Identifier
-
Mp00090:
Permutations
—cycle-as-one-line notation⟶
Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
St000051: Binary trees ⟶ ℤ
Values
[1] => [1] => [1] => [.,.] => 0
[1,2] => [1,2] => [2,1] => [[.,.],.] => 1
[2,1] => [1,2] => [2,1] => [[.,.],.] => 1
[1,2,3] => [1,2,3] => [2,3,1] => [[.,[.,.]],.] => 2
[1,3,2] => [1,2,3] => [2,3,1] => [[.,[.,.]],.] => 2
[2,1,3] => [1,2,3] => [2,3,1] => [[.,[.,.]],.] => 2
[2,3,1] => [1,2,3] => [2,3,1] => [[.,[.,.]],.] => 2
[3,1,2] => [1,3,2] => [2,1,3] => [[.,.],[.,.]] => 1
[3,2,1] => [1,3,2] => [2,1,3] => [[.,.],[.,.]] => 1
[1,2,3,4] => [1,2,3,4] => [2,3,4,1] => [[.,[.,[.,.]]],.] => 3
[1,2,4,3] => [1,2,3,4] => [2,3,4,1] => [[.,[.,[.,.]]],.] => 3
[1,3,2,4] => [1,2,3,4] => [2,3,4,1] => [[.,[.,[.,.]]],.] => 3
[1,3,4,2] => [1,2,3,4] => [2,3,4,1] => [[.,[.,[.,.]]],.] => 3
[1,4,2,3] => [1,2,4,3] => [2,3,1,4] => [[.,[.,.]],[.,.]] => 2
[1,4,3,2] => [1,2,4,3] => [2,3,1,4] => [[.,[.,.]],[.,.]] => 2
[2,1,3,4] => [1,2,3,4] => [2,3,4,1] => [[.,[.,[.,.]]],.] => 3
[2,1,4,3] => [1,2,3,4] => [2,3,4,1] => [[.,[.,[.,.]]],.] => 3
[2,3,1,4] => [1,2,3,4] => [2,3,4,1] => [[.,[.,[.,.]]],.] => 3
[2,3,4,1] => [1,2,3,4] => [2,3,4,1] => [[.,[.,[.,.]]],.] => 3
[2,4,1,3] => [1,2,4,3] => [2,3,1,4] => [[.,[.,.]],[.,.]] => 2
[2,4,3,1] => [1,2,4,3] => [2,3,1,4] => [[.,[.,.]],[.,.]] => 2
[3,1,2,4] => [1,3,2,4] => [2,4,3,1] => [[.,[[.,.],.]],.] => 3
[3,1,4,2] => [1,3,4,2] => [2,1,3,4] => [[.,.],[.,[.,.]]] => 1
[3,2,1,4] => [1,3,2,4] => [2,4,3,1] => [[.,[[.,.],.]],.] => 3
[3,2,4,1] => [1,3,4,2] => [2,1,3,4] => [[.,.],[.,[.,.]]] => 1
[3,4,1,2] => [1,3,2,4] => [2,4,3,1] => [[.,[[.,.],.]],.] => 3
[3,4,2,1] => [1,3,2,4] => [2,4,3,1] => [[.,[[.,.],.]],.] => 3
[4,1,2,3] => [1,4,3,2] => [2,1,4,3] => [[.,.],[[.,.],.]] => 1
[4,1,3,2] => [1,4,2,3] => [2,4,1,3] => [[.,[.,.]],[.,.]] => 2
[4,2,1,3] => [1,4,3,2] => [2,1,4,3] => [[.,.],[[.,.],.]] => 1
[4,2,3,1] => [1,4,2,3] => [2,4,1,3] => [[.,[.,.]],[.,.]] => 2
[4,3,1,2] => [1,4,2,3] => [2,4,1,3] => [[.,[.,.]],[.,.]] => 2
[4,3,2,1] => [1,4,2,3] => [2,4,1,3] => [[.,[.,.]],[.,.]] => 2
[1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[1,2,3,5,4] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[1,2,4,3,5] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[1,2,4,5,3] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[1,2,5,3,4] => [1,2,3,5,4] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => 3
[1,2,5,4,3] => [1,2,3,5,4] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => 3
[1,3,2,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[1,3,2,5,4] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[1,3,4,2,5] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[1,3,4,5,2] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[1,3,5,2,4] => [1,2,3,5,4] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => 3
[1,3,5,4,2] => [1,2,3,5,4] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => 3
[1,4,2,3,5] => [1,2,4,3,5] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => 4
[1,4,2,5,3] => [1,2,4,5,3] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => 2
[1,4,3,2,5] => [1,2,4,3,5] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => 4
[1,4,3,5,2] => [1,2,4,5,3] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => 2
[1,4,5,2,3] => [1,2,4,3,5] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => 4
[1,4,5,3,2] => [1,2,4,3,5] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => 4
[1,5,2,3,4] => [1,2,5,4,3] => [2,3,1,5,4] => [[.,[.,.]],[[.,.],.]] => 2
[1,5,2,4,3] => [1,2,5,3,4] => [2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]] => 3
[1,5,3,2,4] => [1,2,5,4,3] => [2,3,1,5,4] => [[.,[.,.]],[[.,.],.]] => 2
[1,5,3,4,2] => [1,2,5,3,4] => [2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]] => 3
[1,5,4,2,3] => [1,2,5,3,4] => [2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]] => 3
[1,5,4,3,2] => [1,2,5,3,4] => [2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]] => 3
[2,1,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[2,1,3,5,4] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[2,1,4,3,5] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[2,1,4,5,3] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[2,1,5,3,4] => [1,2,3,5,4] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => 3
[2,1,5,4,3] => [1,2,3,5,4] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => 3
[2,3,1,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[2,3,1,5,4] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[2,3,4,1,5] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[2,3,4,5,1] => [1,2,3,4,5] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => 4
[2,3,5,1,4] => [1,2,3,5,4] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => 3
[2,3,5,4,1] => [1,2,3,5,4] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => 3
[2,4,1,3,5] => [1,2,4,3,5] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => 4
[2,4,1,5,3] => [1,2,4,5,3] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => 2
[2,4,3,1,5] => [1,2,4,3,5] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => 4
[2,4,3,5,1] => [1,2,4,5,3] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => 2
[2,4,5,1,3] => [1,2,4,3,5] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => 4
[2,4,5,3,1] => [1,2,4,3,5] => [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => 4
[2,5,1,3,4] => [1,2,5,4,3] => [2,3,1,5,4] => [[.,[.,.]],[[.,.],.]] => 2
[2,5,1,4,3] => [1,2,5,3,4] => [2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]] => 3
[2,5,3,1,4] => [1,2,5,4,3] => [2,3,1,5,4] => [[.,[.,.]],[[.,.],.]] => 2
[2,5,3,4,1] => [1,2,5,3,4] => [2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]] => 3
[2,5,4,1,3] => [1,2,5,3,4] => [2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]] => 3
[2,5,4,3,1] => [1,2,5,3,4] => [2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]] => 3
[3,1,2,4,5] => [1,3,2,4,5] => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => 4
[3,1,2,5,4] => [1,3,2,4,5] => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => 4
[3,1,4,2,5] => [1,3,4,2,5] => [2,5,3,4,1] => [[.,[[.,.],[.,.]]],.] => 4
[3,1,4,5,2] => [1,3,4,5,2] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => 1
[3,1,5,2,4] => [1,3,5,4,2] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => 1
[3,1,5,4,2] => [1,3,5,2,4] => [2,5,3,1,4] => [[.,[[.,.],.]],[.,.]] => 3
[3,2,1,4,5] => [1,3,2,4,5] => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => 4
[3,2,1,5,4] => [1,3,2,4,5] => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => 4
[3,2,4,1,5] => [1,3,4,2,5] => [2,5,3,4,1] => [[.,[[.,.],[.,.]]],.] => 4
[3,2,4,5,1] => [1,3,4,5,2] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => 1
[3,2,5,1,4] => [1,3,5,4,2] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => 1
[3,2,5,4,1] => [1,3,5,2,4] => [2,5,3,1,4] => [[.,[[.,.],.]],[.,.]] => 3
[3,4,1,2,5] => [1,3,2,4,5] => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => 4
[3,4,1,5,2] => [1,3,2,4,5] => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => 4
[3,4,2,1,5] => [1,3,2,4,5] => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => 4
[3,4,2,5,1] => [1,3,2,4,5] => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => 4
[3,4,5,1,2] => [1,3,5,2,4] => [2,5,3,1,4] => [[.,[[.,.],.]],[.,.]] => 3
[3,4,5,2,1] => [1,3,5,2,4] => [2,5,3,1,4] => [[.,[[.,.],.]],[.,.]] => 3
[3,5,1,2,4] => [1,3,2,5,4] => [2,4,3,1,5] => [[.,[[.,.],.]],[.,.]] => 3
[3,5,1,4,2] => [1,3,2,5,4] => [2,4,3,1,5] => [[.,[[.,.],.]],[.,.]] => 3
>>> Load all 873 entries. <<<[3,5,2,1,4] => [1,3,2,5,4] => [2,4,3,1,5] => [[.,[[.,.],.]],[.,.]] => 3
[3,5,2,4,1] => [1,3,2,5,4] => [2,4,3,1,5] => [[.,[[.,.],.]],[.,.]] => 3
[3,5,4,1,2] => [1,3,4,2,5] => [2,5,3,4,1] => [[.,[[.,.],[.,.]]],.] => 4
[3,5,4,2,1] => [1,3,4,2,5] => [2,5,3,4,1] => [[.,[[.,.],[.,.]]],.] => 4
[4,1,2,3,5] => [1,4,3,2,5] => [2,5,4,3,1] => [[.,[[[.,.],.],.]],.] => 4
[4,1,2,5,3] => [1,4,5,3,2] => [2,1,5,3,4] => [[.,.],[[.,.],[.,.]]] => 1
[4,1,3,2,5] => [1,4,2,3,5] => [2,4,5,3,1] => [[.,[[.,[.,.]],.]],.] => 4
[4,1,3,5,2] => [1,4,5,2,3] => [2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]] => 2
[4,1,5,2,3] => [1,4,2,3,5] => [2,4,5,3,1] => [[.,[[.,[.,.]],.]],.] => 4
[4,1,5,3,2] => [1,4,3,5,2] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => 1
[4,2,1,3,5] => [1,4,3,2,5] => [2,5,4,3,1] => [[.,[[[.,.],.],.]],.] => 4
[4,2,1,5,3] => [1,4,5,3,2] => [2,1,5,3,4] => [[.,.],[[.,.],[.,.]]] => 1
[4,2,3,1,5] => [1,4,2,3,5] => [2,4,5,3,1] => [[.,[[.,[.,.]],.]],.] => 4
[4,2,3,5,1] => [1,4,5,2,3] => [2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]] => 2
