Identifier
-
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
St000234: Permutations ⟶ ℤ (values match St000056The decomposition (or block) number of a permutation.)
Values
[.,[.,.]] => [2,1] => [2,1] => [1] => 0
[[.,.],.] => [1,2] => [1,2] => [1] => 0
[.,[.,[.,.]]] => [3,2,1] => [3,1,2] => [1,2] => 1
[.,[[.,.],.]] => [2,3,1] => [3,2,1] => [2,1] => 0
[[.,.],[.,.]] => [1,3,2] => [1,3,2] => [1,2] => 1
[[.,[.,.]],.] => [2,1,3] => [2,1,3] => [2,1] => 0
[[[.,.],.],.] => [1,2,3] => [1,2,3] => [1,2] => 1
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [4,1,2,3] => [1,2,3] => 2
[.,[.,[[.,.],.]]] => [3,4,2,1] => [4,1,3,2] => [1,3,2] => 1
[.,[[.,.],[.,.]]] => [2,4,3,1] => [4,2,1,3] => [2,1,3] => 1
[.,[[.,[.,.]],.]] => [3,2,4,1] => [4,3,2,1] => [3,2,1] => 0
[.,[[[.,.],.],.]] => [2,3,4,1] => [4,2,3,1] => [2,3,1] => 0
[[.,.],[.,[.,.]]] => [1,4,3,2] => [1,4,2,3] => [1,2,3] => 2
[[.,.],[[.,.],.]] => [1,3,4,2] => [1,4,3,2] => [1,3,2] => 1
[[.,[.,.]],[.,.]] => [2,1,4,3] => [2,1,4,3] => [2,1,3] => 1
[[[.,.],.],[.,.]] => [1,2,4,3] => [1,2,4,3] => [1,2,3] => 2
[[.,[.,[.,.]]],.] => [3,2,1,4] => [3,1,2,4] => [3,1,2] => 0
[[.,[[.,.],.]],.] => [2,3,1,4] => [3,2,1,4] => [3,2,1] => 0
[[[.,.],[.,.]],.] => [1,3,2,4] => [1,3,2,4] => [1,3,2] => 1
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3,4] => [2,1,3] => 1
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => [1,2,3] => 2
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [5,1,2,3,4] => [1,2,3,4] => 3
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [5,1,2,4,3] => [1,2,4,3] => 2
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [5,1,3,2,4] => [1,3,2,4] => 2
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [5,1,4,3,2] => [1,4,3,2] => 1
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [5,1,3,4,2] => [1,3,4,2] => 1
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [5,2,1,3,4] => [2,1,3,4] => 2
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [5,2,1,4,3] => [2,1,4,3] => 1
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [5,3,2,1,4] => [3,2,1,4] => 1
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [5,2,3,1,4] => [2,3,1,4] => 1
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [5,4,2,3,1] => [4,2,3,1] => 0
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [5,4,3,2,1] => [4,3,2,1] => 0
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [5,2,4,3,1] => [2,4,3,1] => 0
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [5,3,2,4,1] => [3,2,4,1] => 0
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [5,2,3,4,1] => [2,3,4,1] => 0
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [1,5,2,3,4] => [1,2,3,4] => 3
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [1,5,2,4,3] => [1,2,4,3] => 2
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [1,5,3,2,4] => [1,3,2,4] => 2
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [1,5,4,3,2] => [1,4,3,2] => 1
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [1,5,3,4,2] => [1,3,4,2] => 1
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [2,1,5,3,4] => [2,1,3,4] => 2
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [2,1,5,4,3] => [2,1,4,3] => 1
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [1,2,5,3,4] => [1,2,3,4] => 3
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,4,3] => 2
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [3,1,2,5,4] => [3,1,2,4] => 1
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [3,2,1,5,4] => [3,2,1,4] => 1
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,4] => 2
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,4] => 2
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,4] => 3
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,1,2,3,5] => [4,1,2,3] => 0
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [4,1,3,2,5] => [4,1,3,2] => 0
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [4,2,1,3,5] => [4,2,1,3] => 0
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [4,3,2,1,5] => [4,3,2,1] => 0
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [4,2,3,1,5] => [4,2,3,1] => 0
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [1,4,2,3,5] => [1,4,2,3] => 1
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [1,4,3,2,5] => [1,4,3,2] => 1
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3] => 1
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3] => 2
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,1,2,4,5] => [3,1,2,4] => 1
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,4] => 1
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4] => 2
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4] => 2
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4] => 3
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [6,1,2,3,4,5] => [1,2,3,4,5] => 4
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [6,1,2,3,5,4] => [1,2,3,5,4] => 3
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [6,1,2,4,3,5] => [1,2,4,3,5] => 3
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [6,1,2,5,4,3] => [1,2,5,4,3] => 2
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [6,1,2,4,5,3] => [1,2,4,5,3] => 2
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [6,1,3,2,4,5] => [1,3,2,4,5] => 3
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [6,1,3,2,5,4] => [1,3,2,5,4] => 2
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [6,1,4,3,2,5] => [1,4,3,2,5] => 2
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [6,1,3,4,2,5] => [1,3,4,2,5] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [6,1,5,3,4,2] => [1,5,3,4,2] => 1
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [6,1,5,4,3,2] => [1,5,4,3,2] => 1
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [6,1,3,5,4,2] => [1,3,5,4,2] => 1
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [6,1,4,3,5,2] => [1,4,3,5,2] => 1
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [6,1,3,4,5,2] => [1,3,4,5,2] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [6,2,1,3,4,5] => [2,1,3,4,5] => 3
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [6,2,1,3,5,4] => [2,1,3,5,4] => 2
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [6,2,1,4,3,5] => [2,1,4,3,5] => 2
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [6,2,1,5,4,3] => [2,1,5,4,3] => 1
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [6,2,1,4,5,3] => [2,1,4,5,3] => 1
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [6,3,2,1,4,5] => [3,2,1,4,5] => 2
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [6,3,2,1,5,4] => [3,2,1,5,4] => 1
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [6,2,3,1,4,5] => [2,3,1,4,5] => 2
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [6,2,3,1,5,4] => [2,3,1,5,4] => 1
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [6,4,2,3,1,5] => [4,2,3,1,5] => 1
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [6,4,3,2,1,5] => [4,3,2,1,5] => 1
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [6,2,4,3,1,5] => [2,4,3,1,5] => 1
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [6,3,2,4,1,5] => [3,2,4,1,5] => 1
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [6,2,3,4,1,5] => [2,3,4,1,5] => 1
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [6,5,2,3,4,1] => [5,2,3,4,1] => 0
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [6,5,2,4,3,1] => [5,2,4,3,1] => 0
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [6,5,3,2,4,1] => [5,3,2,4,1] => 0
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => 0
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [6,5,3,4,2,1] => [5,3,4,2,1] => 0
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [6,2,5,3,4,1] => [2,5,3,4,1] => 0
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [6,2,5,4,3,1] => [2,5,4,3,1] => 0
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [6,3,2,5,4,1] => [3,2,5,4,1] => 0
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [6,2,3,5,4,1] => [2,3,5,4,1] => 0
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [6,4,2,3,5,1] => [4,2,3,5,1] => 0
>>> Load all 853 entries. <<<[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [6,4,3,2,5,1] => [4,3,2,5,1] => 0
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [6,2,4,3,5,1] => [2,4,3,5,1] => 0
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [6,3,2,4,5,1] => [3,2,4,5,1] => 0
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [2,3,4,5,1] => 0
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [1,6,2,3,4,5] => [1,2,3,4,5] => 4
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [1,6,2,3,5,4] => [1,2,3,5,4] => 3
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [1,6,2,4,3,5] => [1,2,4,3,5] => 3
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [1,6,2,5,4,3] => [1,2,5,4,3] => 2
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [1,6,2,4,5,3] => [1,2,4,5,3] => 2
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [1,6,3,2,4,5] => [1,3,2,4,5] => 3
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [1,6,3,2,5,4] => [1,3,2,5,4] => 2
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [1,6,4,3,2,5] => [1,4,3,2,5] => 2
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [1,6,3,4,2,5] => [1,3,4,2,5] => 2
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [1,6,5,3,4,2] => [1,5,3,4,2] => 1
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [1,6,5,4,3,2] => [1,5,4,3,2] => 1
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [1,6,3,5,4,2] => [1,3,5,4,2] => 1
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [1,6,4,3,5,2] => [1,4,3,5,2] => 1
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [1,3,4,5,2] => 1
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [2,1,6,3,4,5] => [2,1,3,4,5] => 3
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [2,1,6,3,5,4] => [2,1,3,5,4] => 2
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [2,1,6,4,3,5] => [2,1,4,3,5] => 2
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [2,1,6,5,4,3] => [2,1,5,4,3] => 1
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [2,1,4,5,3] => 1
