Identifier
-
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00252: Permutations —restriction⟶ Permutations
St000546: Permutations ⟶ ℤ
Values
[.,.] => [1] => [] => 0
[.,[.,.]] => [2,1] => [1] => 0
[[.,.],.] => [1,2] => [1] => 0
[.,[.,[.,.]]] => [3,2,1] => [2,1] => 1
[.,[[.,.],.]] => [2,3,1] => [2,1] => 1
[[.,.],[.,.]] => [3,1,2] => [1,2] => 0
[[.,[.,.]],.] => [2,1,3] => [2,1] => 1
[[[.,.],.],.] => [1,2,3] => [1,2] => 0
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [3,2,1] => 2
[.,[.,[[.,.],.]]] => [3,4,2,1] => [3,2,1] => 2
[.,[[.,.],[.,.]]] => [4,2,3,1] => [2,3,1] => 1
[.,[[.,[.,.]],.]] => [3,2,4,1] => [3,2,1] => 2
[.,[[[.,.],.],.]] => [2,3,4,1] => [2,3,1] => 1
[[.,.],[.,[.,.]]] => [4,3,1,2] => [3,1,2] => 1
[[.,.],[[.,.],.]] => [3,4,1,2] => [3,1,2] => 1
[[.,[.,.]],[.,.]] => [4,2,1,3] => [2,1,3] => 0
[[[.,.],.],[.,.]] => [4,1,2,3] => [1,2,3] => 0
[[.,[.,[.,.]]],.] => [3,2,1,4] => [3,2,1] => 2
[[.,[[.,.],.]],.] => [2,3,1,4] => [2,3,1] => 1
[[[.,.],[.,.]],.] => [3,1,2,4] => [3,1,2] => 1
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3] => 0
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3] => 0
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [4,3,2,1] => 3
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [4,3,2,1] => 3
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [3,4,2,1] => 2
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [4,3,2,1] => 3
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [3,4,2,1] => 2
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [4,2,3,1] => 2
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [4,2,3,1] => 2
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [3,2,4,1] => 1
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [2,3,4,1] => 1
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [4,3,2,1] => 3
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [3,4,2,1] => 2
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [4,2,3,1] => 2
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [3,2,4,1] => 1
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [2,3,4,1] => 1
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [4,3,1,2] => 2
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [4,3,1,2] => 2
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [3,4,1,2] => 1
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [4,3,1,2] => 2
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [3,4,1,2] => 1
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [4,2,1,3] => 1
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => [4,2,1,3] => 1
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [4,1,2,3] => 1
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [4,1,2,3] => 1
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [3,2,1,4] => 0
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [2,3,1,4] => 0
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [3,1,2,4] => 0
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [2,1,3,4] => 0
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [1,2,3,4] => 0
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,3,2,1] => 3
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [3,4,2,1] => 2
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [4,2,3,1] => 2
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [3,2,4,1] => 1
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [2,3,4,1] => 1
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [4,3,1,2] => 2
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [3,4,1,2] => 1
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [4,2,1,3] => 1
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [4,1,2,3] => 1
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,2,1,4] => 0
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [2,3,1,4] => 0
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [3,1,2,4] => 0
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4] => 0
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4] => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [5,4,3,2,1] => 4
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [5,4,3,2,1] => 4
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [4,5,3,2,1] => 3
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [5,4,3,2,1] => 4
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [4,5,3,2,1] => 3
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [5,3,4,2,1] => 3
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [5,3,4,2,1] => 3
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [4,3,5,2,1] => 2
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [3,4,5,2,1] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [5,4,3,2,1] => 4
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [4,5,3,2,1] => 3
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [5,3,4,2,1] => 3
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [4,3,5,2,1] => 2
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [3,4,5,2,1] => 2
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [5,4,2,3,1] => 3
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [5,4,2,3,1] => 3
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [4,5,2,3,1] => 2
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [5,4,2,3,1] => 3
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [4,5,2,3,1] => 2
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [5,3,2,4,1] => 2
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [5,3,2,4,1] => 2
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [5,2,3,4,1] => 2
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [5,2,3,4,1] => 2
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [4,3,2,5,1] => 1
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [3,4,2,5,1] => 1
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [4,2,3,5,1] => 1
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [3,2,4,5,1] => 1
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [2,3,4,5,1] => 1
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [5,4,3,2,1] => 4
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [4,5,3,2,1] => 3
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [5,3,4,2,1] => 3
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [4,3,5,2,1] => 2
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [3,4,5,2,1] => 2
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [5,4,2,3,1] => 3
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [4,5,2,3,1] => 2
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [5,3,2,4,1] => 2
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [5,2,3,4,1] => 2
>>> Load all 806 entries. <<<[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [4,3,2,5,1] => 1
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [3,4,2,5,1] => 1
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [4,2,3,5,1] => 1
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [3,2,4,5,1] => 1
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [2,3,4,5,1] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [5,4,3,1,2] => 3
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [5,4,3,1,2] => 3
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [4,5,3,1,2] => 2
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [5,4,3,1,2] => 3
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [4,5,3,1,2] => 2
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [5,3,4,1,2] => 2