[4,2,5,1,3] => [1,4,2,3,5] => [2,4,5,3,1] => [[.,[[.,[.,.]],.]],.] => 4
[4,2,5,3,1] => [1,4,3,5,2] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => 1
[4,3,1,2,5] => [1,4,2,3,5] => [2,4,5,3,1] => [[.,[[.,[.,.]],.]],.] => 4
[4,3,1,5,2] => [1,4,5,2,3] => [2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]] => 2
[4,3,2,1,5] => [1,4,2,3,5] => [2,4,5,3,1] => [[.,[[.,[.,.]],.]],.] => 4
[4,3,2,5,1] => [1,4,5,2,3] => [2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]] => 2
[4,3,5,1,2] => [1,4,2,3,5] => [2,4,5,3,1] => [[.,[[.,[.,.]],.]],.] => 4
[4,3,5,2,1] => [1,4,2,3,5] => [2,4,5,3,1] => [[.,[[.,[.,.]],.]],.] => 4
[4,5,1,2,3] => [1,4,2,5,3] => [2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]] => 2
[4,5,1,3,2] => [1,4,3,2,5] => [2,5,4,3,1] => [[.,[[[.,.],.],.]],.] => 4
[4,5,2,1,3] => [1,4,2,5,3] => [2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]] => 2
[4,5,2,3,1] => [1,4,3,2,5] => [2,5,4,3,1] => [[.,[[[.,.],.],.]],.] => 4
[4,5,3,1,2] => [1,4,2,5,3] => [2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]] => 2
[4,5,3,2,1] => [1,4,2,5,3] => [2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]] => 2
[5,1,2,3,4] => [1,5,4,3,2] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]] => 1
[5,1,2,4,3] => [1,5,3,2,4] => [2,5,4,1,3] => [[.,[[.,.],.]],[.,.]] => 3
[5,1,3,2,4] => [1,5,4,2,3] => [2,5,1,4,3] => [[.,[.,.]],[[.,.],.]] => 2
[5,1,3,4,2] => [1,5,2,3,4] => [2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => 3
[5,1,4,2,3] => [1,5,3,4,2] => [2,1,4,5,3] => [[.,.],[[.,[.,.]],.]] => 1
[5,1,4,3,2] => [1,5,2,3,4] => [2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => 3
[5,2,1,3,4] => [1,5,4,3,2] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]] => 1
[5,2,1,4,3] => [1,5,3,2,4] => [2,5,4,1,3] => [[.,[[.,.],.]],[.,.]] => 3
[5,2,3,1,4] => [1,5,4,2,3] => [2,5,1,4,3] => [[.,[.,.]],[[.,.],.]] => 2
[5,2,3,4,1] => [1,5,2,3,4] => [2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => 3
[5,2,4,1,3] => [1,5,3,4,2] => [2,1,4,5,3] => [[.,.],[[.,[.,.]],.]] => 1
[5,2,4,3,1] => [1,5,2,3,4] => [2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => 3
[5,3,1,2,4] => [1,5,4,2,3] => [2,5,1,4,3] => [[.,[.,.]],[[.,.],.]] => 2
[5,3,1,4,2] => [1,5,2,3,4] => [2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => 3
[5,3,2,1,4] => [1,5,4,2,3] => [2,5,1,4,3] => [[.,[.,.]],[[.,.],.]] => 2
[5,3,2,4,1] => [1,5,2,3,4] => [2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => 3
[5,3,4,1,2] => [1,5,2,3,4] => [2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => 3
[5,3,4,2,1] => [1,5,2,3,4] => [2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => 3
[5,4,1,2,3] => [1,5,3,2,4] => [2,5,4,1,3] => [[.,[[.,.],.]],[.,.]] => 3
[5,4,1,3,2] => [1,5,2,4,3] => [2,4,1,5,3] => [[.,[.,.]],[[.,.],.]] => 2
[5,4,2,1,3] => [1,5,3,2,4] => [2,5,4,1,3] => [[.,[[.,.],.]],[.,.]] => 3
[5,4,2,3,1] => [1,5,2,4,3] => [2,4,1,5,3] => [[.,[.,.]],[[.,.],.]] => 2
[5,4,3,1,2] => [1,5,2,4,3] => [2,4,1,5,3] => [[.,[.,.]],[[.,.],.]] => 2
[5,4,3,2,1] => [1,5,2,4,3] => [2,4,1,5,3] => [[.,[.,.]],[[.,.],.]] => 2
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,2,3,4,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,2,3,5,4,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,2,3,5,6,4] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,2,3,6,4,5] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,2,3,6,5,4] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,2,4,3,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,2,4,3,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,2,4,5,3,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,2,4,5,6,3] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,2,4,6,3,5] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,2,4,6,5,3] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,2,5,3,4,6] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[1,2,5,3,6,4] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[1,2,5,4,3,6] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[1,2,5,4,6,3] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[1,2,5,6,3,4] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[1,2,5,6,4,3] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[1,2,6,3,4,5] => [1,2,3,6,5,4] => [2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,2,6,3,5,4] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,2,6,4,3,5] => [1,2,3,6,5,4] => [2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,2,6,4,5,3] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,2,6,5,3,4] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,2,6,5,4,3] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,3,2,4,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,3,2,4,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,3,2,5,4,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,3,2,5,6,4] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,3,2,6,4,5] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,3,2,6,5,4] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,3,4,2,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,3,4,2,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,3,4,5,2,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,3,4,5,6,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[1,3,4,6,2,5] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,3,4,6,5,2] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,3,5,2,4,6] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[1,3,5,2,6,4] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[1,3,5,4,2,6] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[1,3,5,4,6,2] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[1,3,5,6,2,4] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[1,3,5,6,4,2] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[1,3,6,2,4,5] => [1,2,3,6,5,4] => [2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,3,6,2,5,4] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,3,6,4,2,5] => [1,2,3,6,5,4] => [2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,3,6,4,5,2] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,3,6,5,2,4] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,3,6,5,4,2] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,4,2,3,5,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[1,4,2,3,6,5] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[1,4,2,5,3,6] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[1,4,2,5,6,3] => [1,2,4,5,6,3] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,4,2,6,3,5] => [1,2,4,6,5,3] => [2,3,1,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,4,2,6,5,3] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[1,4,3,2,5,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[1,4,3,2,6,5] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[1,4,3,5,2,6] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[1,4,3,5,6,2] => [1,2,4,5,6,3] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,4,3,6,2,5] => [1,2,4,6,5,3] => [2,3,1,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,4,3,6,5,2] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[1,4,5,2,3,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[1,4,5,2,6,3] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[1,4,5,3,2,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[1,4,5,3,6,2] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[1,4,5,6,2,3] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[1,4,5,6,3,2] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[1,4,6,2,3,5] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[1,4,6,2,5,3] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[1,4,6,3,2,5] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[1,4,6,3,5,2] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[1,4,6,5,2,3] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[1,4,6,5,3,2] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[1,5,2,3,4,6] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.] => 5
[1,5,2,3,6,4] => [1,2,5,6,4,3] => [2,3,1,6,4,5] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,5,2,4,3,6] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[1,5,2,4,6,3] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[1,5,2,6,3,4] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[1,5,2,6,4,3] => [1,2,5,4,6,3] => [2,3,1,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,5,3,2,4,6] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.] => 5