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [1,2,6,3,4,5] => [1,2,3,4,5] => 4
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [1,2,6,3,5,4] => [1,2,3,5,4] => 3
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [1,2,6,4,3,5] => [1,2,4,3,5] => 3
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [1,2,6,5,4,3] => [1,2,5,4,3] => 2
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [1,2,4,5,3] => 2
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [3,1,2,6,4,5] => [3,1,2,4,5] => 2
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [3,1,2,6,5,4] => [3,1,2,5,4] => 1
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [3,2,1,6,4,5] => [3,2,1,4,5] => 2
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [3,2,1,5,4] => 1
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [1,3,2,6,4,5] => [1,3,2,4,5] => 3
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,3,2,5,4] => 2
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [2,1,3,6,4,5] => [2,1,3,4,5] => 3
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [2,1,3,5,4] => 2
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [1,2,3,6,4,5] => [1,2,3,4,5] => 4
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,5,4] => 3
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [4,1,2,3,6,5] => [4,1,2,3,5] => 1
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [4,1,3,2,6,5] => [4,1,3,2,5] => 1
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [4,2,1,3,6,5] => [4,2,1,3,5] => 1
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,5] => 1
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [4,2,3,1,5] => 1
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [1,4,2,3,6,5] => [1,4,2,3,5] => 2
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,5] => 2
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,5] => 2
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,5] => 3
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [3,1,2,4,6,5] => [3,1,2,4,5] => 2
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,5] => 2
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,5] => 3
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,5] => 3
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,5] => 4
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [5,1,2,3,4,6] => [5,1,2,3,4] => 0
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [5,1,2,4,3,6] => [5,1,2,4,3] => 0
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [5,1,3,2,4,6] => [5,1,3,2,4] => 0
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [5,1,4,3,2,6] => [5,1,4,3,2] => 0
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [5,1,3,4,2,6] => [5,1,3,4,2] => 0
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [5,2,1,3,4,6] => [5,2,1,3,4] => 0
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [5,2,1,4,3,6] => [5,2,1,4,3] => 0
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [5,3,2,1,4,6] => [5,3,2,1,4] => 0
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [5,2,3,1,4,6] => [5,2,3,1,4] => 0
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [5,4,2,3,1,6] => [5,4,2,3,1] => 0
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1] => 0
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [5,2,4,3,1,6] => [5,2,4,3,1] => 0
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [5,3,2,4,1,6] => [5,3,2,4,1] => 0
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [5,2,3,4,1] => 0
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [1,5,2,3,4,6] => [1,5,2,3,4] => 1
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [1,5,2,4,3,6] => [1,5,2,4,3] => 1
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [1,5,3,2,4,6] => [1,5,3,2,4] => 1
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2] => 1
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,5,3,4,2] => 1
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [2,1,5,3,4,6] => [2,1,5,3,4] => 1
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3] => 1
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [1,2,5,3,4,6] => [1,2,5,3,4] => 2
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3] => 2
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [3,1,2,5,4,6] => [3,1,2,5,4] => 1
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4] => 1
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4] => 2
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4] => 2
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4] => 3
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [4,1,2,3,5,6] => [4,1,2,3,5] => 1
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [4,1,3,2,5,6] => [4,1,3,2,5] => 1
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [4,2,1,3,5,6] => [4,2,1,3,5] => 1
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5] => 1
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [4,2,3,1,5] => 1
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [1,4,2,3,5,6] => [1,4,2,3,5] => 2
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5] => 2
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5] => 2
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5] => 3
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [3,1,2,4,5,6] => [3,1,2,4,5] => 2
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5] => 2
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5] => 3
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5] => 3
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5] => 4
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [7,1,2,3,4,5,6] => [1,2,3,4,5,6] => 5
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [7,1,2,3,4,6,5] => [1,2,3,4,6,5] => 4
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => [7,1,2,3,5,4,6] => [1,2,3,5,4,6] => 4
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [7,1,2,3,6,5,4] => [1,2,3,6,5,4] => 3
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [7,1,2,3,5,6,4] => [1,2,3,5,6,4] => 3
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [7,1,2,4,3,5,6] => [1,2,4,3,5,6] => 4
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => [7,1,2,4,3,6,5] => [1,2,4,3,6,5] => 3
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => [7,1,2,5,4,3,6] => [1,2,5,4,3,6] => 3
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [7,1,2,4,5,3,6] => [1,2,4,5,3,6] => 3
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [7,1,2,6,4,5,3] => [1,2,6,4,5,3] => 2
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [7,1,2,6,5,4,3] => [1,2,6,5,4,3] => 2
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => [7,1,2,4,6,5,3] => [1,2,4,6,5,3] => 2
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [7,1,2,5,4,6,3] => [1,2,5,4,6,3] => 2
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [7,1,2,4,5,6,3] => [1,2,4,5,6,3] => 2
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [7,1,3,2,4,5,6] => [1,3,2,4,5,6] => 4
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => [7,1,3,2,4,6,5] => [1,3,2,4,6,5] => 3
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => [7,1,3,2,5,4,6] => [1,3,2,5,4,6] => 3
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => [7,1,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [7,1,3,2,5,6,4] => [1,3,2,5,6,4] => 2
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [7,1,4,3,2,5,6] => [1,4,3,2,5,6] => 3
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => [7,1,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [7,1,3,4,2,5,6] => [1,3,4,2,5,6] => 3
[.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => [7,1,3,4,2,6,5] => [1,3,4,2,6,5] => 2
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => [7,1,5,3,4,2,6] => [1,5,3,4,2,6] => 2
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => [7,1,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => [7,1,3,5,4,2,6] => [1,3,5,4,2,6] => 2
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => [7,1,4,3,5,2,6] => [1,4,3,5,2,6] => 2
[.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => [7,1,3,4,5,2,6] => [1,3,4,5,2,6] => 2
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [7,1,6,3,4,5,2] => [1,6,3,4,5,2] => 1
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [7,1,6,3,5,4,2] => [1,6,3,5,4,2] => 1
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => [7,1,6,4,3,5,2] => [1,6,4,3,5,2] => 1
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [7,1,6,5,4,3,2] => [1,6,5,4,3,2] => 1
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [7,1,6,4,5,3,2] => [1,6,4,5,3,2] => 1
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [7,1,3,6,4,5,2] => [1,3,6,4,5,2] => 1
[.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => [7,1,3,6,5,4,2] => [1,3,6,5,4,2] => 1
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => [7,1,4,3,6,5,2] => [1,4,3,6,5,2] => 1
[.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => [7,1,3,4,6,5,2] => [1,3,4,6,5,2] => 1
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [7,1,5,3,4,6,2] => [1,5,3,4,6,2] => 1
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [7,1,5,4,3,6,2] => [1,5,4,3,6,2] => 1
[.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => [7,1,3,5,4,6,2] => [1,3,5,4,6,2] => 1
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [7,1,4,3,5,6,2] => [1,4,3,5,6,2] => 1
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [7,1,3,4,5,6,2] => [1,3,4,5,6,2] => 1
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [7,2,1,3,4,5,6] => [2,1,3,4,5,6] => 4
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => [7,2,1,3,4,6,5] => [2,1,3,4,6,5] => 3
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => [7,2,1,3,5,4,6] => [2,1,3,5,4,6] => 3
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => [7,2,1,3,6,5,4] => [2,1,3,6,5,4] => 2
[.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => [7,2,1,3,5,6,4] => [2,1,3,5,6,4] => 2
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => [7,2,1,4,3,5,6] => [2,1,4,3,5,6] => 3
[.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => [7,2,1,4,3,6,5] => [2,1,4,3,6,5] => 2