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [5,3,4,1,2] => 2
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [4,3,5,1,2] => 1
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [3,4,5,1,2] => 1
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [5,4,3,1,2] => 3
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [4,5,3,1,2] => 2
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [5,3,4,1,2] => 2
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [4,3,5,1,2] => 1
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [3,4,5,1,2] => 1
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [5,4,2,1,3] => 2
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [5,4,2,1,3] => 2
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [4,5,2,1,3] => 1
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [5,4,2,1,3] => 2
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [4,5,2,1,3] => 1
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [5,4,1,2,3] => 2
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [5,4,1,2,3] => 2
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [4,5,1,2,3] => 1
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [5,4,1,2,3] => 2
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [4,5,1,2,3] => 1
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [5,3,2,1,4] => 1
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [5,3,2,1,4] => 1
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [5,2,3,1,4] => 1
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [5,2,3,1,4] => 1
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [5,3,1,2,4] => 1
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [5,3,1,2,4] => 1
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [5,2,1,3,4] => 1
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [5,2,1,3,4] => 1
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [5,1,2,3,4] => 1
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [5,1,2,3,4] => 1
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [4,3,2,1,5] => 0
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [3,4,2,1,5] => 0
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [4,2,3,1,5] => 0
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [3,2,4,1,5] => 0
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [2,3,4,1,5] => 0
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [4,3,1,2,5] => 0
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [3,4,1,2,5] => 0
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [4,2,1,3,5] => 0
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [4,1,2,3,5] => 0
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [3,2,1,4,5] => 0
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [2,3,1,4,5] => 0
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [3,1,2,4,5] => 0
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [2,1,3,4,5] => 0
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [1,2,3,4,5] => 0
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [5,4,3,2,1] => 4
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [4,5,3,2,1] => 3
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [5,3,4,2,1] => 3
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [4,3,5,2,1] => 2
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [3,4,5,2,1] => 2
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [5,4,2,3,1] => 3
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [4,5,2,3,1] => 2
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [5,3,2,4,1] => 2
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [5,2,3,4,1] => 2
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [4,3,2,5,1] => 1
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [3,4,2,5,1] => 1
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [4,2,3,5,1] => 1
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [3,2,4,5,1] => 1
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [2,3,4,5,1] => 1
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [5,4,3,1,2] => 3
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [4,5,3,1,2] => 2
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [5,3,4,1,2] => 2
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [4,3,5,1,2] => 1
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [3,4,5,1,2] => 1
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [5,4,2,1,3] => 2
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [4,5,2,1,3] => 1
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [5,4,1,2,3] => 2
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [4,5,1,2,3] => 1
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [5,3,2,1,4] => 1
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [5,2,3,1,4] => 1
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [5,3,1,2,4] => 1
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [5,2,1,3,4] => 1
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [5,1,2,3,4] => 1
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [4,3,2,1,5] => 0
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [3,4,2,1,5] => 0
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [4,2,3,1,5] => 0
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [3,2,4,1,5] => 0
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [2,3,4,1,5] => 0
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [4,3,1,2,5] => 0
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [3,4,1,2,5] => 0
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [4,2,1,3,5] => 0
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [4,1,2,3,5] => 0
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [3,2,1,4,5] => 0
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [2,3,1,4,5] => 0
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [3,1,2,4,5] => 0
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5] => 0
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5] => 0
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [5,6,4,3,2,1] => 4
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [6,5,4,3,2,1] => 5
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [5,6,4,3,2,1] => 4
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [6,4,5,3,2,1] => 4
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => [6,4,5,3,2,1] => 4
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => [5,4,6,3,2,1] => 3
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [4,5,6,3,2,1] => 3
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [6,5,4,3,2,1] => 5
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [5,6,4,3,2,1] => 4
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => [6,4,5,3,2,1] => 4
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [5,4,6,3,2,1] => 3
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [4,5,6,3,2,1] => 3
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [6,5,3,4,2,1] => 4
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [6,5,3,4,2,1] => 4
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [5,6,3,4,2,1] => 3
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => [6,5,3,4,2,1] => 4
[.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => [5,6,3,4,2,1] => 3
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => [6,4,3,5,2,1] => 3
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => [6,4,3,5,2,1] => 3
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [6,3,4,5,2,1] => 3
[.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => [6,3,4,5,2,1] => 3
