- FindStat

Identifier

Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
St000884: Permutations ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 553 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => 1

[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [8,1,2,3,4,5,7,6] => [7,1,2,3,4,5,8,6] => 2

[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [8,1,2,3,4,7,6,5] => [7,1,2,3,4,8,5,6] => 2

[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [5,4,8,7,6,3,2,1] => [8,1,2,5,4,3,6,7] => [5,1,2,8,3,4,6,7] => 2

[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [3,5,7,8,6,4,2,1] => [8,1,3,2,5,4,7,6] => [3,1,5,2,7,4,8,6] => 4

[.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [3,6,5,7,8,4,2,1] => [8,1,3,2,6,5,7,4] => [3,1,6,2,7,4,8,5] => 4

[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [4,3,5,7,8,6,2,1] => [8,1,4,3,5,2,7,6] => [4,1,5,2,7,3,8,6] => 4

[.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [4,5,6,3,8,7,2,1] => [8,1,6,4,5,3,2,7] => [4,1,5,6,8,2,3,7] => 2

[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [3,5,4,6,8,7,2,1] => [8,1,3,5,4,6,2,7] => [3,1,5,6,2,8,4,7] => 3

[.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [4,3,5,7,6,8,2,1] => [8,1,4,3,5,7,6,2] => [4,1,5,2,7,8,3,6] => 3

[.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [4,3,6,5,7,8,2,1] => [8,1,4,3,6,5,7,2] => [4,1,6,2,7,3,8,5] => 4

[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [2,8,7,6,5,4,3,1] => [8,2,1,3,4,5,6,7] => [2,8,1,3,4,5,6,7] => 1

[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [2,5,4,7,8,6,3,1] => [8,2,1,5,4,3,7,6] => [2,5,1,7,3,4,8,6] => 3

[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [4,5,3,6,2,8,7,1] => [8,6,5,4,3,2,1,7] => [4,5,6,8,1,2,3,7] => 1

[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [2,3,4,5,6,8,7,1] => [8,2,3,4,5,6,1,7] => [2,3,4,5,6,8,1,7] => 1

[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [8,7,2,3,4,5,6,1] => [7,8,1,2,3,4,5,6] => 1

[.,[[.,[[.,.],[.,[[.,.],.]]]],.]] => [3,6,7,5,4,2,8,1] => [8,7,3,2,4,6,5,1] => [3,6,7,1,2,8,4,5] => 2

[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [4,5,3,7,6,2,8,1] => [8,7,5,4,3,2,6,1] => [4,5,7,8,1,2,3,6] => 1

[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [3,5,4,7,6,2,8,1] => [8,7,3,5,4,2,6,1] => [3,5,7,8,1,2,4,6] => 1

[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [8,7,6,3,4,5,2,1] => [6,7,8,1,2,3,4,5] => 1

[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [4,6,5,3,7,2,8,1] => [8,7,6,4,3,5,2,1] => [4,6,7,8,1,2,3,5] => 1

[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [8,7,6,5,4,3,2,1] => [5,6,7,8,1,2,3,4] => 1

[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [3,6,5,4,7,2,8,1] => [8,7,3,6,4,5,2,1] => [3,6,7,8,1,2,4,5] => 1

[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => [8,7,4,3,6,5,2,1] => [4,6,7,1,8,2,3,5] => 2

[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => [8,7,3,4,5,6,2,1] => [3,4,5,6,7,8,1,2] => 1

[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [2,7,6,5,4,3,8,1] => [8,2,7,3,4,5,6,1] => [2,7,8,1,3,4,5,6] => 1

[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [2,5,4,7,6,3,8,1] => [8,2,7,5,4,3,6,1] => [2,5,7,8,1,3,4,6] => 1

[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => [8,3,2,7,6,5,4,1] => [3,6,1,7,8,2,4,5] => 2

[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => [8,5,4,3,2,7,6,1] => [4,5,7,1,2,8,3,6] => 2

[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => [8,3,2,5,4,7,6,1] => [3,5,1,7,2,8,4,6] => 3

[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [2,3,4,5,7,6,8,1] => [8,2,3,4,5,7,6,1] => [2,3,4,5,7,8,1,6] => 1

[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => [8,6,2,3,4,5,7,1] => [6,7,1,2,3,4,8,5] => 2

[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [2,4,5,6,3,7,8,1] => [8,2,6,4,5,3,7,1] => [2,4,5,6,7,1,8,3] => 2

[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [2,4,3,6,5,7,8,1] => [8,2,4,3,6,5,7,1] => [2,4,6,1,7,3,8,5] => 3

[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [2,3,5,4,6,7,8,1] => [8,2,3,5,4,6,7,1] => [2,3,5,6,1,7,8,4] => 2

[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,7,8,1] => 1

[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => [1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 1

[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => [1,8,2,3,4,5,7,6] => [1,7,2,3,4,5,8,6] => 2