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => [7,2,1,5,4,3,6] => [2,1,5,4,3,6] => 2
[.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => [7,2,1,4,5,3,6] => [2,1,4,5,3,6] => 2
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => [7,2,1,6,4,5,3] => [2,1,6,4,5,3] => 1
[.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => [7,2,1,6,5,4,3] => [2,1,6,5,4,3] => 1
[.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => [7,2,1,4,6,5,3] => [2,1,4,6,5,3] => 1
[.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => [7,2,1,5,4,6,3] => [2,1,5,4,6,3] => 1
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => [7,2,1,4,5,6,3] => [2,1,4,5,6,3] => 1
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [7,3,2,1,4,5,6] => [3,2,1,4,5,6] => 3
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => [7,3,2,1,4,6,5] => [3,2,1,4,6,5] => 2
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => [7,3,2,1,5,4,6] => [3,2,1,5,4,6] => 2
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => [7,3,2,1,6,5,4] => [3,2,1,6,5,4] => 1
[.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => [7,3,2,1,5,6,4] => [3,2,1,5,6,4] => 1
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [7,2,3,1,4,5,6] => [2,3,1,4,5,6] => 3
[.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => [7,2,3,1,4,6,5] => [2,3,1,4,6,5] => 2
[.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => [7,2,3,1,5,4,6] => [2,3,1,5,4,6] => 2
[.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => [7,2,3,1,6,5,4] => [2,3,1,6,5,4] => 1
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => [7,2,3,1,5,6,4] => [2,3,1,5,6,4] => 1
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => [7,4,2,3,1,5,6] => [4,2,3,1,5,6] => 2
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => [7,4,2,3,1,6,5] => [4,2,3,1,6,5] => 1
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => [7,4,3,2,1,5,6] => [4,3,2,1,5,6] => 2
[.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => [7,4,3,2,1,6,5] => [4,3,2,1,6,5] => 1
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => [7,2,4,3,1,5,6] => [2,4,3,1,5,6] => 2
[.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => [7,2,4,3,1,6,5] => [2,4,3,1,6,5] => 1
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => [7,3,2,4,1,5,6] => [3,2,4,1,5,6] => 2
[.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => [7,3,2,4,1,6,5] => [3,2,4,1,6,5] => 1
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [7,2,3,4,1,5,6] => [2,3,4,1,5,6] => 2
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [7,2,3,4,1,6,5] => [2,3,4,1,6,5] => 1
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => [7,5,2,3,4,1,6] => [5,2,3,4,1,6] => 1
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => [7,5,2,4,3,1,6] => [5,2,4,3,1,6] => 1
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => [7,5,3,2,4,1,6] => [5,3,2,4,1,6] => 1
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => [7,5,4,3,2,1,6] => [5,4,3,2,1,6] => 1
[.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => [7,5,3,4,2,1,6] => [5,3,4,2,1,6] => 1
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => [7,2,5,3,4,1,6] => [2,5,3,4,1,6] => 1
[.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => [7,2,5,4,3,1,6] => [2,5,4,3,1,6] => 1
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => [7,3,2,5,4,1,6] => [3,2,5,4,1,6] => 1
[.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => [7,2,3,5,4,1,6] => [2,3,5,4,1,6] => 1
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => [7,4,2,3,5,1,6] => [4,2,3,5,1,6] => 1
[.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => [7,4,3,2,5,1,6] => [4,3,2,5,1,6] => 1
[.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => [7,2,4,3,5,1,6] => [2,4,3,5,1,6] => 1
[.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => [7,3,2,4,5,1,6] => [3,2,4,5,1,6] => 1
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [7,2,3,4,5,1,6] => [2,3,4,5,1,6] => 1
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [7,6,2,3,4,5,1] => [6,2,3,4,5,1] => 0
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [7,6,2,3,5,4,1] => [6,2,3,5,4,1] => 0
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => [7,6,2,4,3,5,1] => [6,2,4,3,5,1] => 0
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [7,6,2,5,4,3,1] => [6,2,5,4,3,1] => 0
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [7,6,2,4,5,3,1] => [6,2,4,5,3,1] => 0
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => [7,6,3,2,4,5,1] => [6,3,2,4,5,1] => 0
[.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => [7,6,3,2,5,4,1] => [6,3,2,5,4,1] => 0
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => [7,6,4,3,2,5,1] => [6,4,3,2,5,1] => 0
[.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => [7,6,3,4,2,5,1] => [6,3,4,2,5,1] => 0
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [7,6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => [7,6,3,5,4,2,1] => [6,3,5,4,2,1] => 0
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [7,6,4,3,5,2,1] => [6,4,3,5,2,1] => 0
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [7,6,3,4,5,2,1] => [6,3,4,5,2,1] => 0
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => [7,2,6,3,4,5,1] => [2,6,3,4,5,1] => 0
[.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => [7,2,6,3,5,4,1] => [2,6,3,5,4,1] => 0
[.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => [7,2,6,4,3,5,1] => [2,6,4,3,5,1] => 0
[.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => [7,2,6,5,4,3,1] => [2,6,5,4,3,1] => 0
[.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => [7,2,6,4,5,3,1] => [2,6,4,5,3,1] => 0
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => [7,3,2,6,4,5,1] => [3,2,6,4,5,1] => 0
[.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => [7,3,2,6,5,4,1] => [3,2,6,5,4,1] => 0
[.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [7,2,3,6,4,5,1] => [2,3,6,4,5,1] => 0
[.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => [7,2,3,6,5,4,1] => [2,3,6,5,4,1] => 0
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => [7,4,2,3,6,5,1] => [4,2,3,6,5,1] => 0
[.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => [7,4,3,2,6,5,1] => [4,3,2,6,5,1] => 0
[.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => [7,2,4,3,6,5,1] => [2,4,3,6,5,1] => 0
[.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => [7,3,2,4,6,5,1] => [3,2,4,6,5,1] => 0
[.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => [7,2,3,4,6,5,1] => [2,3,4,6,5,1] => 0
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [7,5,2,3,4,6,1] => [5,2,3,4,6,1] => 0
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [7,5,2,4,3,6,1] => [5,2,4,3,6,1] => 0
[.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => [7,5,3,2,4,6,1] => [5,3,2,4,6,1] => 0
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [7,5,4,3,2,6,1] => [5,4,3,2,6,1] => 0
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [7,5,3,4,2,6,1] => [5,3,4,2,6,1] => 0
[.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => [7,2,5,3,4,6,1] => [2,5,3,4,6,1] => 0
[.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => [7,2,5,4,3,6,1] => [2,5,4,3,6,1] => 0
[.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => [7,3,2,5,4,6,1] => [3,2,5,4,6,1] => 0
[.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [7,2,3,5,4,6,1] => [2,3,5,4,6,1] => 0
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [7,4,2,3,5,6,1] => [4,2,3,5,6,1] => 0
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [7,4,3,2,5,6,1] => [4,3,2,5,6,1] => 0
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [7,2,4,3,5,6,1] => [2,4,3,5,6,1] => 0
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [7,3,2,4,5,6,1] => [3,2,4,5,6,1] => 0
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [2,3,4,5,6,1] => 0
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [1,7,2,3,4,5,6] => [1,2,3,4,5,6] => 5
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => [1,7,2,3,4,6,5] => [1,2,3,4,6,5] => 4
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => [1,7,2,3,5,4,6] => [1,2,3,5,4,6] => 4
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => [1,7,2,3,6,5,4] => [1,2,3,6,5,4] => 3
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => [1,7,2,3,5,6,4] => [1,2,3,5,6,4] => 3
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [1,7,2,4,3,5,6] => [1,2,4,3,5,6] => 4
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => [1,7,2,4,3,6,5] => [1,2,4,3,6,5] => 3
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => [1,7,2,5,4,3,6] => [1,2,5,4,3,6] => 3
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => [1,7,2,4,5,3,6] => [1,2,4,5,3,6] => 3
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => [1,7,2,6,4,5,3] => [1,2,6,4,5,3] => 2
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => [1,7,2,6,5,4,3] => [1,2,6,5,4,3] => 2
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => [1,7,2,4,6,5,3] => [1,2,4,6,5,3] => 2
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => [1,7,2,5,4,6,3] => [1,2,5,4,6,3] => 2
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => [1,7,2,4,5,6,3] => [1,2,4,5,6,3] => 2
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [1,7,3,2,4,5,6] => [1,3,2,4,5,6] => 4
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => [1,7,3,2,4,6,5] => [1,3,2,4,6,5] => 3
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [1,7,3,2,5,4,6] => [1,3,2,5,4,6] => 3
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => [1,7,3,2,6,5,4] => [1,3,2,6,5,4] => 2
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => [1,7,3,2,5,6,4] => [1,3,2,5,6,4] => 2
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => [1,7,4,3,2,5,6] => [1,4,3,2,5,6] => 3
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => [1,7,4,3,2,6,5] => [1,4,3,2,6,5] => 2
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [1,7,3,4,2,5,6] => [1,3,4,2,5,6] => 3
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => [1,7,3,4,2,6,5] => [1,3,4,2,6,5] => 2
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => [1,7,5,3,4,2,6] => [1,5,3,4,2,6] => 2