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => [5,4,3,6,2,1] => 2
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => [4,5,3,6,2,1] => 2
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => [5,3,4,6,2,1] => 2
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => [4,3,5,6,2,1] => 2
[.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => [3,4,5,6,2,1] => 2
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [6,5,4,3,2,1] => 5
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [5,6,4,3,2,1] => 4
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => [6,4,5,3,2,1] => 4
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [5,4,6,3,2,1] => 3
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [4,5,6,3,2,1] => 3
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => [6,5,3,4,2,1] => 4
[.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => [5,6,3,4,2,1] => 3
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => [6,4,3,5,2,1] => 3
[.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [6,3,4,5,2,1] => 3
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [5,4,3,6,2,1] => 2
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [4,5,3,6,2,1] => 2
[.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => [5,3,4,6,2,1] => 2
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [4,3,5,6,2,1] => 2
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [3,4,5,6,2,1] => 2
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [6,5,4,2,3,1] => 4
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [6,5,4,2,3,1] => 4
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [5,6,4,2,3,1] => 3
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => [6,5,4,2,3,1] => 4
[.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [5,6,4,2,3,1] => 3
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [6,4,5,2,3,1] => 3
[.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [6,4,5,2,3,1] => 3
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => [5,4,6,2,3,1] => 2
[.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [4,5,6,2,3,1] => 2
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => [6,5,4,2,3,1] => 4
[.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => [5,6,4,2,3,1] => 3
[.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [6,4,5,2,3,1] => 3
[.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => [5,4,6,2,3,1] => 2
[.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => [4,5,6,2,3,1] => 2
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => [6,5,3,2,4,1] => 3
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => [6,5,3,2,4,1] => 3
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => [5,6,3,2,4,1] => 2
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => [6,5,3,2,4,1] => 3
[.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => [5,6,3,2,4,1] => 2
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [6,5,2,3,4,1] => 3
[.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [6,5,2,3,4,1] => 3
[.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [5,6,2,3,4,1] => 2
[.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => [6,5,2,3,4,1] => 3
[.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => [5,6,2,3,4,1] => 2
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => [6,4,3,2,5,1] => 2
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => [6,4,3,2,5,1] => 2
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => [6,3,4,2,5,1] => 2
[.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => [6,3,4,2,5,1] => 2
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [6,4,2,3,5,1] => 2
[.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => [6,4,2,3,5,1] => 2
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => [6,3,2,4,5,1] => 2
[.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => [6,3,2,4,5,1] => 2
[.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [6,2,3,4,5,1] => 2
[.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => [6,2,3,4,5,1] => 2
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => [5,4,3,2,6,1] => 1
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => [4,5,3,2,6,1] => 1
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => [5,3,4,2,6,1] => 1
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => [4,3,5,2,6,1] => 1
[.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => [3,4,5,2,6,1] => 1
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => [5,4,2,3,6,1] => 1
[.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => [4,5,2,3,6,1] => 1
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => [5,3,2,4,6,1] => 1
[.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [5,2,3,4,6,1] => 1
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => [4,3,2,5,6,1] => 1
[.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => [3,4,2,5,6,1] => 1
[.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => [4,2,3,5,6,1] => 1
[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => [3,2,4,5,6,1] => 1
[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [2,3,4,5,6,1] => 1
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [6,5,4,3,2,1] => 5
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [5,6,4,3,2,1] => 4
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => [6,4,5,3,2,1] => 4
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [5,4,6,3,2,1] => 3
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [4,5,6,3,2,1] => 3
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => [6,5,3,4,2,1] => 4
[.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => [5,6,3,4,2,1] => 3
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => [6,4,3,5,2,1] => 3
[.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => [6,3,4,5,2,1] => 3
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [5,4,3,6,2,1] => 2
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [4,5,3,6,2,1] => 2
[.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => [5,3,4,6,2,1] => 2
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [4,3,5,6,2,1] => 2
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [3,4,5,6,2,1] => 2
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => [6,5,4,2,3,1] => 4
[.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => [5,6,4,2,3,1] => 3
[.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [6,4,5,2,3,1] => 3
[.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => [5,4,6,2,3,1] => 2
[.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => [4,5,6,2,3,1] => 2
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => [6,5,3,2,4,1] => 3
[.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => [5,6,3,2,4,1] => 2
[.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => [6,5,2,3,4,1] => 3
[.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => [5,6,2,3,4,1] => 2
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => [6,4,3,2,5,1] => 2
[.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => [6,3,4,2,5,1] => 2
[.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => [6,4,2,3,5,1] => 2
[.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => [6,3,2,4,5,1] => 2
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => [6,2,3,4,5,1] => 2
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [5,4,3,2,6,1] => 1
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [4,5,3,2,6,1] => 1
[.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => [5,3,4,2,6,1] => 1
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [4,3,5,2,6,1] => 1