[1,5,3,2,6,4] => [1,2,5,6,4,3] => [2,3,1,6,4,5] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,5,3,4,2,6] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[1,5,3,4,6,2] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[1,5,3,6,2,4] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[1,5,3,6,4,2] => [1,2,5,4,6,3] => [2,3,1,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,5,4,2,3,6] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[1,5,4,2,6,3] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[1,5,4,3,2,6] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[1,5,4,3,6,2] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[1,5,4,6,2,3] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[1,5,4,6,3,2] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[1,5,6,2,3,4] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[1,5,6,2,4,3] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.] => 5
[1,5,6,3,2,4] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[1,5,6,3,4,2] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.] => 5
[1,5,6,4,2,3] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[1,5,6,4,3,2] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[1,6,2,3,4,5] => [1,2,6,5,4,3] => [2,3,1,6,5,4] => [[.,[.,.]],[[[.,.],.],.]] => 2
[1,6,2,3,5,4] => [1,2,6,4,3,5] => [2,3,6,5,1,4] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[1,6,2,4,3,5] => [1,2,6,5,3,4] => [2,3,6,1,5,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,6,2,4,5,3] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,6,2,5,3,4] => [1,2,6,4,5,3] => [2,3,1,5,6,4] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[1,6,2,5,4,3] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,6,3,2,4,5] => [1,2,6,5,4,3] => [2,3,1,6,5,4] => [[.,[.,.]],[[[.,.],.],.]] => 2
[1,6,3,2,5,4] => [1,2,6,4,3,5] => [2,3,6,5,1,4] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[1,6,3,4,2,5] => [1,2,6,5,3,4] => [2,3,6,1,5,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,6,3,4,5,2] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,6,3,5,2,4] => [1,2,6,4,5,3] => [2,3,1,5,6,4] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[1,6,3,5,4,2] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,6,4,2,3,5] => [1,2,6,5,3,4] => [2,3,6,1,5,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,6,4,2,5,3] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,6,4,3,2,5] => [1,2,6,5,3,4] => [2,3,6,1,5,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,6,4,3,5,2] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,6,4,5,2,3] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,6,4,5,3,2] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[1,6,5,2,3,4] => [1,2,6,4,3,5] => [2,3,6,5,1,4] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[1,6,5,2,4,3] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,6,5,3,2,4] => [1,2,6,4,3,5] => [2,3,6,5,1,4] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[1,6,5,3,4,2] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,6,5,4,2,3] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[1,6,5,4,3,2] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[2,1,3,4,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,1,3,4,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,1,3,5,4,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,1,3,5,6,4] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,1,3,6,4,5] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,1,3,6,5,4] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,1,4,3,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,1,4,3,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,1,4,5,3,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,1,4,5,6,3] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,1,4,6,3,5] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,1,4,6,5,3] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,1,5,3,4,6] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[2,1,5,3,6,4] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[2,1,5,4,3,6] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[2,1,5,4,6,3] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[2,1,5,6,3,4] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[2,1,5,6,4,3] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[2,1,6,3,4,5] => [1,2,3,6,5,4] => [2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[2,1,6,3,5,4] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,1,6,4,3,5] => [1,2,3,6,5,4] => [2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[2,1,6,4,5,3] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,1,6,5,3,4] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,1,6,5,4,3] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,3,1,4,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,3,1,4,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,3,1,5,4,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,3,1,5,6,4] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,3,1,6,4,5] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,3,1,6,5,4] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,3,4,1,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,3,4,1,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,3,4,5,1,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,3,4,5,6,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
[2,3,4,6,1,5] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,3,4,6,5,1] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,3,5,1,4,6] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[2,3,5,1,6,4] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[2,3,5,4,1,6] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[2,3,5,4,6,1] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[2,3,5,6,1,4] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[2,3,5,6,4,1] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => 5
[2,3,6,1,4,5] => [1,2,3,6,5,4] => [2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[2,3,6,1,5,4] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,3,6,4,1,5] => [1,2,3,6,5,4] => [2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[2,3,6,4,5,1] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,3,6,5,1,4] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,3,6,5,4,1] => [1,2,3,6,4,5] => [2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,4,1,3,5,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[2,4,1,3,6,5] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[2,4,1,5,3,6] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[2,4,1,5,6,3] => [1,2,4,5,6,3] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[2,4,1,6,3,5] => [1,2,4,6,5,3] => [2,3,1,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[2,4,1,6,5,3] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[2,4,3,1,5,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[2,4,3,1,6,5] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[2,4,3,5,1,6] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[2,4,3,5,6,1] => [1,2,4,5,6,3] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[2,4,3,6,1,5] => [1,2,4,6,5,3] => [2,3,1,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[2,4,3,6,5,1] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[2,4,5,1,3,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[2,4,5,1,6,3] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[2,4,5,3,1,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[2,4,5,3,6,1] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[2,4,5,6,1,3] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[2,4,5,6,3,1] => [1,2,4,6,3,5] => [2,3,6,4,1,5] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[2,4,6,1,3,5] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[2,4,6,1,5,3] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[2,4,6,3,1,5] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[2,4,6,3,5,1] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[2,4,6,5,1,3] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[2,4,6,5,3,1] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.] => 5
[2,5,1,3,4,6] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.] => 5
[2,5,1,3,6,4] => [1,2,5,6,4,3] => [2,3,1,6,4,5] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[2,5,1,4,3,6] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[2,5,1,4,6,3] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[2,5,1,6,3,4] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[2,5,1,6,4,3] => [1,2,5,4,6,3] => [2,3,1,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[2,5,3,1,4,6] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.] => 5