[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => [1,8,2,3,4,6,5,7] => [1,6,2,3,4,8,5,7] => 2

[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => [1,8,2,3,4,7,6,5] => [1,7,2,3,4,8,5,6] => 2

[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => [1,8,2,3,7,5,6,4] => [1,7,2,3,8,4,5,6] => 2

[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,4,8,7,6,5,3,2] => [1,8,2,4,3,5,6,7] => [1,4,2,8,3,5,6,7] => 2

[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,4,6,8,7,5,3,2] => [1,8,2,4,3,6,5,7] => [1,4,2,6,3,8,5,7] => 3

[[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,4,7,6,8,5,3,2] => [1,8,2,4,3,7,6,5] => [1,4,2,7,3,8,5,6] => 3

[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,7,6,5,4,8,3,2] => [1,8,2,7,4,5,6,3] => [1,7,2,8,3,4,5,6] => 2

[[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => [1,6,7,5,4,8,3,2] => [1,8,2,7,4,6,5,3] => [1,6,2,7,3,8,4,5] => 3

[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,4,6,7,5,8,3,2] => [1,8,2,4,7,6,5,3] => [1,4,2,6,7,8,3,5] => 2

[[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,5,4,7,6,8,3,2] => [1,8,2,5,4,7,6,3] => [1,5,2,7,3,8,4,6] => 3

[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => [1,8,6,3,4,5,2,7] => [1,6,8,2,3,4,5,7] => 1

[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,7,6,5,4,3,8,2] => [1,8,7,3,4,5,6,2] => [1,7,8,2,3,4,5,6] => 1

[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => [2,1,8,3,4,5,6,7] => [2,1,8,3,4,5,6,7] => 2

[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => [2,1,8,3,4,6,7,5] => [2,1,6,3,4,7,8,5] => 3

[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => [2,1,8,3,5,4,7,6] => [2,1,5,3,7,4,8,6] => 4

[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [2,1,6,5,7,8,4,3] => [2,1,8,3,6,5,7,4] => [2,1,6,3,7,4,8,5] => 4

[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => [2,1,8,7,6,5,4,3] => [2,1,6,7,8,3,4,5] => 2

[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => [2,1,8,5,4,7,6,3] => [2,1,5,7,3,8,4,6] => 3

[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,2,7,8,6,5,4,3] => [1,2,8,3,4,5,7,6] => [1,2,7,3,4,5,8,6] => 2

[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,3,2,8,7,6,5,4] => [1,3,2,8,4,5,6,7] => [1,3,2,8,4,5,6,7] => 2

[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,3,2,6,8,7,5,4] => [1,3,2,8,4,6,5,7] => [1,3,2,6,4,8,5,7] => 3

[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [2,1,3,8,7,6,5,4] => [2,1,3,8,4,5,6,7] => [2,1,3,8,4,5,6,7] => 2

[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => [1,2,3,8,4,5,6,7] => [1,2,3,8,4,5,6,7] => 1

[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => [1,2,3,8,4,6,5,7] => [1,2,3,6,4,8,5,7] => 2

[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,2,3,7,6,8,5,4] => [1,2,3,8,4,7,6,5] => [1,2,3,7,4,8,5,6] => 2

[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4] => [1,2,3,5,6,7,8,4] => 1

[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => [4,1,2,3,8,5,6,7] => [4,1,2,3,8,5,6,7] => 2

[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => [4,1,3,2,8,5,7,6] => [3,1,4,2,7,5,8,6] => 4

[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [3,4,2,1,6,8,7,5] => [4,1,3,2,8,6,5,7] => [3,1,4,2,6,8,5,7] => 3

[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [2,4,3,1,7,8,6,5] => [4,2,1,3,8,5,7,6] => [2,4,1,3,7,5,8,6] => 3

[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => [4,3,2,1,8,7,6,5] => [3,4,1,2,7,8,5,6] => 2

[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [2,3,4,1,6,7,8,5] => 2

[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,5,6,7] => [2,1,4,3,8,5,6,7] => 3

[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => [2,1,4,3,8,5,7,6] => [2,1,4,3,7,5,8,6] => 4

[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,7,6,5] => [2,1,4,3,7,8,5,6] => 3

[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,5,4,3,2,8,7,6] => [1,5,2,3,4,8,6,7] => [1,5,2,3,4,8,6,7] => 2

[[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,4,5,3,2,8,7,6] => [1,5,2,4,3,8,6,7] => [1,4,2,5,3,8,6,7] => 3

[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,3,2,5,4,8,7,6] => [1,3,2,5,4,8,6,7] => [1,3,2,5,4,8,6,7] => 3

[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,5,4,8,7,6] => [1,2,3,5,4,8,6,7] => [1,2,3,5,4,8,6,7] => 2