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [3,4,5,2,6,1] => 1
[.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => [5,4,2,3,6,1] => 1
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => [4,5,2,3,6,1] => 1
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => [5,3,2,4,6,1] => 1
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => [5,2,3,4,6,1] => 1
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [4,3,2,5,6,1] => 1
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [3,4,2,5,6,1] => 1
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => [4,2,3,5,6,1] => 1
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [3,2,4,5,6,1] => 1
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [2,3,4,5,6,1] => 1
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [6,5,4,3,1,2] => 4
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [6,5,4,3,1,2] => 4
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [5,6,4,3,1,2] => 3
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => [6,5,4,3,1,2] => 4
[[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [5,6,4,3,1,2] => 3
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [6,4,5,3,1,2] => 3
[[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [6,4,5,3,1,2] => 3
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => [5,4,6,3,1,2] => 2
[[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [4,5,6,3,1,2] => 2
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => [6,5,4,3,1,2] => 4
[[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => [5,6,4,3,1,2] => 3
[[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [6,4,5,3,1,2] => 3
[[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => [5,4,6,3,1,2] => 2
[[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => [4,5,6,3,1,2] => 2
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [6,5,3,4,1,2] => 3
[[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [6,5,3,4,1,2] => 3
[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [5,6,3,4,1,2] => 2
[[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => [6,5,3,4,1,2] => 3
[[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [5,6,3,4,1,2] => 2
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [6,4,3,5,1,2] => 2
[[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => [6,4,3,5,1,2] => 2
[[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [6,3,4,5,1,2] => 2
[[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [6,3,4,5,1,2] => 2
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => [5,4,3,6,1,2] => 1
[[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => [4,5,3,6,1,2] => 1
[[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [5,3,4,6,1,2] => 1
[[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => [4,3,5,6,1,2] => 1
[[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [3,4,5,6,1,2] => 1
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => [6,5,4,3,1,2] => 4
[[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => [5,6,4,3,1,2] => 3
[[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => [6,4,5,3,1,2] => 3
[[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => [5,4,6,3,1,2] => 2
[[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => [4,5,6,3,1,2] => 2
[[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [6,5,3,4,1,2] => 3
[[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => [5,6,3,4,1,2] => 2
[[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => [6,4,3,5,1,2] => 2
[[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [6,3,4,5,1,2] => 2
[[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => [5,4,3,6,1,2] => 1
[[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => [4,5,3,6,1,2] => 1
[[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => [5,3,4,6,1,2] => 1
[[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => [4,3,5,6,1,2] => 1
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => [3,4,5,6,1,2] => 1
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => [6,5,4,2,1,3] => 3
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => [6,5,4,2,1,3] => 3
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => [5,6,4,2,1,3] => 2
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => [6,5,4,2,1,3] => 3
[[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => [5,6,4,2,1,3] => 2
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => [6,4,5,2,1,3] => 2
[[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => [6,4,5,2,1,3] => 2
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => [5,4,6,2,1,3] => 1
[[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => [4,5,6,2,1,3] => 1
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => [6,5,4,2,1,3] => 3
[[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => [5,6,4,2,1,3] => 2
[[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => [6,4,5,2,1,3] => 2
[[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => [5,4,6,2,1,3] => 1
[[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => [4,5,6,2,1,3] => 1
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [6,5,4,1,2,3] => 3
[[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [6,5,4,1,2,3] => 3
[[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [5,6,4,1,2,3] => 2
[[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => [6,5,4,1,2,3] => 3
[[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => [5,6,4,1,2,3] => 2
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [6,4,5,1,2,3] => 2
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [6,4,5,1,2,3] => 2
[[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => [5,4,6,1,2,3] => 1
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [4,5,6,1,2,3] => 1
[[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => [6,5,4,1,2,3] => 3
[[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => [5,6,4,1,2,3] => 2
[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => [6,4,5,1,2,3] => 2
[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => [5,4,6,1,2,3] => 1
[[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => [4,5,6,1,2,3] => 1
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => [6,5,3,2,1,4] => 2
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => [6,5,3,2,1,4] => 2
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => [5,6,3,2,1,4] => 1
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => [6,5,3,2,1,4] => 2
[[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => [5,6,3,2,1,4] => 1
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => [6,5,2,3,1,4] => 2
[[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => [6,5,2,3,1,4] => 2
[[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => [5,6,2,3,1,4] => 1
[[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => [6,5,2,3,1,4] => 2
[[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => [5,6,2,3,1,4] => 1
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [6,5,3,1,2,4] => 2
[[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => [6,5,3,1,2,4] => 2
[[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [5,6,3,1,2,4] => 1
[[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => [6,5,3,1,2,4] => 2
[[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => [5,6,3,1,2,4] => 1
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => [6,5,2,1,3,4] => 2
[[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => [6,5,2,1,3,4] => 2
[[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => [5,6,2,1,3,4] => 1