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [1,7,5,4,3,2,6] => [1,5,4,3,2,6] => 2
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => [1,7,3,5,4,2,6] => [1,3,5,4,2,6] => 2
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => [1,7,4,3,5,2,6] => [1,4,3,5,2,6] => 2
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => [1,7,3,4,5,2,6] => [1,3,4,5,2,6] => 2
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => [1,7,6,3,4,5,2] => [1,6,3,4,5,2] => 1
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => [1,7,6,3,5,4,2] => [1,6,3,5,4,2] => 1
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => [1,7,6,4,3,5,2] => [1,6,4,3,5,2] => 1
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => [1,7,6,5,4,3,2] => [1,6,5,4,3,2] => 1
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => [1,7,6,4,5,3,2] => [1,6,4,5,3,2] => 1
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => [1,7,3,6,4,5,2] => [1,3,6,4,5,2] => 1
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => [1,7,3,6,5,4,2] => [1,3,6,5,4,2] => 1
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => [1,7,4,3,6,5,2] => [1,4,3,6,5,2] => 1
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => [1,7,3,4,6,5,2] => [1,3,4,6,5,2] => 1
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => [1,7,5,3,4,6,2] => [1,5,3,4,6,2] => 1
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => [1,7,5,4,3,6,2] => [1,5,4,3,6,2] => 1
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => [1,7,3,5,4,6,2] => [1,3,5,4,6,2] => 1
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => [1,7,4,3,5,6,2] => [1,4,3,5,6,2] => 1
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [1,3,4,5,6,2] => 1
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [2,1,7,3,4,5,6] => [2,1,3,4,5,6] => 4
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => [2,1,7,3,4,6,5] => [2,1,3,4,6,5] => 3
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => [2,1,7,3,5,4,6] => [2,1,3,5,4,6] => 3
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => [2,1,7,3,6,5,4] => [2,1,3,6,5,4] => 2
[[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => [2,1,7,3,5,6,4] => [2,1,3,5,6,4] => 2
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => [2,1,7,4,3,5,6] => [2,1,4,3,5,6] => 3
[[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => [2,1,7,4,3,6,5] => [2,1,4,3,6,5] => 2
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => [2,1,7,5,4,3,6] => [2,1,5,4,3,6] => 2
[[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => [2,1,7,4,5,3,6] => [2,1,4,5,3,6] => 2
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => [2,1,7,6,4,5,3] => [2,1,6,4,5,3] => 1
[[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => [2,1,7,6,5,4,3] => [2,1,6,5,4,3] => 1
[[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => [2,1,7,4,6,5,3] => [2,1,4,6,5,3] => 1
[[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => [2,1,7,5,4,6,3] => [2,1,5,4,6,3] => 1
[[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [2,1,4,5,6,3] => 1
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [1,2,7,3,4,5,6] => [1,2,3,4,5,6] => 5
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => [1,2,7,3,4,6,5] => [1,2,3,4,6,5] => 4
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => [1,2,7,3,5,4,6] => [1,2,3,5,4,6] => 4
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => [1,2,7,3,6,5,4] => [1,2,3,6,5,4] => 3
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => [1,2,7,3,5,6,4] => [1,2,3,5,6,4] => 3
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => [1,2,7,4,3,5,6] => [1,2,4,3,5,6] => 4
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => [1,2,7,4,3,6,5] => [1,2,4,3,6,5] => 3
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => [1,2,7,5,4,3,6] => [1,2,5,4,3,6] => 3
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => [1,2,7,4,5,3,6] => [1,2,4,5,3,6] => 3
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => [1,2,7,6,4,5,3] => [1,2,6,4,5,3] => 2
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => [1,2,7,6,5,4,3] => [1,2,6,5,4,3] => 2
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => [1,2,7,4,6,5,3] => [1,2,4,6,5,3] => 2
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => [1,2,7,5,4,6,3] => [1,2,5,4,6,3] => 2
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [1,2,4,5,6,3] => 2
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => [3,1,2,7,4,5,6] => [3,1,2,4,5,6] => 3
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => [3,1,2,7,4,6,5] => [3,1,2,4,6,5] => 2
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => [3,1,2,7,5,4,6] => [3,1,2,5,4,6] => 2
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => [3,1,2,7,6,5,4] => [3,1,2,6,5,4] => 1
[[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => [3,1,2,7,5,6,4] => [3,1,2,5,6,4] => 1
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => [3,2,1,7,4,5,6] => [3,2,1,4,5,6] => 3
[[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => [3,2,1,7,4,6,5] => [3,2,1,4,6,5] => 2
[[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => [3,2,1,7,5,4,6] => [3,2,1,5,4,6] => 2
[[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => [3,2,1,7,6,5,4] => [3,2,1,6,5,4] => 1
[[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [3,2,1,5,6,4] => 1
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [1,3,2,7,4,5,6] => [1,3,2,4,5,6] => 4
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => [1,3,2,7,4,6,5] => [1,3,2,4,6,5] => 3
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => [1,3,2,7,5,4,6] => [1,3,2,5,4,6] => 3
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => [1,3,2,7,6,5,4] => [1,3,2,6,5,4] => 2
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [1,3,2,5,6,4] => 2
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => [2,1,3,7,4,5,6] => [2,1,3,4,5,6] => 4
[[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => [2,1,3,7,4,6,5] => [2,1,3,4,6,5] => 3
[[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => [2,1,3,7,5,4,6] => [2,1,3,5,4,6] => 3
[[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => [2,1,3,7,6,5,4] => [2,1,3,6,5,4] => 2
[[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [2,1,3,5,6,4] => 2
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [1,2,3,7,4,5,6] => [1,2,3,4,5,6] => 5
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => [1,2,3,7,4,6,5] => [1,2,3,4,6,5] => 4
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => [1,2,3,7,5,4,6] => [1,2,3,5,4,6] => 4
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => [1,2,3,7,6,5,4] => [1,2,3,6,5,4] => 3
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [1,2,3,5,6,4] => 3
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => [4,1,2,3,7,5,6] => [4,1,2,3,5,6] => 2
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => [4,1,2,3,7,6,5] => [4,1,2,3,6,5] => 1
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => [4,1,3,2,7,5,6] => [4,1,3,2,5,6] => 2
[[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => [4,1,3,2,7,6,5] => [4,1,3,2,6,5] => 1
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => [4,2,1,3,7,5,6] => [4,2,1,3,5,6] => 2
[[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => [4,2,1,3,7,6,5] => [4,2,1,3,6,5] => 1
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => [4,3,2,1,7,5,6] => [4,3,2,1,5,6] => 2
[[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => [4,3,2,1,7,6,5] => [4,3,2,1,6,5] => 1
[[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => [4,2,3,1,7,5,6] => [4,2,3,1,5,6] => 2
[[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [4,2,3,1,6,5] => 1
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [1,4,2,3,7,5,6] => [1,4,2,3,5,6] => 3
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => [1,4,2,3,7,6,5] => [1,4,2,3,6,5] => 2
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => [1,4,3,2,7,5,6] => [1,4,3,2,5,6] => 3
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [1,4,3,2,6,5] => 2
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => [2,1,4,3,7,5,6] => [2,1,4,3,5,6] => 3
[[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [2,1,4,3,6,5] => 2
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [1,2,4,3,7,5,6] => [1,2,4,3,5,6] => 4
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [1,2,4,3,6,5] => 3
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => [3,1,2,4,7,5,6] => [3,1,2,4,5,6] => 3
[[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => [3,1,2,4,7,6,5] => [3,1,2,4,6,5] => 2
[[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => [3,2,1,4,7,5,6] => [3,2,1,4,5,6] => 3
[[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [3,2,1,4,6,5] => 2
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [1,3,2,4,7,5,6] => [1,3,2,4,5,6] => 4
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [1,3,2,4,6,5] => 3
[[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => [2,1,3,4,7,5,6] => [2,1,3,4,5,6] => 4
[[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [2,1,3,4,6,5] => 3
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [1,2,3,4,7,5,6] => [1,2,3,4,5,6] => 5
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [1,2,3,4,6,5] => 4
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => [5,1,2,3,4,7,6] => [5,1,2,3,4,6] => 1
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => [5,1,2,4,3,7,6] => [5,1,2,4,3,6] => 1
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => [5,1,3,2,4,7,6] => [5,1,3,2,4,6] => 1
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => [5,1,4,3,2,7,6] => [5,1,4,3,2,6] => 1
[[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => [5,1,3,4,2,7,6] => [5,1,3,4,2,6] => 1
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => [5,2,1,3,4,7,6] => [5,2,1,3,4,6] => 1
[[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => [5,2,1,4,3,7,6] => [5,2,1,4,3,6] => 1
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => [5,3,2,1,4,7,6] => [5,3,2,1,4,6] => 1
[[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => [5,2,3,1,4,7,6] => [5,2,3,1,4,6] => 1
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => [5,4,2,3,1,7,6] => [5,4,2,3,1,6] => 1