[2,5,3,1,6,4] => [1,2,5,6,4,3] => [2,3,1,6,4,5] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[2,5,3,4,1,6] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[2,5,3,4,6,1] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[2,5,3,6,1,4] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[2,5,3,6,4,1] => [1,2,5,4,6,3] => [2,3,1,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[2,5,4,1,3,6] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[2,5,4,1,6,3] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[2,5,4,3,1,6] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[2,5,4,3,6,1] => [1,2,5,6,3,4] => [2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[2,5,4,6,1,3] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[2,5,4,6,3,1] => [1,2,5,3,4,6] => [2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => 5
[2,5,6,1,3,4] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[2,5,6,1,4,3] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.] => 5
[2,5,6,3,1,4] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[2,5,6,3,4,1] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.] => 5
[2,5,6,4,1,3] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[2,5,6,4,3,1] => [1,2,5,3,6,4] => [2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[2,6,1,3,4,5] => [1,2,6,5,4,3] => [2,3,1,6,5,4] => [[.,[.,.]],[[[.,.],.],.]] => 2
[2,6,1,3,5,4] => [1,2,6,4,3,5] => [2,3,6,5,1,4] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[2,6,1,4,3,5] => [1,2,6,5,3,4] => [2,3,6,1,5,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[2,6,1,4,5,3] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,6,1,5,3,4] => [1,2,6,4,5,3] => [2,3,1,5,6,4] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[2,6,1,5,4,3] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,6,3,1,4,5] => [1,2,6,5,4,3] => [2,3,1,6,5,4] => [[.,[.,.]],[[[.,.],.],.]] => 2
[2,6,3,1,5,4] => [1,2,6,4,3,5] => [2,3,6,5,1,4] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[2,6,3,4,1,5] => [1,2,6,5,3,4] => [2,3,6,1,5,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[2,6,3,4,5,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,6,3,5,1,4] => [1,2,6,4,5,3] => [2,3,1,5,6,4] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[2,6,3,5,4,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,6,4,1,3,5] => [1,2,6,5,3,4] => [2,3,6,1,5,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[2,6,4,1,5,3] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,6,4,3,1,5] => [1,2,6,5,3,4] => [2,3,6,1,5,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[2,6,4,3,5,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,6,4,5,1,3] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,6,4,5,3,1] => [1,2,6,3,4,5] => [2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[2,6,5,1,3,4] => [1,2,6,4,3,5] => [2,3,6,5,1,4] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[2,6,5,1,4,3] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[2,6,5,3,1,4] => [1,2,6,4,3,5] => [2,3,6,5,1,4] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[2,6,5,3,4,1] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[2,6,5,4,1,3] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[2,6,5,4,3,1] => [1,2,6,3,5,4] => [2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[3,1,2,4,5,6] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,1,2,4,6,5] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,1,2,5,4,6] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,1,2,5,6,4] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,1,2,6,4,5] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,1,2,6,5,4] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,1,4,2,5,6] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,1,4,2,6,5] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,1,4,5,2,6] => [1,3,4,5,2,6] => [2,6,3,4,5,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,1,4,5,6,2] => [1,3,4,5,6,2] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 1
[3,1,4,6,2,5] => [1,3,4,6,5,2] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 1
[3,1,4,6,5,2] => [1,3,4,6,2,5] => [2,6,3,4,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,1,5,2,4,6] => [1,3,5,4,2,6] => [2,6,3,5,4,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,1,5,2,6,4] => [1,3,5,6,4,2] => [2,1,3,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]] => 1
[3,1,5,4,2,6] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,1,5,4,6,2] => [1,3,5,6,2,4] => [2,6,3,1,4,5] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[3,1,5,6,2,4] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,1,5,6,4,2] => [1,3,5,4,6,2] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => 1
[3,1,6,2,4,5] => [1,3,6,5,4,2] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => 1
[3,1,6,2,5,4] => [1,3,6,4,2,5] => [2,6,3,5,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,1,6,4,2,5] => [1,3,6,5,2,4] => [2,6,3,1,5,4] => [[.,[[.,.],.]],[[.,.],.]] => 3
[3,1,6,4,5,2] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,1,6,5,2,4] => [1,3,6,4,5,2] => [2,1,3,5,6,4] => [[.,.],[.,[[.,[.,.]],.]]] => 1
[3,1,6,5,4,2] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,2,1,4,5,6] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,2,1,4,6,5] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,2,1,5,4,6] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,2,1,5,6,4] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,2,1,6,4,5] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,2,1,6,5,4] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,2,4,1,5,6] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,2,4,1,6,5] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,2,4,5,1,6] => [1,3,4,5,2,6] => [2,6,3,4,5,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,2,4,5,6,1] => [1,3,4,5,6,2] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 1
[3,2,4,6,1,5] => [1,3,4,6,5,2] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 1
[3,2,4,6,5,1] => [1,3,4,6,2,5] => [2,6,3,4,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,2,5,1,4,6] => [1,3,5,4,2,6] => [2,6,3,5,4,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,2,5,1,6,4] => [1,3,5,6,4,2] => [2,1,3,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]] => 1
[3,2,5,4,1,6] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,2,5,4,6,1] => [1,3,5,6,2,4] => [2,6,3,1,4,5] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[3,2,5,6,1,4] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,2,5,6,4,1] => [1,3,5,4,6,2] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => 1
[3,2,6,1,4,5] => [1,3,6,5,4,2] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => 1
[3,2,6,1,5,4] => [1,3,6,4,2,5] => [2,6,3,5,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,2,6,4,1,5] => [1,3,6,5,2,4] => [2,6,3,1,5,4] => [[.,[[.,.],.]],[[.,.],.]] => 3
[3,2,6,4,5,1] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,2,6,5,1,4] => [1,3,6,4,5,2] => [2,1,3,5,6,4] => [[.,.],[.,[[.,[.,.]],.]]] => 1
[3,2,6,5,4,1] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,4,1,2,5,6] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,4,1,2,6,5] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,4,1,5,2,6] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,4,1,5,6,2] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,4,1,6,2,5] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,4,1,6,5,2] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,4,2,1,5,6] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,4,2,1,6,5] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,4,2,5,1,6] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,4,2,5,6,1] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,4,2,6,1,5] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,4,2,6,5,1] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,4,5,1,2,6] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,4,5,1,6,2] => [1,3,5,6,2,4] => [2,6,3,1,4,5] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[3,4,5,2,1,6] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,4,5,2,6,1] => [1,3,5,6,2,4] => [2,6,3,1,4,5] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[3,4,5,6,1,2] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,4,5,6,2,1] => [1,3,5,2,4,6] => [2,5,3,6,4,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,4,6,1,2,5] => [1,3,6,5,2,4] => [2,6,3,1,5,4] => [[.,[[.,.],.]],[[.,.],.]] => 3
[3,4,6,1,5,2] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,4,6,2,1,5] => [1,3,6,5,2,4] => [2,6,3,1,5,4] => [[.,[[.,.],.]],[[.,.],.]] => 3