[[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => [6,5,2,1,3,4] => 2
[[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => [5,6,2,1,3,4] => 1
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [6,5,1,2,3,4] => 2
[[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => [6,5,1,2,3,4] => 2
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [5,6,1,2,3,4] => 1
[[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => [6,5,1,2,3,4] => 2
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => [5,6,1,2,3,4] => 1
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => [6,4,3,2,1,5] => 1
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => [6,4,3,2,1,5] => 1
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => [6,3,4,2,1,5] => 1
[[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => [6,3,4,2,1,5] => 1
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => [6,4,2,3,1,5] => 1
[[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => [6,4,2,3,1,5] => 1
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => [6,3,2,4,1,5] => 1
[[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => [6,3,2,4,1,5] => 1
[[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => [6,2,3,4,1,5] => 1
[[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => [6,2,3,4,1,5] => 1
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [6,4,3,1,2,5] => 1
[[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => [6,4,3,1,2,5] => 1
[[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [6,3,4,1,2,5] => 1
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => [6,3,4,1,2,5] => 1
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => [6,4,2,1,3,5] => 1
[[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => [6,4,2,1,3,5] => 1
[[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [6,4,1,2,3,5] => 1
[[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [6,4,1,2,3,5] => 1
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => [6,3,2,1,4,5] => 1
[[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => [6,3,2,1,4,5] => 1
[[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => [6,2,3,1,4,5] => 1
[[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => [6,2,3,1,4,5] => 1
[[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => [6,3,1,2,4,5] => 1
[[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => [6,3,1,2,4,5] => 1
[[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => [6,2,1,3,4,5] => 1
[[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => [6,2,1,3,4,5] => 1
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [6,1,2,3,4,5] => 1
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => [6,1,2,3,4,5] => 1
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => [5,4,3,2,1,6] => 0
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => [4,5,3,2,1,6] => 0
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => [5,3,4,2,1,6] => 0
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => [4,3,5,2,1,6] => 0
[[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => [3,4,5,2,1,6] => 0
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => [5,4,2,3,1,6] => 0
[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => [4,5,2,3,1,6] => 0
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => [5,3,2,4,1,6] => 0
[[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => [5,2,3,4,1,6] => 0
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => [4,3,2,5,1,6] => 0
[[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => [3,4,2,5,1,6] => 0
[[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => [4,2,3,5,1,6] => 0
[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => [3,2,4,5,1,6] => 0
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => [2,3,4,5,1,6] => 0
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => [5,4,3,1,2,6] => 0
[[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => [4,5,3,1,2,6] => 0
[[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [5,3,4,1,2,6] => 0
[[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => [4,3,5,1,2,6] => 0
[[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => [3,4,5,1,2,6] => 0
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => [5,4,2,1,3,6] => 0
[[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => [4,5,2,1,3,6] => 0
[[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [5,4,1,2,3,6] => 0
[[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [4,5,1,2,3,6] => 0
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => [5,3,2,1,4,6] => 0
[[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => [5,2,3,1,4,6] => 0
[[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => [5,3,1,2,4,6] => 0
[[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => [5,2,1,3,4,6] => 0
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [5,1,2,3,4,6] => 0
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => [4,3,2,1,5,6] => 0
[[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => [3,4,2,1,5,6] => 0
[[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => [4,2,3,1,5,6] => 0
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => [3,2,4,1,5,6] => 0
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => [2,3,4,1,5,6] => 0
[[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => [4,3,1,2,5,6] => 0
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => [3,4,1,2,5,6] => 0
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => [4,2,1,3,5,6] => 0
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => [4,1,2,3,5,6] => 0
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => [3,2,1,4,5,6] => 0
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => [2,3,1,4,5,6] => 0
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => [3,1,2,4,5,6] => 0
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => [2,1,3,4,5,6] => 0
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1] => 5
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1] => 4
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => [6,4,5,3,2,1] => 4
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1] => 3
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1] => 3
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => [6,5,3,4,2,1] => 4
[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => [5,6,3,4,2,1] => 3
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => [6,4,3,5,2,1] => 3
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => [6,3,4,5,2,1] => 3
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1] => 2
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1] => 2
[[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => [5,3,4,6,2,1] => 2
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1] => 2
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1] => 2
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => [6,5,4,2,3,1] => 4
[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => [5,6,4,2,3,1] => 3
[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => [6,4,5,2,3,1] => 3
[[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => [5,4,6,2,3,1] => 2
[[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => [4,5,6,2,3,1] => 2
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => [6,5,3,2,4,1] => 3
[[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => [5,6,3,2,4,1] => 2
[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => [6,5,2,3,4,1] => 3
[[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => [5,6,2,3,4,1] => 2