[[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => [5,4,3,2,1,7,6] => [5,4,3,2,1,6] => 1
[[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => [5,2,4,3,1,7,6] => [5,2,4,3,1,6] => 1
[[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => [5,3,2,4,1,7,6] => [5,3,2,4,1,6] => 1
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [5,2,3,4,1,6] => 1
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => [1,5,2,3,4,7,6] => [1,5,2,3,4,6] => 2
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => [1,5,2,4,3,7,6] => [1,5,2,4,3,6] => 2
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => [1,5,3,2,4,7,6] => [1,5,3,2,4,6] => 2
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => [1,5,4,3,2,7,6] => [1,5,4,3,2,6] => 2
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [1,5,3,4,2,6] => 2
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => [2,1,5,3,4,7,6] => [2,1,5,3,4,6] => 2
[[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [2,1,5,4,3,6] => 2
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [1,2,5,3,4,7,6] => [1,2,5,3,4,6] => 3
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,6] => 3
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => [3,1,2,5,4,7,6] => [3,1,2,5,4,6] => 2
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [3,2,1,5,4,6] => 2
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,3,2,5,4,6] => 3
[[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [2,1,3,5,4,6] => 3
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,2,3,5,4,6] => 4
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => [4,1,2,3,5,7,6] => [4,1,2,3,5,6] => 2
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => [4,1,3,2,5,7,6] => [4,1,3,2,5,6] => 2
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => [4,2,1,3,5,7,6] => [4,2,1,3,5,6] => 2
[[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => [4,3,2,1,5,7,6] => [4,3,2,1,5,6] => 2
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [4,2,3,1,5,6] => 2
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [1,4,2,3,5,7,6] => [1,4,2,3,5,6] => 3
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [1,4,3,2,5,6] => 3
[[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [2,1,4,3,5,6] => 3
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,2,4,3,5,6] => 4
[[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => [3,1,2,4,5,7,6] => [3,1,2,4,5,6] => 3
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [3,2,1,4,5,6] => 3
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,3,2,4,5,6] => 4
[[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [2,1,3,4,5,6] => 4
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,6] => 5
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5] => 0
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [6,1,2,3,5,4,7] => [6,1,2,3,5,4] => 0
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => [6,1,2,4,3,5,7] => [6,1,2,4,3,5] => 0
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [6,1,2,5,4,3,7] => [6,1,2,5,4,3] => 0
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [6,1,2,4,5,3,7] => [6,1,2,4,5,3] => 0
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => [6,1,3,2,4,5,7] => [6,1,3,2,4,5] => 0
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => [6,1,3,2,5,4,7] => [6,1,3,2,5,4] => 0
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => [6,1,4,3,2,5,7] => [6,1,4,3,2,5] => 0
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [6,1,3,4,2,5,7] => [6,1,3,4,2,5] => 0
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [6,1,5,3,4,2,7] => [6,1,5,3,4,2] => 0
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [6,1,5,4,3,2,7] => [6,1,5,4,3,2] => 0
[[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [6,1,3,5,4,2,7] => [6,1,3,5,4,2] => 0
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [6,1,4,3,5,2,7] => [6,1,4,3,5,2] => 0
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [6,1,3,4,5,2,7] => [6,1,3,4,5,2] => 0
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => [6,2,1,3,4,5,7] => [6,2,1,3,4,5] => 0
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => [6,2,1,3,5,4,7] => [6,2,1,3,5,4] => 0
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [6,2,1,4,3,5,7] => [6,2,1,4,3,5] => 0
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => [6,2,1,5,4,3,7] => [6,2,1,5,4,3] => 0
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => [6,2,1,4,5,3,7] => [6,2,1,4,5,3] => 0
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => [6,3,2,1,4,5,7] => [6,3,2,1,4,5] => 0
[[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => [6,3,2,1,5,4,7] => [6,3,2,1,5,4] => 0
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [6,2,3,1,4,5,7] => [6,2,3,1,4,5] => 0
[[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => [6,2,3,1,5,4,7] => [6,2,3,1,5,4] => 0
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => [6,4,2,3,1,5,7] => [6,4,2,3,1,5] => 0
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [6,4,3,2,1,5,7] => [6,4,3,2,1,5] => 0
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => [6,2,4,3,1,5,7] => [6,2,4,3,1,5] => 0
[[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => [6,3,2,4,1,5,7] => [6,3,2,4,1,5] => 0
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [6,2,3,4,1,5,7] => [6,2,3,4,1,5] => 0
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [6,5,2,3,4,1,7] => [6,5,2,3,4,1] => 0
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [6,5,2,4,3,1,7] => [6,5,2,4,3,1] => 0
[[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => [6,5,3,2,4,1,7] => [6,5,3,2,4,1] => 0
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1] => 0
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [6,5,3,4,2,1,7] => [6,5,3,4,2,1] => 0
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [6,2,5,3,4,1,7] => [6,2,5,3,4,1] => 0
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => [6,2,5,4,3,1,7] => [6,2,5,4,3,1] => 0
[[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => [6,3,2,5,4,1,7] => [6,3,2,5,4,1] => 0
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [6,2,3,5,4,1,7] => [6,2,3,5,4,1] => 0
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [6,4,2,3,5,1,7] => [6,4,2,3,5,1] => 0
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [6,4,3,2,5,1,7] => [6,4,3,2,5,1] => 0
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [6,2,4,3,5,1,7] => [6,2,4,3,5,1] => 0
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [6,3,2,4,5,1,7] => [6,3,2,4,5,1] => 0
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [6,2,3,4,5,1] => 0
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => [1,6,2,3,4,5,7] => [1,6,2,3,4,5] => 1
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => [1,6,2,3,5,4,7] => [1,6,2,3,5,4] => 1
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [1,6,2,4,3,5,7] => [1,6,2,4,3,5] => 1
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => [1,6,2,5,4,3,7] => [1,6,2,5,4,3] => 1
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [1,6,2,4,5,3,7] => [1,6,2,4,5,3] => 1
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [1,6,3,2,4,5,7] => [1,6,3,2,4,5] => 1
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [1,6,3,2,5,4,7] => [1,6,3,2,5,4] => 1
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [1,6,4,3,2,5,7] => [1,6,4,3,2,5] => 1
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [1,6,3,4,2,5,7] => [1,6,3,4,2,5] => 1
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [1,6,5,3,4,2,7] => [1,6,5,3,4,2] => 1
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2] => 1
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [1,6,3,5,4,2,7] => [1,6,3,5,4,2] => 1
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [1,6,4,3,5,2,7] => [1,6,4,3,5,2] => 1
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [1,6,3,4,5,2] => 1
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => [2,1,6,3,4,5,7] => [2,1,6,3,4,5] => 1
[[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => [2,1,6,3,5,4,7] => [2,1,6,3,5,4] => 1
[[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => [2,1,6,4,3,5,7] => [2,1,6,4,3,5] => 1
[[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3] => 1
[[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [2,1,6,4,5,3] => 1
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [1,2,6,3,4,5,7] => [1,2,6,3,4,5] => 2
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [1,2,6,3,5,4,7] => [1,2,6,3,5,4] => 2
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [1,2,6,4,3,5,7] => [1,2,6,4,3,5] => 2
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3] => 2
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [1,2,6,4,5,3] => 2
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => [3,1,2,6,4,5,7] => [3,1,2,6,4,5] => 1
[[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => [3,1,2,6,5,4,7] => [3,1,2,6,5,4] => 1
[[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => [3,2,1,6,4,5,7] => [3,2,1,6,4,5] => 1
[[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4] => 1
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [1,3,2,6,4,5,7] => [1,3,2,6,4,5] => 2
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4] => 2
[[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => [2,1,3,6,4,5,7] => [2,1,3,6,4,5] => 2
[[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [2,1,3,6,5,4] => 2
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [1,2,3,6,4,5,7] => [1,2,3,6,4,5] => 3
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4] => 3
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => [4,1,2,3,6,5,7] => [4,1,2,3,6,5] => 1
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => [4,1,3,2,6,5,7] => [4,1,3,2,6,5] => 1
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => [4,2,1,3,6,5,7] => [4,2,1,3,6,5] => 1
[[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5] => 1
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [4,2,3,1,6,5] => 1
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [1,4,2,3,6,5,7] => [1,4,2,3,6,5] => 2