[3,4,6,2,5,1] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,4,6,5,1,2] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,4,6,5,2,1] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,5,1,2,4,6] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,5,1,2,6,4] => [1,3,2,5,6,4] => [2,4,3,1,5,6] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[3,5,1,4,2,6] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,5,1,4,6,2] => [1,3,2,5,6,4] => [2,4,3,1,5,6] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[3,5,1,6,2,4] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,5,1,6,4,2] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,5,2,1,4,6] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,5,2,1,6,4] => [1,3,2,5,6,4] => [2,4,3,1,5,6] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[3,5,2,4,1,6] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,5,2,4,6,1] => [1,3,2,5,6,4] => [2,4,3,1,5,6] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[3,5,2,6,1,4] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,5,2,6,4,1] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,5,4,1,2,6] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,5,4,1,6,2] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,5,4,2,1,6] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,5,4,2,6,1] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,5,4,6,1,2] => [1,3,4,6,2,5] => [2,6,3,4,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,5,4,6,2,1] => [1,3,4,6,2,5] => [2,6,3,4,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,5,6,1,2,4] => [1,3,6,4,2,5] => [2,6,3,5,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,5,6,1,4,2] => [1,3,6,2,5,4] => [2,5,3,1,6,4] => [[.,[[.,.],.]],[[.,.],.]] => 3
[3,5,6,2,1,4] => [1,3,6,4,2,5] => [2,6,3,5,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,5,6,2,4,1] => [1,3,6,2,5,4] => [2,5,3,1,6,4] => [[.,[[.,.],.]],[[.,.],.]] => 3
[3,5,6,4,1,2] => [1,3,6,2,5,4] => [2,5,3,1,6,4] => [[.,[[.,.],.]],[[.,.],.]] => 3
[3,5,6,4,2,1] => [1,3,6,2,5,4] => [2,5,3,1,6,4] => [[.,[[.,.],.]],[[.,.],.]] => 3
[3,6,1,2,4,5] => [1,3,2,6,5,4] => [2,4,3,1,6,5] => [[.,[[.,.],.]],[[.,.],.]] => 3
[3,6,1,2,5,4] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,6,1,4,2,5] => [1,3,2,6,5,4] => [2,4,3,1,6,5] => [[.,[[.,.],.]],[[.,.],.]] => 3
[3,6,1,4,5,2] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,6,1,5,2,4] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,6,1,5,4,2] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,6,2,1,4,5] => [1,3,2,6,5,4] => [2,4,3,1,6,5] => [[.,[[.,.],.]],[[.,.],.]] => 3
[3,6,2,1,5,4] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,6,2,4,1,5] => [1,3,2,6,5,4] => [2,4,3,1,6,5] => [[.,[[.,.],.]],[[.,.],.]] => 3
[3,6,2,4,5,1] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,6,2,5,1,4] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,6,2,5,4,1] => [1,3,2,6,4,5] => [2,4,3,6,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,6,4,1,2,5] => [1,3,4,2,6,5] => [2,5,3,4,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,6,4,1,5,2] => [1,3,4,2,6,5] => [2,5,3,4,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,6,4,2,1,5] => [1,3,4,2,6,5] => [2,5,3,4,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,6,4,2,5,1] => [1,3,4,2,6,5] => [2,5,3,4,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[3,6,4,5,1,2] => [1,3,4,5,2,6] => [2,6,3,4,5,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,6,4,5,2,1] => [1,3,4,5,2,6] => [2,6,3,4,5,1] => [[.,[[.,.],[.,[.,.]]]],.] => 5
[3,6,5,1,2,4] => [1,3,5,2,6,4] => [2,5,3,1,4,6] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[3,6,5,1,4,2] => [1,3,5,4,2,6] => [2,6,3,5,4,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,6,5,2,1,4] => [1,3,5,2,6,4] => [2,5,3,1,4,6] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[3,6,5,2,4,1] => [1,3,5,4,2,6] => [2,6,3,5,4,1] => [[.,[[.,.],[[.,.],.]]],.] => 5
[3,6,5,4,1,2] => [1,3,5,2,6,4] => [2,5,3,1,4,6] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[3,6,5,4,2,1] => [1,3,5,2,6,4] => [2,5,3,1,4,6] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[4,1,2,3,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,1,2,3,6,5] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,1,2,5,3,6] => [1,4,5,3,2,6] => [2,6,5,3,4,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,1,2,5,6,3] => [1,4,5,6,3,2] => [2,1,6,3,4,5] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[4,1,2,6,3,5] => [1,4,6,5,3,2] => [2,1,6,3,5,4] => [[.,.],[[.,.],[[.,.],.]]] => 1
[4,1,2,6,5,3] => [1,4,6,3,2,5] => [2,6,5,3,1,4] => [[.,[[[.,.],.],.]],[.,.]] => 4
[4,1,3,2,5,6] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,1,3,2,6,5] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,1,3,5,2,6] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,1,3,5,6,2] => [1,4,5,6,2,3] => [2,6,1,3,4,5] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[4,1,3,6,2,5] => [1,4,6,5,2,3] => [2,6,1,3,5,4] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[4,1,3,6,5,2] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,1,5,2,3,6] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,1,5,2,6,3] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,1,5,3,2,6] => [1,4,3,5,2,6] => [2,6,4,3,5,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,1,5,3,6,2] => [1,4,3,5,6,2] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[4,1,5,6,2,3] => [1,4,6,3,5,2] => [2,1,5,3,6,4] => [[.,.],[[.,.],[[.,.],.]]] => 1
[4,1,5,6,3,2] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,1,6,2,3,5] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,1,6,2,5,3] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,1,6,3,2,5] => [1,4,3,6,5,2] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => 1
[4,1,6,3,5,2] => [1,4,3,6,2,5] => [2,6,4,3,1,5] => [[.,[[[.,.],.],.]],[.,.]] => 4
[4,1,6,5,2,3] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,1,6,5,3,2] => [1,4,5,3,6,2] => [2,1,5,3,4,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[4,2,1,3,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,2,1,3,6,5] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,2,1,5,3,6] => [1,4,5,3,2,6] => [2,6,5,3,4,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,2,1,5,6,3] => [1,4,5,6,3,2] => [2,1,6,3,4,5] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[4,2,1,6,3,5] => [1,4,6,5,3,2] => [2,1,6,3,5,4] => [[.,.],[[.,.],[[.,.],.]]] => 1
[4,2,1,6,5,3] => [1,4,6,3,2,5] => [2,6,5,3,1,4] => [[.,[[[.,.],.],.]],[.,.]] => 4
[4,2,3,1,5,6] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,2,3,1,6,5] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,2,3,5,1,6] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,2,3,5,6,1] => [1,4,5,6,2,3] => [2,6,1,3,4,5] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[4,2,3,6,1,5] => [1,4,6,5,2,3] => [2,6,1,3,5,4] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[4,2,3,6,5,1] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,2,5,1,3,6] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,2,5,1,6,3] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,2,5,3,1,6] => [1,4,3,5,2,6] => [2,6,4,3,5,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,2,5,3,6,1] => [1,4,3,5,6,2] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[4,2,5,6,1,3] => [1,4,6,3,5,2] => [2,1,5,3,6,4] => [[.,.],[[.,.],[[.,.],.]]] => 1
[4,2,5,6,3,1] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,2,6,1,3,5] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,2,6,1,5,3] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,2,6,3,1,5] => [1,4,3,6,5,2] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => 1
[4,2,6,3,5,1] => [1,4,3,6,2,5] => [2,6,4,3,1,5] => [[.,[[[.,.],.],.]],[.,.]] => 4