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => [6,4,3,2,5,1] => 2
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => [6,3,4,2,5,1] => 2
[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => [6,4,2,3,5,1] => 2
[[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => [6,3,2,4,5,1] => 2
[[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => [6,2,3,4,5,1] => 2
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1] => 1
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1] => 1
[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => [5,3,4,2,6,1] => 1
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1] => 1
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1] => 1
[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => [5,4,2,3,6,1] => 1
[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => [4,5,2,3,6,1] => 1
[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => [5,3,2,4,6,1] => 1
[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => [5,2,3,4,6,1] => 1
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1] => 1
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1] => 1
[[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => [4,2,3,5,6,1] => 1
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1] => 1
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1] => 1
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => [6,5,4,3,1,2] => 4
[[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => [5,6,4,3,1,2] => 3
[[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => [6,4,5,3,1,2] => 3
[[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => [5,4,6,3,1,2] => 2
[[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => [4,5,6,3,1,2] => 2
[[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => [6,5,3,4,1,2] => 3
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => [5,6,3,4,1,2] => 2
[[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => [6,4,3,5,1,2] => 2
[[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => [6,3,4,5,1,2] => 2
[[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => [5,4,3,6,1,2] => 1
[[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => [4,5,3,6,1,2] => 1
[[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => [5,3,4,6,1,2] => 1
[[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => [4,3,5,6,1,2] => 1
[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => [3,4,5,6,1,2] => 1
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => [6,5,4,2,1,3] => 3
[[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => [5,6,4,2,1,3] => 2
[[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => [6,4,5,2,1,3] => 2
[[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => [5,4,6,2,1,3] => 1
[[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => [4,5,6,2,1,3] => 1
[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [6,5,4,1,2,3] => 3
[[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => [5,6,4,1,2,3] => 2
[[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [6,4,5,1,2,3] => 2
[[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => [5,4,6,1,2,3] => 1
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [4,5,6,1,2,3] => 1
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => [6,5,3,2,1,4] => 2
[[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => [5,6,3,2,1,4] => 1
[[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => [6,5,2,3,1,4] => 2
[[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => [5,6,2,3,1,4] => 1
[[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => [6,5,3,1,2,4] => 2
[[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => [5,6,3,1,2,4] => 1
[[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => [6,5,2,1,3,4] => 2
[[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => [5,6,2,1,3,4] => 1
[[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [6,5,1,2,3,4] => 2
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => [5,6,1,2,3,4] => 1
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => [6,4,3,2,1,5] => 1
[[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => [6,3,4,2,1,5] => 1
[[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => [6,4,2,3,1,5] => 1
[[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => [6,3,2,4,1,5] => 1
[[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => [6,2,3,4,1,5] => 1
[[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => [6,4,3,1,2,5] => 1
[[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => [6,3,4,1,2,5] => 1
[[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => [6,4,2,1,3,5] => 1
[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [6,4,1,2,3,5] => 1
[[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => [6,3,2,1,4,5] => 1
[[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => [6,2,3,1,4,5] => 1
[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => [6,3,1,2,4,5] => 1
[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => [6,2,1,3,4,5] => 1
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5] => 1
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6] => 0
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6] => 0
[[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => [5,3,4,2,1,6] => 0
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6] => 0
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6] => 0
[[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => [5,4,2,3,1,6] => 0
[[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => [4,5,2,3,1,6] => 0
[[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => [5,3,2,4,1,6] => 0
[[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => [5,2,3,4,1,6] => 0
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6] => 0
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6] => 0
[[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => [4,2,3,5,1,6] => 0
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6] => 0
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6] => 0
[[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => [5,4,3,1,2,6] => 0
[[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => [4,5,3,1,2,6] => 0
[[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => [5,3,4,1,2,6] => 0
[[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => [4,3,5,1,2,6] => 0
[[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => [3,4,5,1,2,6] => 0
[[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => [5,4,2,1,3,6] => 0
[[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => [4,5,2,1,3,6] => 0
[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => [5,4,1,2,3,6] => 0
[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => [4,5,1,2,3,6] => 0
[[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => [5,3,2,1,4,6] => 0
[[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => [5,2,3,1,4,6] => 0
[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => [5,3,1,2,4,6] => 0
[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => [5,2,1,3,4,6] => 0
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6] => 0
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6] => 0
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6] => 0
[[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => [4,2,3,1,5,6] => 0
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6] => 0
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6] => 0
[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => [4,3,1,2,5,6] => 0