[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,4,3,2,5,8,7,6] => [1,4,2,3,5,8,6,7] => [1,4,2,3,5,8,6,7] => 2

[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => [3,1,2,4,5,8,6,7] => [3,1,2,4,5,8,6,7] => 2

[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [2,3,1,4,5,7,8,6] => 2

[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,3,2,4,5,8,7,6] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,8,6,7] => 2

[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 1

[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => [6,1,2,3,4,5,8,7] => [6,1,2,3,4,5,8,7] => 2

[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [3,5,6,4,2,1,8,7] => [6,1,3,2,5,4,8,7] => [3,1,5,2,6,4,8,7] => 4

[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [4,3,5,6,2,1,8,7] => [6,1,4,3,5,2,8,7] => [4,1,5,2,6,3,8,7] => 4

[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => [6,5,4,3,2,1,8,7] => [4,5,6,1,2,3,8,7] => 2

[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => [6,3,2,5,4,1,8,7] => [3,5,1,6,2,4,8,7] => 3

[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => [6,2,3,4,5,1,8,7] => [2,3,4,5,6,1,8,7] => 2

[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [2,1,6,3,4,5,8,7] => [2,1,6,3,4,5,8,7] => 3

[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => [2,1,6,3,5,4,8,7] => [2,1,5,3,6,4,8,7] => 4

[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => [2,1,6,5,4,3,8,7] => [2,1,5,6,3,4,8,7] => 3

[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => [4,1,2,3,6,5,8,7] => [4,1,2,3,6,5,8,7] => 3

[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => [4,1,3,2,6,5,8,7] => [3,1,4,2,6,5,8,7] => 4

[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [3,4,1,2,6,5,8,7] => 3

[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4

[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [5,4,3,2,1,6,8,7] => [5,1,2,3,4,6,8,7] => [5,1,2,3,4,6,8,7] => 2

[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => 2

[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 1

[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,6,8] => 1

[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [7,1,2,6,4,5,3,8] => [6,1,2,7,3,4,5,8] => 2

[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => [7,2,1,3,4,5,6,8] => [2,7,1,3,4,5,6,8] => 1

[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => [7,5,2,3,4,1,6,8] => [5,7,1,2,3,4,6,8] => 1

[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => [7,6,2,3,4,5,1,8] => [6,7,1,2,3,4,5,8] => 1

[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => [7,6,5,3,4,2,1,8] => [5,6,7,1,2,3,4,8] => 1

[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [2,3,4,5,6,7,1,8] => 1

[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,7,6,5,4,3,2,8] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6,8] => 1

[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => [1,7,2,3,4,6,5,8] => [1,6,2,3,4,7,5,8] => 2

[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,4,7,6,5,3,2,8] => [1,7,2,4,3,5,6,8] => [1,4,2,7,3,5,6,8] => 2

[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,5,4,7,6,3,2,8] => [1,7,2,5,4,3,6,8] => [1,5,2,7,3,4,6,8] => 2

[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,5,4,6,7,3,2,8] => [1,7,2,5,4,6,3,8] => [1,5,2,6,3,7,4,8] => 3

[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,4,5,6,3,7,2,8] => [1,7,6,4,5,3,2,8] => [1,4,5,6,7,2,3,8] => 1

[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,3,5,4,6,7,2,8] => [1,7,3,5,4,6,2,8] => [1,3,5,6,2,7,4,8] => 2

[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,3,2,7,6,5,4,8] => [1,3,2,7,4,5,6,8] => [1,3,2,7,4,5,6,8] => 2

[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,3,2,6,7,5,4,8] => [1,3,2,7,4,6,5,8] => [1,3,2,6,4,7,5,8] => 3

[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,7,6,5,4,8] => [1,2,3,7,4,5,6,8] => [1,2,3,7,4,5,6,8] => 1

[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,2,3,6,7,5,4,8] => [1,2,3,7,4,6,5,8] => [1,2,3,6,4,7,5,8] => 2

[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [1,4,2,3,7,5,6,8] => [1,4,2,3,7,5,6,8] => 2

[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [1,3,4,2,6,7,5,8] => 2

[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,5,4,3,2,7,6,8] => [1,5,2,3,4,7,6,8] => [1,5,2,3,4,7,6,8] => 2

[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,4,5,3,2,7,6,8] => [1,5,2,4,3,7,6,8] => [1,4,2,5,3,7,6,8] => 3

[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => 3

[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => 2

[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,4,3,2,5,7,6,8] => [1,4,2,3,5,7,6,8] => [1,4,2,3,5,7,6,8] => 2

[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => 2

[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => 1

[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7,8] => 1

[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [6,5,4,3,2,1,7,8] => [4,5,6,1,2,3,7,8] => 1

[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => [2,3,4,5,6,1,7,8] => 1

[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,6,5,4,3,2,7,8] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7,8] => 1