[4,2,6,5,1,3] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,2,6,5,3,1] => [1,4,5,3,6,2] => [2,1,5,3,4,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[4,3,1,2,5,6] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,3,1,2,6,5] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,3,1,5,2,6] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,3,1,5,6,2] => [1,4,5,6,2,3] => [2,6,1,3,4,5] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[4,3,1,6,2,5] => [1,4,6,5,2,3] => [2,6,1,3,5,4] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[4,3,1,6,5,2] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,3,2,1,5,6] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,3,2,1,6,5] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,3,2,5,1,6] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,3,2,5,6,1] => [1,4,5,6,2,3] => [2,6,1,3,4,5] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[4,3,2,6,1,5] => [1,4,6,5,2,3] => [2,6,1,3,5,4] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[4,3,2,6,5,1] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,3,5,1,2,6] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,3,5,1,6,2] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,3,5,2,1,6] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,3,5,2,6,1] => [1,4,2,3,5,6] => [2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,3,5,6,1,2] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,3,5,6,2,1] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,3,6,1,2,5] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,3,6,1,5,2] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,3,6,2,1,5] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,3,6,2,5,1] => [1,4,2,3,6,5] => [2,4,5,3,1,6] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,3,6,5,1,2] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,3,6,5,2,1] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,5,1,2,3,6] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,5,1,2,6,3] => [1,4,2,5,6,3] => [2,4,1,3,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[4,5,1,3,2,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,5,1,3,6,2] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,5,1,6,2,3] => [1,4,6,3,2,5] => [2,6,5,3,1,4] => [[.,[[[.,.],.],.]],[.,.]] => 4
[4,5,1,6,3,2] => [1,4,6,2,5,3] => [2,5,1,3,6,4] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[4,5,2,1,3,6] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,5,2,1,6,3] => [1,4,2,5,6,3] => [2,4,1,3,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[4,5,2,3,1,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,5,2,3,6,1] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,5,2,6,1,3] => [1,4,6,3,2,5] => [2,6,5,3,1,4] => [[.,[[[.,.],.],.]],[.,.]] => 4
[4,5,2,6,3,1] => [1,4,6,2,5,3] => [2,5,1,3,6,4] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[4,5,3,1,2,6] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,5,3,1,6,2] => [1,4,2,5,6,3] => [2,4,1,3,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[4,5,3,2,1,6] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,5,3,2,6,1] => [1,4,2,5,6,3] => [2,4,1,3,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[4,5,3,6,1,2] => [1,4,6,2,5,3] => [2,5,1,3,6,4] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[4,5,3,6,2,1] => [1,4,6,2,5,3] => [2,5,1,3,6,4] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[4,5,6,1,2,3] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,5,6,1,3,2] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,5,6,2,1,3] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,5,6,2,3,1] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => [[.,[[.,[.,.]],[.,.]]],.] => 5
[4,5,6,3,1,2] => [1,4,3,6,2,5] => [2,6,4,3,1,5] => [[.,[[[.,.],.],.]],[.,.]] => 4
[4,5,6,3,2,1] => [1,4,3,6,2,5] => [2,6,4,3,1,5] => [[.,[[[.,.],.],.]],[.,.]] => 4
[4,6,1,2,3,5] => [1,4,2,6,5,3] => [2,4,1,3,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[4,6,1,2,5,3] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,6,1,3,2,5] => [1,4,3,2,6,5] => [2,5,4,3,1,6] => [[.,[[[.,.],.],.]],[.,.]] => 4
[4,6,1,3,5,2] => [1,4,3,2,6,5] => [2,5,4,3,1,6] => [[.,[[[.,.],.],.]],[.,.]] => 4
[4,6,1,5,2,3] => [1,4,5,2,6,3] => [2,5,1,3,4,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[4,6,1,5,3,2] => [1,4,5,3,2,6] => [2,6,5,3,4,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,6,2,1,3,5] => [1,4,2,6,5,3] => [2,4,1,3,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[4,6,2,1,5,3] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,6,2,3,1,5] => [1,4,3,2,6,5] => [2,5,4,3,1,6] => [[.,[[[.,.],.],.]],[.,.]] => 4
[4,6,2,3,5,1] => [1,4,3,2,6,5] => [2,5,4,3,1,6] => [[.,[[[.,.],.],.]],[.,.]] => 4
[4,6,2,5,1,3] => [1,4,5,2,6,3] => [2,5,1,3,4,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[4,6,2,5,3,1] => [1,4,5,3,2,6] => [2,6,5,3,4,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,6,3,1,2,5] => [1,4,2,6,5,3] => [2,4,1,3,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[4,6,3,1,5,2] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,6,3,2,1,5] => [1,4,2,6,5,3] => [2,4,1,3,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[4,6,3,2,5,1] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,6,3,5,1,2] => [1,4,5,2,6,3] => [2,5,1,3,4,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[4,6,3,5,2,1] => [1,4,5,2,6,3] => [2,5,1,3,4,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[4,6,5,1,2,3] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,6,5,1,3,2] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,6,5,2,1,3] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,6,5,2,3,1] => [1,4,2,6,3,5] => [2,4,6,3,1,5] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[4,6,5,3,1,2] => [1,4,3,5,2,6] => [2,6,4,3,5,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[4,6,5,3,2,1] => [1,4,3,5,2,6] => [2,6,4,3,5,1] => [[.,[[[.,.],.],[.,.]]],.] => 5
[5,1,2,3,4,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => [[.,[[[[.,.],.],.],.]],.] => 5
[5,1,2,3,6,4] => [1,5,6,4,3,2] => [2,1,6,5,3,4] => [[.,.],[[[.,.],.],[.,.]]] => 1
[5,1,2,4,3,6] => [1,5,3,2,4,6] => [2,5,4,6,3,1] => [[.,[[[.,.],[.,.]],.]],.] => 5
[5,1,2,4,6,3] => [1,5,6,3,2,4] => [2,6,5,1,3,4] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[5,1,2,6,3,4] => [1,5,3,2,4,6] => [2,5,4,6,3,1] => [[.,[[[.,.],[.,.]],.]],.] => 5
[5,1,2,6,4,3] => [1,5,4,6,3,2] => [2,1,6,4,3,5] => [[.,.],[[[.,.],.],[.,.]]] => 1
[5,1,3,2,4,6] => [1,5,4,2,3,6] => [2,5,6,4,3,1] => [[.,[[[.,[.,.]],.],.]],.] => 5
[5,1,3,2,6,4] => [1,5,6,4,2,3] => [2,6,1,5,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,1,3,4,2,6] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,1,3,4,6,2] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,1,3,6,2,4] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,1,3,6,4,2] => [1,5,4,6,2,3] => [2,6,1,4,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,1,4,2,3,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => [[.,[[[.,.],[.,.]],.]],.] => 5
[5,1,4,2,6,3] => [1,5,6,3,4,2] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => 1
[5,1,4,3,2,6] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,1,4,3,6,2] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,1,4,6,2,3] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,1,4,6,3,2] => [1,5,3,4,6,2] => [2,1,4,5,3,6] => [[.,.],[[.,[.,.]],[.,.]]] => 1
[5,1,6,2,3,4] => [1,5,3,6,4,2] => [2,1,4,6,3,5] => [[.,.],[[.,[.,.]],[.,.]]] => 1
[5,1,6,2,4,3] => [1,5,4,2,3,6] => [2,5,6,4,3,1] => [[.,[[[.,[.,.]],.],.]],.] => 5
[5,1,6,3,2,4] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,1,6,3,4,2] => [1,5,4,3,6,2] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => 1
[5,1,6,4,2,3] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,1,6,4,3,2] => [1,5,3,6,2,4] => [2,6,4,1,3,5] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[5,2,1,3,4,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => [[.,[[[[.,.],.],.],.]],.] => 5
[5,2,1,3,6,4] => [1,5,6,4,3,2] => [2,1,6,5,3,4] => [[.,.],[[[.,.],.],[.,.]]] => 1
[5,2,1,4,3,6] => [1,5,3,2,4,6] => [2,5,4,6,3,1] => [[.,[[[.,.],[.,.]],.]],.] => 5
[5,2,1,4,6,3] => [1,5,6,3,2,4] => [2,6,5,1,3,4] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[5,2,1,6,3,4] => [1,5,3,2,4,6] => [2,5,4,6,3,1] => [[.,[[[.,.],[.,.]],.]],.] => 5
[5,2,1,6,4,3] => [1,5,4,6,3,2] => [2,1,6,4,3,5] => [[.,.],[[[.,.],.],[.,.]]] => 1
[5,2,3,1,4,6] => [1,5,4,2,3,6] => [2,5,6,4,3,1] => [[.,[[[.,[.,.]],.],.]],.] => 5
[5,2,3,1,6,4] => [1,5,6,4,2,3] => [2,6,1,5,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,2,3,4,1,6] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,2,3,4,6,1] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,2,3,6,1,4] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,2,3,6,4,1] => [1,5,4,6,2,3] => [2,6,1,4,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,2,4,1,3,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => [[.,[[[.,.],[.,.]],.]],.] => 5
[5,2,4,1,6,3] => [1,5,6,3,4,2] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => 1
[5,2,4,3,1,6] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,2,4,3,6,1] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,2,4,6,1,3] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,2,4,6,3,1] => [1,5,3,4,6,2] => [2,1,4,5,3,6] => [[.,.],[[.,[.,.]],[.,.]]] => 1
[5,2,6,1,3,4] => [1,5,3,6,4,2] => [2,1,4,6,3,5] => [[.,.],[[.,[.,.]],[.,.]]] => 1
[5,2,6,1,4,3] => [1,5,4,2,3,6] => [2,5,6,4,3,1] => [[.,[[[.,[.,.]],.],.]],.] => 5