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => [3,4,1,2,5,6] => 0
[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => [4,2,1,3,5,6] => 0
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6] => 0
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6] => 0
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6] => 0
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6] => 0
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6] => 0
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6] => 0
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 6
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 6
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [7,6,5,4,3,2,1] => 6
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [7,6,5,4,3,2,1] => 6
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [7,6,5,4,3,2,1] => 6
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [7,6,5,4,3,2,1] => 6
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,1] => 6
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => [3,4,5,2,6,7,1] => 1
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => [5,2,3,4,6,7,1] => 1
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => [4,3,2,5,6,7,1] => 1
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => [3,4,2,5,6,7,1] => 1
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => [4,2,3,5,6,7,1] => 1
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,1] => 1
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,1] => 1
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [7,6,5,4,3,1,2] => 5
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [7,6,5,4,3,1,2] => 5
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [7,6,5,3,4,1,2] => 4
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [7,5,6,3,4,1,2] => 3
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [7,5,6,3,4,1,2] => 3
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,4,1,2] => [7,6,5,3,4,1,2] => 4
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => [7,5,6,3,4,1,2] => 3
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => [6,5,7,3,4,1,2] => 2
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => [3,4,5,6,7,1,2] => 1
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => [7,6,5,4,3,1,2] => 5
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => [3,4,5,6,7,1,2] => 1
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [7,6,5,4,1,2,3] => 4
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => [7,6,4,5,1,2,3] => 3
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [6,7,4,5,1,2,3] => 2
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => [7,4,5,6,1,2,3] => 2
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => [7,4,5,6,1,2,3] => 2
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => [6,7,4,5,1,2,3] => 2
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [7,6,5,1,2,3,4] => 3
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => [7,6,5,1,2,3,4] => 3
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => [7,6,5,1,2,3,4] => 3
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [7,5,6,1,2,3,4] => 2
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => [7,5,6,1,2,3,4] => 2
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => [5,6,7,1,2,3,4] => 1
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => [7,6,5,1,2,3,4] => 3
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => [7,5,6,1,2,3,4] => 2
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => [5,6,7,1,2,3,4] => 1
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [6,7,8,3,4,1,2,5] => [6,7,3,4,1,2,5] => 1
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => [7,6,1,2,3,4,5] => 2
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => [7,6,1,2,3,4,5] => 2
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => [6,7,1,2,3,4,5] => 1
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5] => [7,6,1,2,3,4,5] => 2
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => [6,7,1,2,3,4,5] => 1
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6] => [7,5,1,2,3,4,6] => 1
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => [7,5,1,2,3,4,6] => 1
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [7,8,3,2,4,1,5,6] => [7,3,2,4,1,5,6] => 1
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [7,8,2,3,4,1,5,6] => [7,2,3,4,1,5,6] => 1
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [7,8,3,4,1,2,5,6] => [7,3,4,1,2,5,6] => 1
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [7,8,4,2,1,3,5,6] => [7,4,2,1,3,5,6] => 1
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => [7,4,1,2,3,5,6] => 1
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [8,7,3,2,1,4,5,6] => [7,3,2,1,4,5,6] => 1
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [7,8,3,2,1,4,5,6] => [7,3,2,1,4,5,6] => 1
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [7,8,2,1,3,4,5,6] => [7,2,1,3,4,5,6] => 1
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => 1
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 0
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [8,4,5,6,3,2,1,7] => [4,5,6,3,2,1,7] => 0
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => [5,6,3,4,1,2,7] => 0
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => [5,6,1,2,3,4,7] => 0
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [8,4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 0
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => 0
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => 0
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 0
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => 0
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => 0
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 0
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1] => 6
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1] => 1
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1] => 1
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => [7,6,5,4,3,1,2] => 5
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [7,6,5,4,1,2,3] => 4
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => [7,4,5,6,1,2,3] => 2
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [5,4,6,7,1,2,3,8] => [5,4,6,7,1,2,3] => 1
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => [7,6,5,1,2,3,4] => 3
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [7,5,6,1,2,3,4,8] => [7,5,6,1,2,3,4] => 2
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => [5,6,7,1,2,3,4] => 1
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => [6,7,1,2,3,4,5] => 1
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => [7,5,1,2,3,4,6] => 1
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [7,3,1,2,4,5,6,8] => [7,3,1,2,4,5,6] => 1
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8] => [7,2,1,3,4,5,6] => 1
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,6] => 1
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7] => 0
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7] => 0
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7] => 0
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => [5,6,3,4,1,2,7] => 0
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => [4,5,6,1,2,3,7] => 0
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7] => 0
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7] => 0
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7] => 0
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7] => 0