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5] => 2
[[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5] => 2
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5] => 3
[[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => [3,1,2,4,6,5,7] => [3,1,2,4,6,5] => 2
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [3,2,1,4,6,5] => 2
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5] => 3
[[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5] => 3
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5] => 4
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6] => 1
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [5,1,2,4,3,6,7] => [5,1,2,4,3,6] => 1
[[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => [5,1,3,2,4,6,7] => [5,1,3,2,4,6] => 1
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [5,1,4,3,2,6,7] => [5,1,4,3,2,6] => 1
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [5,1,3,4,2,6,7] => [5,1,3,4,2,6] => 1
[[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => [5,2,1,3,4,6,7] => [5,2,1,3,4,6] => 1
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => [5,2,1,4,3,6,7] => [5,2,1,4,3,6] => 1
[[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => [5,3,2,1,4,6,7] => [5,3,2,1,4,6] => 1
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [5,2,3,1,4,6,7] => [5,2,3,1,4,6] => 1
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [5,4,2,3,1,6,7] => [5,4,2,3,1,6] => 1
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6] => 1
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [5,2,4,3,1,6,7] => [5,2,4,3,1,6] => 1
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [5,3,2,4,1,6,7] => [5,3,2,4,1,6] => 1
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [5,2,3,4,1,6] => 1
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => [1,5,2,3,4,6,7] => [1,5,2,3,4,6] => 2
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [1,5,2,4,3,6,7] => [1,5,2,4,3,6] => 2
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [1,5,3,2,4,6,7] => [1,5,3,2,4,6] => 2
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6] => 2
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [1,5,3,4,2,6] => 2
[[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => [2,1,5,3,4,6,7] => [2,1,5,3,4,6] => 2
[[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [2,1,5,4,3,6] => 2
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [1,2,5,3,4,6,7] => [1,2,5,3,4,6] => 3
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6] => 3
[[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => [3,1,2,5,4,6,7] => [3,1,2,5,4,6] => 2
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [3,2,1,5,4,6] => 2
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6] => 3
[[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6] => 3
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6] => 4
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6] => 2
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [4,1,3,2,5,6,7] => [4,1,3,2,5,6] => 2
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [4,2,1,3,5,6,7] => [4,2,1,3,5,6] => 2
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6] => 2
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [4,2,3,1,5,6] => 2
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [1,4,2,3,5,6,7] => [1,4,2,3,5,6] => 3
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6] => 3
[[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6] => 3
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6] => 4
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6] => 3
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6] => 3
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6] => 4
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6] => 4
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6] => 5
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 6
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [8,1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 5
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [8,1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => 4
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => [8,1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => 4
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [8,1,2,3,7,5,6,4] => [1,2,3,7,5,6,4] => 3
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => [8,1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => 3
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [5,7,6,8,4,3,2,1] => [8,1,2,3,5,7,6,4] => [1,2,3,5,7,6,4] => 3
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [8,1,2,3,6,5,7,4] => [1,2,3,6,5,7,4] => 3
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [8,1,2,3,5,6,7,4] => [1,2,3,5,6,7,4] => 3
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [4,6,8,7,5,3,2,1] => [8,1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => 4
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [4,7,6,8,5,3,2,1] => [8,1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => 3
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [5,6,4,8,7,3,2,1] => [8,1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => 3
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [4,5,6,8,7,3,2,1] => [8,1,2,4,5,6,3,7] => [1,2,4,5,6,3,7] => 3
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [3,7,8,6,5,4,2,1] => [8,1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => 4
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [3,7,6,8,5,4,2,1] => [8,1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => 3
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => [8,1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => 4
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [3,5,7,8,6,4,2,1] => [8,1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => 3
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [3,6,5,8,7,4,2,1] => [8,1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => 3
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [4,3,8,7,6,5,2,1] => [8,1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => 4
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [4,3,7,8,6,5,2,1] => [8,1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => 3
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [4,3,6,8,7,5,2,1] => [8,1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => 3
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [4,3,7,6,8,5,2,1] => [8,1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => 2
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [3,4,7,6,8,5,2,1] => [8,1,3,4,2,7,6,5] => [1,3,4,2,7,6,5] => 2
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [3,4,6,7,8,5,2,1] => [8,1,3,4,2,6,7,5] => [1,3,4,2,6,7,5] => 2
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [5,4,3,7,8,6,2,1] => [8,1,5,3,4,2,7,6] => [1,5,3,4,2,7,6] => 2
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => [8,1,3,4,5,6,7,2] => [1,3,4,5,6,7,2] => 1
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [2,8,7,6,5,4,3,1] => [8,2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 5
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => [8,2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => 4
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [2,6,5,8,7,4,3,1] => [8,2,1,3,6,5,4,7] => [2,1,3,6,5,4,7] => 3
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [2,4,6,8,7,5,3,1] => [8,2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => 3
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [2,5,4,7,8,6,3,1] => [8,2,1,5,4,3,7,6] => [2,1,5,4,3,7,6] => 2
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [3,2,8,7,6,5,4,1] => [8,3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 4
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [3,2,6,8,7,5,4,1] => [8,3,2,1,4,6,5,7] => [3,2,1,4,6,5,7] => 3
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [3,2,6,5,8,7,4,1] => [8,3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => 2
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [2,3,8,7,6,5,4,1] => [8,2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => 4
[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [2,3,5,7,8,6,4,1] => [8,2,3,1,5,4,7,6] => [2,3,1,5,4,7,6] => 2
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => [8,2,3,1,5,6,4,7] => [2,3,1,5,6,4,7] => 2
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [2,3,7,6,5,8,4,1] => [8,2,3,1,7,5,6,4] => [2,3,1,7,5,6,4] => 1
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [3,4,2,8,7,6,5,1] => [8,4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 3
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [3,4,2,7,8,6,5,1] => [8,4,3,2,1,5,7,6] => [4,3,2,1,5,7,6] => 2
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [2,3,4,8,7,6,5,1] => [8,2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => 3
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [4,5,3,6,2,8,7,1] => [8,6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 1
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1] => 0
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [3,5,6,4,7,2,8,1] => [8,7,3,6,5,4,2,1] => [7,3,6,5,4,2,1] => 0
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => [8,7,4,3,6,5,2,1] => [7,4,3,6,5,2,1] => 0
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => [8,7,5,4,3,6,2,1] => [7,5,4,3,6,2,1] => 0
[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [3,5,4,6,7,2,8,1] => [8,7,3,5,4,6,2,1] => [7,3,5,4,6,2,1] => 0
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [2,4,6,5,7,3,8,1] => [8,2,7,4,6,5,3,1] => [2,7,4,6,5,3,1] => 0
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => [8,3,2,7,6,5,4,1] => [3,2,7,6,5,4,1] => 0
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => [8,5,4,3,2,7,6,1] => [5,4,3,2,7,6,1] => 0
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => [8,3,2,5,4,7,6,1] => [3,2,5,4,7,6,1] => 0
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => [1,8,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 6