[5,2,6,3,1,4] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,2,6,3,4,1] => [1,5,4,3,6,2] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => 1
[5,2,6,4,1,3] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,2,6,4,3,1] => [1,5,3,6,2,4] => [2,6,4,1,3,5] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[5,3,1,2,4,6] => [1,5,4,2,3,6] => [2,5,6,4,3,1] => [[.,[[[.,[.,.]],.],.]],.] => 5
[5,3,1,2,6,4] => [1,5,6,4,2,3] => [2,6,1,5,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,3,1,4,2,6] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,3,1,4,6,2] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,3,1,6,2,4] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,3,1,6,4,2] => [1,5,4,6,2,3] => [2,6,1,4,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,3,2,1,4,6] => [1,5,4,2,3,6] => [2,5,6,4,3,1] => [[.,[[[.,[.,.]],.],.]],.] => 5
[5,3,2,1,6,4] => [1,5,6,4,2,3] => [2,6,1,5,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,3,2,4,1,6] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,3,2,4,6,1] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,3,2,6,1,4] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,3,2,6,4,1] => [1,5,4,6,2,3] => [2,6,1,4,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,3,4,1,2,6] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,3,4,1,6,2] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,3,4,2,1,6] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,3,4,2,6,1] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,3,4,6,1,2] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,3,4,6,2,1] => [1,5,2,3,4,6] => [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => 5
[5,3,6,1,2,4] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,3,6,1,4,2] => [1,5,4,2,3,6] => [2,5,6,4,3,1] => [[.,[[[.,[.,.]],.],.]],.] => 5
[5,3,6,2,1,4] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,3,6,2,4,1] => [1,5,4,2,3,6] => [2,5,6,4,3,1] => [[.,[[[.,[.,.]],.],.]],.] => 5
[5,3,6,4,1,2] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,3,6,4,2,1] => [1,5,2,3,6,4] => [2,4,5,1,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,4,1,2,3,6] => [1,5,3,2,4,6] => [2,5,4,6,3,1] => [[.,[[[.,.],[.,.]],.]],.] => 5
[5,4,1,2,6,3] => [1,5,6,3,2,4] => [2,6,5,1,3,4] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[5,4,1,3,2,6] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [[.,[[.,[[.,.],.]],.]],.] => 5
[5,4,1,3,6,2] => [1,5,6,2,4,3] => [2,5,1,6,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,4,1,6,2,3] => [1,5,2,4,6,3] => [2,4,1,5,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,4,1,6,3,2] => [1,5,3,2,4,6] => [2,5,4,6,3,1] => [[.,[[[.,.],[.,.]],.]],.] => 5
[5,4,2,1,3,6] => [1,5,3,2,4,6] => [2,5,4,6,3,1] => [[.,[[[.,.],[.,.]],.]],.] => 5
[5,4,2,1,6,3] => [1,5,6,3,2,4] => [2,6,5,1,3,4] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[5,4,2,3,1,6] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [[.,[[.,[[.,.],.]],.]],.] => 5
[5,4,2,3,6,1] => [1,5,6,2,4,3] => [2,5,1,6,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,4,2,6,1,3] => [1,5,2,4,6,3] => [2,4,1,5,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,4,2,6,3,1] => [1,5,3,2,4,6] => [2,5,4,6,3,1] => [[.,[[[.,.],[.,.]],.]],.] => 5
[5,4,3,1,2,6] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [[.,[[.,[[.,.],.]],.]],.] => 5
[5,4,3,1,6,2] => [1,5,6,2,4,3] => [2,5,1,6,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,4,3,2,1,6] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [[.,[[.,[[.,.],.]],.]],.] => 5
[5,4,3,2,6,1] => [1,5,6,2,4,3] => [2,5,1,6,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,4,3,6,1,2] => [1,5,2,4,6,3] => [2,4,1,5,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,4,3,6,2,1] => [1,5,2,4,6,3] => [2,4,1,5,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,4,6,1,2,3] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [[.,[[.,[[.,.],.]],.]],.] => 5
[5,4,6,1,3,2] => [1,5,3,6,2,4] => [2,6,4,1,3,5] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[5,4,6,2,1,3] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [[.,[[.,[[.,.],.]],.]],.] => 5
[5,4,6,2,3,1] => [1,5,3,6,2,4] => [2,6,4,1,3,5] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[5,4,6,3,1,2] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [[.,[[.,[[.,.],.]],.]],.] => 5
[5,4,6,3,2,1] => [1,5,2,4,3,6] => [2,4,6,5,3,1] => [[.,[[.,[[.,.],.]],.]],.] => 5
[5,6,1,2,3,4] => [1,5,3,2,6,4] => [2,5,4,1,3,6] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[5,6,1,2,4,3] => [1,5,4,2,6,3] => [2,5,1,4,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,6,1,3,2,4] => [1,5,2,6,4,3] => [2,4,1,6,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,6,1,3,4,2] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => [[.,[[[[.,.],.],.],.]],.] => 5
[5,6,1,4,2,3] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,6,1,4,3,2] => [1,5,3,2,6,4] => [2,5,4,1,3,6] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[5,6,2,1,3,4] => [1,5,3,2,6,4] => [2,5,4,1,3,6] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[5,6,2,1,4,3] => [1,5,4,2,6,3] => [2,5,1,4,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,6,2,3,1,4] => [1,5,2,6,4,3] => [2,4,1,6,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,6,2,3,4,1] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => [[.,[[[[.,.],.],.],.]],.] => 5
[5,6,2,4,1,3] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,6,2,4,3,1] => [1,5,3,2,6,4] => [2,5,4,1,3,6] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[5,6,3,1,2,4] => [1,5,2,6,4,3] => [2,4,1,6,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,6,3,1,4,2] => [1,5,4,2,6,3] => [2,5,1,4,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,6,3,2,1,4] => [1,5,2,6,4,3] => [2,4,1,6,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,6,3,2,4,1] => [1,5,4,2,6,3] => [2,5,1,4,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[5,6,3,4,1,2] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,6,3,4,2,1] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,6,4,1,2,3] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,6,4,1,3,2] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => [[.,[[[.,.],[.,.]],.]],.] => 5
[5,6,4,2,1,3] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,6,4,2,3,1] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => [[.,[[[.,.],[.,.]],.]],.] => 5
[5,6,4,3,1,2] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,6,4,3,2,1] => [1,5,2,6,3,4] => [2,4,6,1,3,5] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[6,1,2,3,4,5] => [1,6,5,4,3,2] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => 1
[6,1,2,3,5,4] => [1,6,4,3,2,5] => [2,6,5,4,1,3] => [[.,[[[.,.],.],.]],[.,.]] => 4
[6,1,2,4,3,5] => [1,6,5,3,2,4] => [2,6,5,1,4,3] => [[.,[[.,.],.]],[[.,.],.]] => 3
[6,1,2,4,5,3] => [1,6,3,2,4,5] => [2,5,4,6,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[6,1,2,5,3,4] => [1,6,4,5,3,2] => [2,1,6,4,5,3] => [[.,.],[[[.,.],[.,.]],.]] => 1
[6,1,2,5,4,3] => [1,6,3,2,4,5] => [2,5,4,6,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[6,1,3,2,4,5] => [1,6,5,4,2,3] => [2,6,1,5,4,3] => [[.,[.,.]],[[[.,.],.],.]] => 2
[6,1,3,2,5,4] => [1,6,4,2,3,5] => [2,5,6,4,1,3] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[6,1,3,4,2,5] => [1,6,5,2,3,4] => [2,5,6,1,4,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,1,3,4,5,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,1,3,5,2,4] => [1,6,4,5,2,3] => [2,6,1,4,5,3] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[6,1,3,5,4,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,1,4,2,3,5] => [1,6,5,3,4,2] => [2,1,5,6,4,3] => [[.,.],[[[.,[.,.]],.],.]] => 1
[6,1,4,2,5,3] => [1,6,3,4,2,5] => [2,6,4,5,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[6,1,4,3,2,5] => [1,6,5,2,3,4] => [2,5,6,1,4,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,1,4,3,5,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,1,4,5,2,3] => [1,6,3,4,5,2] => [2,1,4,5,6,3] => [[.,.],[[.,[.,[.,.]]],.]] => 1
[6,1,4,5,3,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,1,5,2,3,4] => [1,6,4,2,3,5] => [2,5,6,4,1,3] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[6,1,5,2,4,3] => [1,6,3,5,4,2] => [2,1,4,6,5,3] => [[.,.],[[.,[[.,.],.]],.]] => 1
[6,1,5,3,2,4] => [1,6,4,3,5,2] => [2,1,5,4,6,3] => [[.,.],[[[.,.],[.,.]],.]] => 1
[6,1,5,3,4,2] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,1,5,4,2,3] => [1,6,3,5,2,4] => [2,6,4,1,5,3] => [[.,[[.,.],.]],[[.,.],.]] => 3
[6,1,5,4,3,2] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,2,1,3,4,5] => [1,6,5,4,3,2] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => 1
