},{2},{3,6},{4,5,7}} => [1,2,6,5,7,3,4] => [1,2,4,7,3,6,5] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 3

{{1},{2},{3,6},{4,5},{7}} => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]] => 3

{{1,7},{2},{3},{4,5,6}} => [7,2,3,5,6,4,1] => [6,4,1,3,5,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 3

{{1},{2,7},{3},{4,5,6}} => [1,7,3,5,6,4,2] => [1,6,4,2,5,7,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => 4

{{1},{2},{3,7},{4,5,6}} => [1,2,7,5,6,4,3] => [1,2,6,4,3,7,5] => [.,[.,[[[.,.],.],[[.,.],.]]]] => 3

{{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1

{{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1

{{1,7},{2},{3},{4,5},{6}} => [7,2,3,5,4,6,1] => [6,1,3,5,4,7,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => 4

{{1},{2,7},{3},{4,5},{6}} => [1,7,3,5,4,6,2] => [1,6,2,5,4,7,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => 4

{{1},{2},{3,7},{4,5},{6}} => [1,2,7,5,4,6,3] => [1,2,6,3,7,5,4] => [.,[.,[[.,.],[[[.,.],.],.]]]] => 3

{{1},{2},{3},{4,5,7},{6}} => [1,2,3,5,7,6,4] => [1,2,3,7,6,4,5] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => 2

{{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 2

{{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1

{{1,6,7},{2},{3},{4},{5}} => [6,2,3,4,5,7,1] => [7,1,3,4,5,6,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 4

{{1,6},{2,7},{3},{4},{5}} => [6,7,3,4,5,1,2] => [2,5,1,4,7,3,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3

{{1,6},{2},{3,7},{4},{5}} => [6,2,7,4,5,1,3] => [3,5,1,7,4,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => 4

{{1,6},{2},{3},{4,7},{5}} => [6,2,3,7,5,1,4] => [4,7,5,1,3,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => 4

{{1,6},{2},{3},{4},{5,7}} => [6,2,3,4,7,1,5] => [5,7,1,3,4,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 4

{{1,6},{2},{3},{4},{5},{7}} => [6,2,3,4,5,1,7] => [5,1,3,4,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3

{{1,7},{2,6},{3},{4},{5}} => [7,6,3,4,5,2,1] => [5,2,1,4,7,6,3] => [[[.,.],.],[[.,[[.,.],.]],.]] => 3

{{1},{2,6,7},{3},{4},{5}} => [1,6,3,4,5,7,2] => [1,7,2,4,5,6,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => 4

{{1},{2,6},{3,7},{4},{5}} => [1,6,7,4,5,2,3] => [1,3,5,2,7,4,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3

{{1},{2,6},{3},{4,7},{5}} => [1,6,3,7,5,2,4] => [1,4,7,5,2,6,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => 4

{{1},{2,6},{3},{4},{5,7}} => [1,6,3,4,7,2,5] => [1,5,7,2,4,6,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 4

{{1},{2,6},{3},{4},{5},{7}} => [1,6,3,4,5,2,7] => [1,5,2,4,6,3,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3

{{1,7},{2},{3,6},{4},{5}} => [7,2,6,4,5,3,1] => [5,3,1,6,4,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => 3

{{1},{2,7},{3,6},{4},{5}} => [1,7,6,4,5,3,2] => [1,5,3,2,7,6,4] => [.,[[[.,.],.],[[[.,.],.],.]]] => 4

{{1},{2},{3,6,7},{4},{5}} => [1,2,6,4,5,7,3] => [1,2,7,3,5,6,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 3

{{1},{2},{3,6},{4,7},{5}} => [1,2,6,7,5,3,4] => [1,2,4,7,5,3,6] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => 3

{{1},{2},{3,6},{4},{5,7}} => [1,2,6,4,7,3,5] => [1,2,5,7,3,6,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 3

{{1},{2},{3,6},{4},{5},{7}} => [1,2,6,4,5,3,7] => [1,2,5,3,6,4,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2

{{1,7},{2},{3},{4,6},{5}} => [7,2,3,6,5,4,1] => [6,5,4,1,3,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2

{{1},{2,7},{3},{4,6},{5}} => [1,7,3,6,5,4,2] => [1,6,5,4,2,7,3] => [.,[[[[.,.],.],.],[[.,.],.]]] => 4

{{1},{2},{3,7},{4,6},{5}} => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]] => 4

{{1},{2},{3},{4,6,7},{5}} => [1,2,3,6,5,7,4] => [1,2,3,7,4,6,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 2

{{1},{2},{3},{4,6},{5,7}} => [1,2,3,6,7,4,5] => [1,2,3,5,7,4,6] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2

{{1},{2},{3},{4,6},{5},{7}} => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => 2

{{1,7},{2},{3},{4},{5,6}} => [7,2,3,4,6,5,1] => [6,5,1,3,4,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 3

{{1},{2,7},{3},{4},{5,6}} => [1,7,3,4,6,5,2] => [1,6,5,2,4,7,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => 4

{{1},{2},{3,7},{4},{5,6}} => [1,2,7,4,6,5,3] => [1,2,6,5,3,7,4] => [.,[.,[[[.,.],.],[[.,.],.]]]] => 3

{{1},{2},{3},{4,7},{5,6}} => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]] => 3

{{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 1

{{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 1

{{1,7},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,1] => [6,1,3,4,5,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 4

{{1},{2,7},{3},{4},{5},{6}} => [1,7,3,4,5,6,2] => [1,6,2,4,5,7,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => 4

{{1},{2},{3,7},{4},{5},{6}} => [1,2,7,4,5,6,3] => [1,2,6,3,5,7,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 3

{{1},{2},{3},{4,7},{5},{6}} => [1,2,3,7,5,6,4] => [1,2,3,6,4,7,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 2

{{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => 2

{{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1

{{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 0

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$F_{1} = 1$

$F_{2} = 2$

$F_{3} = 4 + q$

$F_{4} = 7 + 7\ q + q^{2}$

$F_{5} = 12 + 23\ q + 16\ q^{2} + q^{3}$

$F_{6} = 20 + 61\ q + 83\ q^{2} + 38\ q^{3} + q^{4}$

$F_{7} = 32 + 143\ q + 301\ q^{2} + 294\ q^{3} + 106\ q^{4} + q^{5}$

Description

The number of internal nodes of a binary tree.
That is, the total number of nodes of the tree minus St000203The number of external nodes of a binary tree.. A counting formula for the total number of internal nodes across all binary trees of size

$n$ is given in [1]. This is equivalent to the number of internal triangles in all triangulations of an

$(n+1)$ -gon.

Map

to permutation

Description

Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.

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

invert Laguerre heap

Description

The permutation obtained by inverting the corresponding Laguerre heap, according to Viennot.
Let

$\pi$ be a permutation. Following Viennot [1], we associate to

$\pi$ a heap of pieces, by considering each decreasing run

$(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of

$\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.