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => [1,8,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 5
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => [1,8,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 5
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,4,8,7,6,5,3,2] => [1,8,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 5
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,4,6,8,7,5,3,2] => [1,8,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => 4
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,3,8,7,6,5,4,2] => [1,8,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 5
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => [1,8,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => 3
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,3,6,7,5,8,4,2] => [1,8,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => 2
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,4,5,3,8,7,6,2] => [1,8,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => 3
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,4,5,3,7,8,6,2] => [1,8,5,4,3,2,7,6] => [1,5,4,3,2,7,6] => 2
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,7,6,5,4,3,8,2] => [1,8,7,3,4,5,6,2] => [1,7,3,4,5,6,2] => 1
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,4,6,7,5,3,8,2] => [1,8,7,4,3,6,5,2] => [1,7,4,3,6,5,2] => 1
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,5,4,7,6,3,8,2] => [1,8,7,5,4,3,6,2] => [1,7,5,4,3,6,2] => 1
[[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,4,5,7,6,3,8,2] => [1,8,7,4,5,3,6,2] => [1,7,4,5,3,6,2] => 1
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,5,6,4,7,3,8,2] => [1,8,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 1
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,5,4,6,7,3,8,2] => [1,8,7,5,4,6,3,2] => [1,7,5,4,6,3,2] => 1
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,4,5,6,7,3,8,2] => [1,8,7,4,5,6,3,2] => [1,7,4,5,6,3,2] => 1
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,4,5,3,6,7,8,2] => [1,8,5,4,3,6,7,2] => [1,5,4,3,6,7,2] => 1
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => [1,8,4,3,5,6,7,2] => [1,4,3,5,6,7,2] => 1
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => [2,1,8,3,4,5,6,7] => [2,1,3,4,5,6,7] => 5
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [2,1,7,6,8,5,4,3] => [2,1,8,3,4,7,6,5] => [2,1,3,4,7,6,5] => 3
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => [2,1,8,3,4,6,7,5] => [2,1,3,4,6,7,5] => 3
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => [2,1,8,3,5,4,7,6] => [2,1,3,5,4,7,6] => 3
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [2,1,4,6,8,7,5,3] => [2,1,8,4,3,6,5,7] => [2,1,4,3,6,5,7] => 3
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [2,1,4,5,7,8,6,3] => [2,1,8,4,5,3,7,6] => [2,1,4,5,3,7,6] => 2
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => [2,1,8,7,6,5,4,3] => [2,1,7,6,5,4,3] => 1
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [2,1,4,7,6,5,8,3] => [2,1,8,4,7,5,6,3] => [2,1,4,7,5,6,3] => 1
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => [1,2,8,3,4,6,7,5] => [1,2,3,4,6,7,5] => 4
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,2,6,5,7,8,4,3] => [1,2,8,3,6,5,7,4] => [1,2,3,6,5,7,4] => 3
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => [1,2,8,4,3,5,6,7] => [1,2,4,3,5,6,7] => 5
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,2,5,4,8,7,6,3] => [1,2,8,5,4,3,6,7] => [1,2,5,4,3,6,7] => 4
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,2,4,5,7,8,6,3] => [1,2,8,4,5,3,7,6] => [1,2,4,5,3,7,6] => 3
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,2,7,6,5,4,8,3] => [1,2,8,7,4,5,6,3] => [1,2,7,4,5,6,3] => 2
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => [1,2,8,5,4,6,7,3] => [1,2,5,4,6,7,3] => 2
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [3,2,1,6,7,8,5,4] => [3,1,2,8,4,6,7,5] => [3,1,2,4,6,7,5] => 2
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [3,2,1,6,7,5,8,4] => [3,1,2,8,7,6,5,4] => [3,1,2,7,6,5,4] => 1
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [2,3,1,5,7,8,6,4] => [3,2,1,8,5,4,7,6] => [3,2,1,5,4,7,6] => 2
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [2,3,1,6,7,5,8,4] => [3,2,1,8,7,6,5,4] => [3,2,1,7,6,5,4] => 1
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,3,2,8,7,6,5,4] => [1,3,2,8,4,5,6,7] => [1,3,2,4,5,6,7] => 5
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,3,2,6,8,7,5,4] => [1,3,2,8,4,6,5,7] => [1,3,2,4,6,5,7] => 4
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,3,2,6,7,5,8,4] => [1,3,2,8,7,6,5,4] => [1,3,2,7,6,5,4] => 2
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [2,1,3,8,7,6,5,4] => [2,1,3,8,4,5,6,7] => [2,1,3,4,5,6,7] => 5
[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [2,1,3,6,7,5,8,4] => [2,1,3,8,7,6,5,4] => [2,1,3,7,6,5,4] => 2
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [2,1,3,5,7,6,8,4] => [2,1,3,8,5,7,6,4] => [2,1,3,5,7,6,4] => 2
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => [1,2,3,8,4,5,6,7] => [1,2,3,4,5,6,7] => 6
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => [1,2,3,8,4,6,5,7] => [1,2,3,4,6,5,7] => 5
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,2,3,7,6,5,8,4] => [1,2,3,8,7,5,6,4] => [1,2,3,7,5,6,4] => 3
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,2,3,6,7,5,8,4] => [1,2,3,8,7,6,5,4] => [1,2,3,7,6,5,4] => 3
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,2,3,5,7,6,8,4] => [1,2,3,8,5,7,6,4] => [1,2,3,5,7,6,4] => 3
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => [1,2,3,8,6,5,7,4] => [1,2,3,6,5,7,4] => 3
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4] => [1,2,3,5,6,7,4] => 3
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => [4,1,2,3,8,5,6,7] => [4,1,2,3,5,6,7] => 3
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [4,3,2,1,7,8,6,5] => [4,1,2,3,8,5,7,6] => [4,1,2,3,5,7,6] => 2
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [4,3,2,1,6,8,7,5] => [4,1,2,3,8,6,5,7] => [4,1,2,3,6,5,7] => 2
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [3,4,2,1,8,7,6,5] => [4,1,3,2,8,5,6,7] => [4,1,3,2,5,6,7] => 3
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [3,4,2,1,7,6,8,5] => [4,1,3,2,8,7,6,5] => [4,1,3,2,7,6,5] => 1
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [2,4,3,1,8,7,6,5] => [4,2,1,3,8,5,6,7] => [4,2,1,3,5,6,7] => 3
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => [4,3,2,1,8,5,6,7] => [4,3,2,1,5,6,7] => 3
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [3,2,4,1,7,8,6,5] => [4,3,2,1,8,5,7,6] => [4,3,2,1,5,7,6] => 2
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => [4,3,2,1,8,6,5,7] => [4,3,2,1,6,5,7] => 2
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => [4,3,2,1,8,7,6,5] => [4,3,2,1,7,6,5] => 1
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [2,3,4,1,8,7,6,5] => [4,2,3,1,8,5,6,7] => [4,2,3,1,5,6,7] => 3
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,4,3,2,8,7,6,5] => [1,4,2,3,8,5,6,7] => [1,4,2,3,5,6,7] => 4
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => [1,4,2,3,8,7,6,5] => [1,4,2,3,7,6,5] => 2
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,3,4,2,8,7,6,5] => [1,4,3,2,8,5,6,7] => [1,4,3,2,5,6,7] => 4
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,3,4,2,7,6,8,5] => [1,4,3,2,8,7,6,5] => [1,4,3,2,7,6,5] => 2
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,5,6,7] => [2,1,4,3,5,6,7] => 4
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => [2,1,4,3,8,5,7,6] => [2,1,4,3,5,7,6] => 3
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => [2,1,4,3,8,6,5,7] => [2,1,4,3,6,5,7] => 3
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,7,6,5] => [2,1,4,3,7,6,5] => 2
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => [2,1,4,3,6,7,5] => 2
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,4,3,8,7,6,5] => [1,2,4,3,8,5,6,7] => [1,2,4,3,5,6,7] => 5
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,2,4,3,7,6,8,5] => [1,2,4,3,8,7,6,5] => [1,2,4,3,7,6,5] => 3
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [3,2,1,4,8,7,6,5] => [3,1,2,4,8,5,6,7] => [3,1,2,4,5,6,7] => 4
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [2,3,1,4,8,7,6,5] => [3,2,1,4,8,5,6,7] => [3,2,1,4,5,6,7] => 4
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [2,3,1,4,7,6,8,5] => [3,2,1,4,8,7,6,5] => [3,2,1,4,7,6,5] => 2
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,3,2,4,8,7,6,5] => [1,3,2,4,8,5,6,7] => [1,3,2,4,5,6,7] => 5
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,3,2,4,7,6,8,5] => [1,3,2,4,8,7,6,5] => [1,3,2,4,7,6,5] => 3
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [2,1,3,4,8,7,6,5] => [2,1,3,4,8,5,6,7] => [2,1,3,4,5,6,7] => 5
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [2,1,3,4,7,6,8,5] => [2,1,3,4,8,7,6,5] => [2,1,3,4,7,6,5] => 3
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,8,7,6,5] => [1,2,3,4,8,5,6,7] => [1,2,3,4,5,6,7] => 6
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => [1,2,3,4,8,7,6,5] => [1,2,3,4,7,6,5] => 4
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5] => [1,2,3,4,6,7,5] => 4
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [4,3,2,5,1,8,7,6] => [5,4,2,3,1,8,6,7] => [5,4,2,3,1,6,7] => 2
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [3,4,2,5,1,8,7,6] => [5,4,3,2,1,8,6,7] => [5,4,3,2,1,6,7] => 2
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [3,4,2,5,1,7,8,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,7,6] => 1
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,5,4,3,2,8,7,6] => [1,5,2,3,4,8,6,7] => [1,5,2,3,4,6,7] => 3
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,2,4,5,3,8,7,6] => [1,2,5,4,3,8,6,7] => [1,2,5,4,3,6,7] => 4
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,3,2,5,4,8,7,6] => [1,3,2,5,4,8,6,7] => [1,3,2,5,4,6,7] => 4
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,5,4,8,7,6] => [1,2,3,5,4,8,6,7] => [1,2,3,5,4,6,7] => 5