[6,2,1,3,5,4] => [1,6,4,3,2,5] => [2,6,5,4,1,3] => [[.,[[[.,.],.],.]],[.,.]] => 4
[6,2,1,4,3,5] => [1,6,5,3,2,4] => [2,6,5,1,4,3] => [[.,[[.,.],.]],[[.,.],.]] => 3
[6,2,1,4,5,3] => [1,6,3,2,4,5] => [2,5,4,6,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[6,2,1,5,3,4] => [1,6,4,5,3,2] => [2,1,6,4,5,3] => [[.,.],[[[.,.],[.,.]],.]] => 1
[6,2,1,5,4,3] => [1,6,3,2,4,5] => [2,5,4,6,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[6,2,3,1,4,5] => [1,6,5,4,2,3] => [2,6,1,5,4,3] => [[.,[.,.]],[[[.,.],.],.]] => 2
[6,2,3,1,5,4] => [1,6,4,2,3,5] => [2,5,6,4,1,3] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[6,2,3,4,1,5] => [1,6,5,2,3,4] => [2,5,6,1,4,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,2,3,4,5,1] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,2,3,5,1,4] => [1,6,4,5,2,3] => [2,6,1,4,5,3] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[6,2,3,5,4,1] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,2,4,1,3,5] => [1,6,5,3,4,2] => [2,1,5,6,4,3] => [[.,.],[[[.,[.,.]],.],.]] => 1
[6,2,4,1,5,3] => [1,6,3,4,2,5] => [2,6,4,5,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[6,2,4,3,1,5] => [1,6,5,2,3,4] => [2,5,6,1,4,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,2,4,3,5,1] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,2,4,5,1,3] => [1,6,3,4,5,2] => [2,1,4,5,6,3] => [[.,.],[[.,[.,[.,.]]],.]] => 1
[6,2,4,5,3,1] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,2,5,1,3,4] => [1,6,4,2,3,5] => [2,5,6,4,1,3] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[6,2,5,1,4,3] => [1,6,3,5,4,2] => [2,1,4,6,5,3] => [[.,.],[[.,[[.,.],.]],.]] => 1
[6,2,5,3,1,4] => [1,6,4,3,5,2] => [2,1,5,4,6,3] => [[.,.],[[[.,.],[.,.]],.]] => 1
[6,2,5,3,4,1] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,2,5,4,1,3] => [1,6,3,5,2,4] => [2,6,4,1,5,3] => [[.,[[.,.],.]],[[.,.],.]] => 3
[6,2,5,4,3,1] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,3,1,2,4,5] => [1,6,5,4,2,3] => [2,6,1,5,4,3] => [[.,[.,.]],[[[.,.],.],.]] => 2
[6,3,1,2,5,4] => [1,6,4,2,3,5] => [2,5,6,4,1,3] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[6,3,1,4,2,5] => [1,6,5,2,3,4] => [2,5,6,1,4,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,3,1,4,5,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,3,1,5,2,4] => [1,6,4,5,2,3] => [2,6,1,4,5,3] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[6,3,1,5,4,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,3,2,1,4,5] => [1,6,5,4,2,3] => [2,6,1,5,4,3] => [[.,[.,.]],[[[.,.],.],.]] => 2
[6,3,2,1,5,4] => [1,6,4,2,3,5] => [2,5,6,4,1,3] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[6,3,2,4,1,5] => [1,6,5,2,3,4] => [2,5,6,1,4,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,3,2,4,5,1] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,3,2,5,1,4] => [1,6,4,5,2,3] => [2,6,1,4,5,3] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[6,3,2,5,4,1] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,3,4,1,2,5] => [1,6,5,2,3,4] => [2,5,6,1,4,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,3,4,1,5,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,3,4,2,1,5] => [1,6,5,2,3,4] => [2,5,6,1,4,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,3,4,2,5,1] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,3,4,5,1,2] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,3,4,5,2,1] => [1,6,2,3,4,5] => [2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[6,3,5,1,2,4] => [1,6,4,2,3,5] => [2,5,6,4,1,3] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[6,3,5,1,4,2] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,3,5,2,1,4] => [1,6,4,2,3,5] => [2,5,6,4,1,3] => [[.,[[.,[.,.]],.]],[.,.]] => 4
[6,3,5,2,4,1] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,3,5,4,1,2] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,3,5,4,2,1] => [1,6,2,3,5,4] => [2,4,5,1,6,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,4,1,2,3,5] => [1,6,5,3,2,4] => [2,6,5,1,4,3] => [[.,[[.,.],.]],[[.,.],.]] => 3
[6,4,1,2,5,3] => [1,6,3,2,4,5] => [2,5,4,6,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[6,4,1,3,2,5] => [1,6,5,2,4,3] => [2,5,1,6,4,3] => [[.,[.,.]],[[[.,.],.],.]] => 2
[6,4,1,3,5,2] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[6,4,1,5,2,3] => [1,6,3,2,4,5] => [2,5,4,6,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[6,4,1,5,3,2] => [1,6,2,4,5,3] => [2,4,1,5,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[6,4,2,1,3,5] => [1,6,5,3,2,4] => [2,6,5,1,4,3] => [[.,[[.,.],.]],[[.,.],.]] => 3
[6,4,2,1,5,3] => [1,6,3,2,4,5] => [2,5,4,6,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[6,4,2,3,1,5] => [1,6,5,2,4,3] => [2,5,1,6,4,3] => [[.,[.,.]],[[[.,.],.],.]] => 2
[6,4,2,3,5,1] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[6,4,2,5,1,3] => [1,6,3,2,4,5] => [2,5,4,6,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[6,4,2,5,3,1] => [1,6,2,4,5,3] => [2,4,1,5,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[6,4,3,1,2,5] => [1,6,5,2,4,3] => [2,5,1,6,4,3] => [[.,[.,.]],[[[.,.],.],.]] => 2
[6,4,3,1,5,2] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[6,4,3,2,1,5] => [1,6,5,2,4,3] => [2,5,1,6,4,3] => [[.,[.,.]],[[[.,.],.],.]] => 2
[6,4,3,2,5,1] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[6,4,3,5,1,2] => [1,6,2,4,5,3] => [2,4,1,5,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[6,4,3,5,2,1] => [1,6,2,4,5,3] => [2,4,1,5,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[6,4,5,1,2,3] => [1,6,3,5,2,4] => [2,6,4,1,5,3] => [[.,[[.,.],.]],[[.,.],.]] => 3
[6,4,5,1,3,2] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[6,4,5,2,1,3] => [1,6,3,5,2,4] => [2,6,4,1,5,3] => [[.,[[.,.],.]],[[.,.],.]] => 3
[6,4,5,2,3,1] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[6,4,5,3,1,2] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[6,4,5,3,2,1] => [1,6,2,4,3,5] => [2,4,6,5,1,3] => [[.,[.,[[.,.],.]]],[.,.]] => 4
[6,5,1,2,3,4] => [1,6,4,2,5,3] => [2,5,1,4,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[6,5,1,2,4,3] => [1,6,3,2,5,4] => [2,5,4,1,6,3] => [[.,[[.,.],.]],[[.,.],.]] => 3
[6,5,1,3,2,4] => [1,6,4,3,2,5] => [2,6,5,4,1,3] => [[.,[[[.,.],.],.]],[.,.]] => 4
[6,5,1,3,4,2] => [1,6,2,5,4,3] => [2,4,1,6,5,3] => [[.,[.,.]],[[[.,.],.],.]] => 2
[6,5,1,4,2,3] => [1,6,3,2,5,4] => [2,5,4,1,6,3] => [[.,[[.,.],.]],[[.,.],.]] => 3
[6,5,1,4,3,2] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,5,2,1,3,4] => [1,6,4,2,5,3] => [2,5,1,4,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[6,5,2,1,4,3] => [1,6,3,2,5,4] => [2,5,4,1,6,3] => [[.,[[.,.],.]],[[.,.],.]] => 3
[6,5,2,3,1,4] => [1,6,4,3,2,5] => [2,6,5,4,1,3] => [[.,[[[.,.],.],.]],[.,.]] => 4
[6,5,2,3,4,1] => [1,6,2,5,4,3] => [2,4,1,6,5,3] => [[.,[.,.]],[[[.,.],.],.]] => 2
[6,5,2,4,1,3] => [1,6,3,2,5,4] => [2,5,4,1,6,3] => [[.,[[.,.],.]],[[.,.],.]] => 3
[6,5,2,4,3,1] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,5,3,1,2,4] => [1,6,4,2,5,3] => [2,5,1,4,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[6,5,3,1,4,2] => [1,6,2,5,4,3] => [2,4,1,6,5,3] => [[.,[.,.]],[[[.,.],.],.]] => 2
[6,5,3,2,1,4] => [1,6,4,2,5,3] => [2,5,1,4,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[6,5,3,2,4,1] => [1,6,2,5,4,3] => [2,4,1,6,5,3] => [[.,[.,.]],[[[.,.],.],.]] => 2
[6,5,3,4,1,2] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,5,3,4,2,1] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,5,4,1,2,3] => [1,6,3,4,2,5] => [2,6,4,5,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[6,5,4,1,3,2] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,5,4,2,1,3] => [1,6,3,4,2,5] => [2,6,4,5,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => 4
[6,5,4,2,3,1] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,5,4,3,1,2] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[6,5,4,3,2,1] => [1,6,2,5,3,4] => [2,4,6,1,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => 3
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Generating function
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Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,4 4,8,12 12,24,36,48 48,96,144,192,240
$F_{1} = 1$
$F_{2} = 2\ q$
$F_{3} = 2\ q + 4\ q^{2}$
$F_{4} = 4\ q + 8\ q^{2} + 12\ q^{3}$
$F_{5} = 12\ q + 24\ q^{2} + 36\ q^{3} + 48\ q^{4}$
$F_{6} = 48\ q + 96\ q^{2} + 144\ q^{3} + 192\ q^{4} + 240\ q^{5}$
Description
The size of the left subtree of a binary tree.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $\pi^{-1}c$ where $c = (1,\ldots,n)$ is the long cycle.
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.
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.
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