[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,4,6,5,3,2,7,8] => [1,6,2,4,3,5,7,8] => [1,4,2,6,3,5,7,8] => 2

[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [1,2,5,4,6,3,7,8] => [1,2,6,5,4,3,7,8] => [1,2,5,6,3,4,7,8] => 1

[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,3,2,6,5,4,7,8] => [1,3,2,6,4,5,7,8] => [1,3,2,6,4,5,7,8] => 2

[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,2,3,6,5,4,7,8] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7,8] => 1

[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => 2

[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1

[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [2,3,4,5,1,6,7,8] => 1

[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,5,4,3,2,6,7,8] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7,8] => 1

[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,4,5,3,2,6,7,8] => [1,5,2,4,3,6,7,8] => [1,4,2,5,3,6,7,8] => 2

[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => 2

[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 1

[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [3,4,1,2,5,6,7,8] => 1

[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,4,3,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7,8] => 1

[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 1

[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => 1

[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0

[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => 1

[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => [9,1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,9,7] => 2

[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,9,1] => 1

[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0

[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [10,1,2,3,4,5,6,7,8,9] => [10,1,2,3,4,5,6,7,8,9] => 1

[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => [10,1,2,3,4,5,6,7,9,8] => [9,1,2,3,4,5,6,7,10,8] => 2

[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,10,1] => 1

[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0

[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => [9,8,2,3,4,5,6,7,1] => [8,9,1,2,3,4,5,6,7] => 1

[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [8,1,2,3,4,5,6,7,9] => [8,1,2,3,4,5,6,7,9] => 1

[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => [10,9,2,3,4,5,6,7,8,1] => [9,10,1,2,3,4,5,6,7,8] => 1

[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [9,1,2,3,4,5,6,7,8,10] => [9,1,2,3,4,5,6,7,8,10] => 1

[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => 5

[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 1

[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 1

[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => 1

[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,10,11,1] => 1

[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => [1,9,2,3,4,5,6,7,8] => [1,9,2,3,4,5,6,7,8] => 1

[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,8,9,7,6,5,4,3,2] => [1,9,2,3,4,5,6,8,7] => [1,8,2,3,4,5,6,9,7] => 2

[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => [1,10,2,3,4,5,6,7,8,9] => [1,10,2,3,4,5,6,7,8,9] => 1

[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => [10,1,2,3,4,5,6,7,8,9,11] => [10,1,2,3,4,5,6,7,8,9,11] => 1

[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,11,10,9,8,7,6,5,4,3,2] => [1,11,2,3,4,5,6,7,8,9,10] => [1,11,2,3,4,5,6,7,8,9,10] => 1

[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => [10,9,8,7,6,5,4,3,2,1] => [6,7,8,9,10,1,2,3,4,5] => 1

[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => [7,6,8,5,9,4,10,3,11,2,12,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [7,8,9,10,11,12,1,2,3,4,5,6] => 1

[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [2,1,9,8,7,6,5,4,3] => [2,1,9,3,4,5,6,7,8] => [2,1,9,3,4,5,6,7,8] => 2

[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [7,6,5,4,3,2,1,9,8] => [7,1,2,3,4,5,6,9,8] => [7,1,2,3,4,5,6,9,8] => 2

[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => [7,1,2,3,4,5,6,8,9] => [7,1,2,3,4,5,6,8,9] => 1

[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => 1

[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => 1

[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,9,8,7,6,5,4,3,1] => [9,2,1,3,4,5,6,7,8] => [2,9,1,3,4,5,6,7,8] => 1

[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,9,8,1] => [9,2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,9,1,8] => 1

[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => 1

[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => [8,2,3,4,5,6,7,1,9] => [2,3,4,5,6,7,8,1,9] => 1

[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => [7,2,3,4,5,6,1,8,9] => [2,3,4,5,6,7,1,8,9] => 1

[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => [9,2,3,4,5,6,7,8,1,10] => [2,3,4,5,6,7,8,9,1,10] => 1

[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [2,8,7,6,5,4,3,1,9] => [8,2,1,3,4,5,6,7,9] => [2,8,1,3,4,5,6,7,9] => 1

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$F_{1} = 1$

$F_{2} = 1 + q$

$F_{3} = 1 + 4\ q$

$F_{4} = 1 + 11\ q + 2\ q^{2}$

$F_{5} = 1 + 26\ q + 15\ q^{2}$

$F_{6} = 1 + 57\ q + 69\ q^{2} + 5\ q^{3}$

Description

The number of isolated descents of a permutation.
A descent

$i$ is isolated if neither

$i+1$ nor

$i-1$ are descents. If a permutation has only isolated descents, then it is called primitive in [1].

Map

to 312-avoiding permutation

Description

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

Map

Corteel

Description

Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.

Map

first fundamental transformation

Description

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