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [4,3,2,1,5,8,7,6] => [4,1,2,3,5,8,6,7] => [4,1,2,3,5,6,7] => 3
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [4,3,2,1,5,7,8,6] => [4,1,2,3,5,8,7,6] => [4,1,2,3,5,7,6] => 2
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => [4,3,2,1,5,8,6,7] => [4,3,2,1,5,6,7] => 3
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [3,2,4,1,5,7,8,6] => [4,3,2,1,5,8,7,6] => [4,3,2,1,5,7,6] => 2
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,4,3,2,5,8,7,6] => [1,4,2,3,5,8,6,7] => [1,4,2,3,5,6,7] => 4
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => [3,1,2,4,5,8,6,7] => [3,1,2,4,5,6,7] => 4
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,7,6] => 3
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,3,2,4,5,8,7,6] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,6,7] => 5
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,6,7] => 6
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,7,6] => 5
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => [6,1,2,3,4,5,8,7] => [6,1,2,3,4,5,7] => 1
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [3,2,6,5,4,1,8,7] => [6,3,2,1,4,5,8,7] => [6,3,2,1,4,5,7] => 1
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [3,4,2,6,5,1,8,7] => [6,4,3,2,1,5,8,7] => [6,4,3,2,1,5,7] => 1
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,7] => 1
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [3,4,5,2,6,1,8,7] => [6,5,3,4,2,1,8,7] => [6,5,3,4,2,1,7] => 1
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => [6,3,2,5,4,1,8,7] => [6,3,2,5,4,1,7] => 1
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [2,1,6,3,4,5,8,7] => [2,1,6,3,4,5,7] => 2
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,7] => 2
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => [2,1,6,4,5,3,7] => 2
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => [4,1,2,3,6,5,8,7] => [4,1,2,3,6,5,7] => 2
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,7] => 2
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,7] => 3
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [5,4,3,2,1,6,8,7] => [5,1,2,3,4,6,8,7] => [5,1,2,3,4,6,7] => 2
[[[.,[[.,[[.,.],.]],.]],.],[.,.]] => [3,4,2,5,1,6,8,7] => [5,4,3,2,1,6,8,7] => [5,4,3,2,1,6,7] => 2
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [2,1,4,5,3,6,8,7] => [2,1,5,4,3,6,8,7] => [2,1,5,4,3,6,7] => 3
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [4,3,2,1,5,6,8,7] => [4,1,2,3,5,6,8,7] => [4,1,2,3,5,6,7] => 3
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [3,2,4,1,5,6,8,7] => [4,3,2,1,5,6,8,7] => [4,3,2,1,5,6,7] => 3
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,7] => 5
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7] => 6
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,6] => 0
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => [7,2,1,3,4,5,6,8] => [7,2,1,3,4,5,6] => 0
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [3,4,2,7,6,5,1,8] => [7,4,3,2,1,5,6,8] => [7,4,3,2,1,5,6] => 0
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1] => 0
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [3,5,4,6,2,7,1,8] => [7,6,3,5,4,2,1,8] => [7,6,3,5,4,2,1] => 0
[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [4,3,5,6,2,7,1,8] => [7,6,4,3,5,2,1,8] => [7,6,4,3,5,2,1] => 0
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => [7,6,3,4,5,2,1,8] => [7,6,3,4,5,2,1] => 0
[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [2,3,5,6,4,7,1,8] => [7,2,3,6,5,4,1,8] => [7,2,3,6,5,4,1] => 0
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [2,3,4,6,5,7,1,8] => [7,2,3,4,6,5,1,8] => [7,2,3,4,6,5,1] => 0
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,7,6,5,4,3,2,8] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6] => 1
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => [1,7,2,3,4,6,5,8] => [1,7,2,3,4,6,5] => 1
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,4,7,6,5,3,2,8] => [1,7,2,4,3,5,6,8] => [1,7,2,4,3,5,6] => 1
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,4,5,6,7,3,2,8] => [1,7,2,4,5,6,3,8] => [1,7,2,4,5,6,3] => 1
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,3,2,7,6,5,4,8] => [1,3,2,7,4,5,6,8] => [1,3,2,7,4,5,6] => 2
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,7,6,5,4,8] => [1,2,3,7,4,5,6,8] => [1,2,3,7,4,5,6] => 3
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,2,3,6,7,5,4,8] => [1,2,3,7,4,6,5,8] => [1,2,3,7,4,6,5] => 3
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8] => [4,1,2,3,7,5,6,8] => [4,1,2,3,7,5,6] => 1
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [3,2,4,1,6,7,5,8] => [4,3,2,1,7,6,5,8] => [4,3,2,1,7,6,5] => 1
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [1,4,2,3,7,5,6,8] => [1,4,2,3,7,5,6] => 2
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5] => 2
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => [3,2,1,4,7,6,5] => 2
[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [3,4,2,5,1,7,6,8] => [5,4,3,2,1,7,6,8] => [5,4,3,2,1,7,6] => 1
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,5,4,3,2,7,6,8] => [1,5,2,3,4,7,6,8] => [1,5,2,3,4,7,6] => 2
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [3,2,1,5,4,7,6] => 2
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6] => 3
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6] => 4
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8] => [4,1,2,3,5,7,6,8] => [4,1,2,3,5,7,6] => 2
[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [3,2,4,1,5,7,6,8] => [4,3,2,1,5,7,6,8] => [4,3,2,1,5,7,6] => 2
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,4,3,2,5,7,6,8] => [1,4,2,3,5,7,6,8] => [1,4,2,3,5,7,6] => 3
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6] => 4
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6] => 5
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7] => 1
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [2,3,6,5,4,1,7,8] => [6,2,3,1,4,5,7,8] => [6,2,3,1,4,5,7] => 1
[[[.,[[.,[[.,.],.]],[.,.]]],.],.] => [3,4,2,6,5,1,7,8] => [6,4,3,2,1,5,7,8] => [6,4,3,2,1,5,7] => 1
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7] => 1
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,6,5,4,3,2,7,8] => [1,6,2,3,4,5,7,8] => [1,6,2,3,4,5,7] => 2
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,4,6,5,3,2,7,8] => [1,6,2,4,3,5,7,8] => [1,6,2,4,3,5,7] => 2
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,2,5,6,4,3,7,8] => [1,2,6,3,5,4,7,8] => [1,2,6,3,5,4,7] => 3
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,3,2,6,5,4,7,8] => [1,3,2,6,4,5,7,8] => [1,3,2,6,4,5,7] => 3
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,2,3,6,5,4,7,8] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7] => 4
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => [4,1,2,3,6,5,7,8] => [4,1,2,3,6,5,7] => 2
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [3,2,4,1,6,5,7,8] => [4,3,2,1,6,5,7,8] => [4,3,2,1,6,5,7] => 2
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7] => 4
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7] => 2
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7] => 2
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [5,2,3,4,1,6,7] => 2
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,5,4,3,2,6,7,8] => [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7] => 3
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7] => 4
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7] => 5
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [4,1,2,3,5,6,7,8] => [4,1,2,3,5,6,7] => 3
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => [4,1,3,2,5,6,7,8] => [4,1,3,2,5,6,7] => 3
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7] => 3
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,4,3,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7] => 4
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7] => 4
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7] => 4
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7] => 5
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7] => 5
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7] => 6
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Generating function
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Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,3 4,6,4 10,15,12,5 28,42,36,20,6 84,126,112,70,30,7
$F_{2} = 2$
$F_{3} = 2 + 3\ q$
$F_{4} = 4 + 6\ q + 4\ q^{2}$
$F_{5} = 10 + 15\ q + 12\ q^{2} + 5\ q^{3}$
$F_{6} = 28 + 42\ q + 36\ q^{2} + 20\ q^{3} + 6\ q^{4}$
$F_{7} = 84 + 126\ q + 112\ q^{2} + 70\ q^{3} + 30\ q^{4} + 7\ q^{5}$
Description
The number of global ascents of a permutation.
The global ascents are the integers $i$ such that
$$C(\pi)=\{i\in [n-1] \mid \forall 1 \leq j \leq i < k \leq n: \pi(j) < \pi(k)\}.$$
Equivalently, by the pigeonhole principle,
$$C(\pi)=\{i\in [n-1] \mid \forall 1 \leq j \leq i: \pi(j) \leq i \}.$$
For $n > 1$ it can also be described as an occurrence of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
According to [2], this is also the cardinality of the connectivity set of a permutation. The permutation is connected, when the connectivity set is empty. This gives oeis:A003319.
The global ascents are the integers $i$ such that
$$C(\pi)=\{i\in [n-1] \mid \forall 1 \leq j \leq i < k \leq n: \pi(j) < \pi(k)\}.$$
Equivalently, by the pigeonhole principle,
$$C(\pi)=\{i\in [n-1] \mid \forall 1 \leq j \leq i: \pi(j) \leq i \}.$$
For $n > 1$ it can also be described as an occurrence of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
According to [2], this is also the cardinality of the connectivity set of a permutation. The permutation is connected, when the connectivity set is empty. This gives oeis:A003319.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
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
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.
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