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7] => 0
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7] => 0
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => [3,4,1,2,5,6,7] => 0
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => [4,1,2,3,5,6,7] => 0
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7] => 0
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7] => 0
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7] => 0
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7] => 0
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 7
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 7
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,1] => 1
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8] => 0
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 8
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 8
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2] => [3,4,5,6,7,8,1,2] => 1
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,1] => 1
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9] => 0
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 7
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 7
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => [8,7,6,5,4,3,2,1] => 7
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => [8,7,6,5,4,3,2,1] => 7
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => [8,7,6,5,4,3,2,1] => 7
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => [8,7,6,5,4,3,2,1] => 7
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1] => 7
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 8
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 8
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 8
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 8
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => [9,8,7,6,5,4,3,2,1] => 8
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => [9,8,7,6,5,4,3,2,1] => 8
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,3,1,2,9] => [8,7,6,5,4,3,1,2] => 6
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => [9,8,7,6,5,4,3,2,1] => 8
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1] => 8
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [9,7,8,5,6,3,4,1,2] => 4
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => 0
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,1] => 1
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => 0
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [4,2,3,5,6,7,8,9,1] => [4,2,3,5,6,7,8,1] => 1
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => [3,4,2,5,6,7,8,1] => 1
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => [3,2,4,5,6,7,8,9,1] => 1
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => [2,3,4,5,6,7,8,9,10,1] => 1
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => 1
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => [7,8,1,2,3,4,5,6] => 1
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => [6,7,8,1,2,3,4,5] => 1
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => 1
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => 1
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => [8,9,1,2,3,4,5,6,7] => 1
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => [7,8,9,1,2,3,4,5,6] => 1
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => [6,7,8,9,1,2,3,4,5] => 1
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [8,7,6,5,4,3,1,2] => 6
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [9,8,7,6,5,4,3,1,2] => 7
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1] => 9
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => [7,6,8,5,4,3,2,1] => 5
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => [8,7,6,5,4,1,2,3] => 5
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8] => 0
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8] => 0
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8] => 0
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8] => 0
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8] => 0
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8] => 0
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9] => 0
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9] => 0
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9] => 0
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9] => 0
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9] => 0
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9] => 0
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9] => 0
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10] => 0
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => [2,3,4,5,6,7,8,1] => 1
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => [2,3,4,5,6,7,1,8] => 0
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => [2,3,4,5,6,7,8,9,1] => 1
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => [7,1,2,3,4,5,6,8] => 0
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => [8,1,2,3,4,5,6,7] => 1
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => [9,1,2,3,4,5,6,7,8] => 1
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => [9,8,7,6,5,4,1,2,3] => 6
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => 1
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => [8,7,1,2,3,4,5,6] => 2
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => [8,7,6,1,2,3,4,5] => 3
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => [8,7,6,5,1,2,3,4] => 4
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => [9,8,1,2,3,4,5,6,7] => 2
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => [9,8,7,1,2,3,4,5,6] => 3
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => [9,8,7,6,1,2,3,4,5] => 4
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => [9,8,7,6,5,1,2,3,4] => 5
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [3,4,1,2,5,6,7,8,9] => [3,4,1,2,5,6,7,8] => 0
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Generating function
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Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,3 4,6,4 10,15,12,5 28,42,36,20,6 84,126,112,70,30,7
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 2 + 3\ q$
$F_{4} = 4 + 6\ q + 4\ q^{2}$
$F_{5} = 10 + 15\ q + 12\ q^{2} + 5\ q^{3}$
$F_{6} = 28 + 42\ q + 36\ q^{2} + 20\ q^{3} + 6\ q^{4}$
$F_{7} = 84 + 126\ q + 112\ q^{2} + 70\ q^{3} + 30\ q^{4} + 7\ q^{5}$
Description
The number of global descents of a permutation.
The global descents are the integers in the set
$$C(\pi)=\{i\in [n-1] : \forall 1 \leq j \leq i < k \leq n :\quad \pi(j) > \pi(k)\}.$$
In particular, if $i\in C(\pi)$ then $i$ is a descent.
For the number of global ascents, see St000234The number of global ascents of a permutation..
The global descents are the integers in the set
$$C(\pi)=\{i\in [n-1] : \forall 1 \leq j \leq i < k \leq n :\quad \pi(j) > \pi(k)\}.$$
In particular, if $i\in C(\pi)$ then $i$ is a descent.
For the number of global ascents, see St000234The number of global ascents of a permutation..
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.
This map is undefined for the empty permutation.
Map
to 132-avoiding permutation
Description
Return a 132-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 maximal element of the Sylvester class.
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 maximal element of the Sylvester class.
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