Identifier
-
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St000476: Dyck paths ⟶ ℤ
Values
[.,[.,.]] => [2,1] => [2,1] => [1,1,0,0] => 0
[[.,.],.] => [1,2] => [1,2] => [1,0,1,0] => 1
[.,[.,[.,.]]] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0] => 0
[.,[[.,.],.]] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0] => 0
[[.,.],[.,.]] => [1,3,2] => [1,3,2] => [1,0,1,1,0,0] => 1
[[.,[.,.]],.] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0] => 2
[[[.,.],.],.] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0] => 2
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => 0
[.,[.,[[.,.],.]]] => [3,4,2,1] => [4,3,1,2] => [1,1,1,1,0,0,0,0] => 0
[.,[[.,.],[.,.]]] => [2,4,3,1] => [4,1,3,2] => [1,1,1,1,0,0,0,0] => 0
[.,[[.,[.,.]],.]] => [3,2,4,1] => [4,2,1,3] => [1,1,1,1,0,0,0,0] => 0
[.,[[[.,.],.],.]] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => 0
[[.,.],[.,[.,.]]] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => 1
[[.,.],[[.,.],.]] => [1,3,4,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => 1
[[.,[.,.]],[.,.]] => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 2
[[[.,.],.],[.,.]] => [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 2
[[.,[.,[.,.]]],.] => [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 3
[[.,[[.,.],.]],.] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 3
[[[.,.],[.,.]],.] => [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => 3
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 3
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => 0
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => 0
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0] => 0
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0] => 0
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0] => 1
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => 1
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 2
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 2
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 3
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 3
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 3
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 3
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 3
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => 4
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => 4
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 4
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 4
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 4
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 4
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => 4
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 4
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 4
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [6,5,1,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [6,5,1,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [6,5,1,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [6,1,5,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [6,1,5,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [6,1,5,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [6,1,5,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [6,2,1,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [6,3,1,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [6,2,1,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [6,4,1,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [6,2,1,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
>>> Load all 1061 entries. <<<[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [1,6,5,4,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [1,6,5,2,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [1,6,5,3,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [1,6,5,2,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [1,6,2,5,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [1,6,3,2,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [1,6,4,3,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [1,6,4,2,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [1,6,3,2,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [2,1,6,5,3,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [2,1,6,3,5,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [2,1,6,4,3,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [1,2,6,5,3,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [1,2,6,3,5,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [1,2,6,4,3,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [4,3,1,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [4,1,3,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [4,2,1,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => 4
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 4
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 4
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => 4
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [5,4,1,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [5,1,4,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [5,1,4,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [5,1,2,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [5,1,3,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [1,5,4,2,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [1,5,3,2,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 5
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 5
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 5
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 5
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 5
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 5
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => 5
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => 5
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [4,1,3,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 5
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 5
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => 5
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => 5
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 5
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 5
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => 5
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => [7,6,5,4,1,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [7,6,5,1,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => [7,6,5,1,4,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => [7,6,5,2,1,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [7,6,5,1,2,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => [7,6,5,1,3,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [7,6,1,5,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => [7,6,1,5,4,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => [7,6,1,5,2,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => [7,6,1,5,3,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [7,6,1,5,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [7,6,2,1,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => [7,6,2,1,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [7,6,1,2,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => [7,6,1,2,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => [7,6,3,2,1,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => [7,6,3,1,2,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => [7,6,1,3,2,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => [7,6,2,1,3,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => [7,6,1,2,3,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [7,6,4,3,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => [7,6,4,1,3,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [7,6,4,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [7,6,1,4,3,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => [7,6,1,4,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => [7,6,2,1,4,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => [7,6,1,2,4,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [7,6,3,2,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => [7,6,1,3,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [7,6,2,1,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [7,1,6,5,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => [7,1,6,5,4,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => [7,1,6,5,2,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => [7,1,6,5,3,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => [7,1,6,5,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => [7,1,6,2,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => [7,1,6,2,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => [7,1,6,3,2,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => [7,1,6,2,3,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => [7,1,6,4,3,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => [7,1,6,4,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => [7,1,6,2,4,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => [7,1,6,3,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => [7,1,6,2,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [7,2,1,6,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => [7,2,1,6,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => [7,2,1,6,3,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => [7,2,1,6,4,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => [7,2,1,6,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [7,1,2,6,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => [7,1,2,6,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => [7,1,2,6,3,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => [7,1,2,6,4,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => [7,1,2,6,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => [7,3,2,1,6,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => [7,3,2,1,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => [7,3,1,2,6,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => [7,3,1,2,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => [7,1,3,2,6,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => [7,1,3,2,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => [7,2,1,3,6,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => [7,2,1,3,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [7,1,2,3,6,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [7,1,2,3,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => [7,4,3,2,1,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => [7,4,3,1,2,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => [7,4,1,3,2,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => [7,4,2,1,3,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => [7,4,1,2,3,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => [7,1,4,3,2,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => [7,1,4,2,3,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => [7,2,1,4,3,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => [7,1,2,4,3,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => [7,3,2,1,4,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => [7,3,1,2,4,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => [7,1,3,2,4,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => [7,2,1,3,4,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [7,1,2,3,4,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [7,5,4,3,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => [7,5,4,1,3,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [7,5,4,2,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [7,5,4,1,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => [7,5,1,4,3,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => [7,5,1,4,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => [7,5,2,1,4,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => [7,5,1,2,4,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => [7,5,1,3,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => [7,1,5,4,3,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => [7,1,5,4,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => [7,1,5,2,4,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => [7,1,5,3,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => [7,1,5,2,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => [7,2,1,5,4,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => [7,2,1,5,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [7,1,2,5,4,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => [7,1,2,5,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => [7,3,2,1,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => [7,3,1,2,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => [7,1,3,2,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => [7,2,1,3,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => [7,1,2,3,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [7,4,3,2,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [7,4,3,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => [7,4,1,3,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => [7,1,4,3,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => [7,1,4,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => [7,2,1,4,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [7,1,2,4,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [7,3,2,1,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [7,1,3,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => [1,7,6,5,4,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => [1,7,6,5,2,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => [1,7,6,5,3,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => [1,7,6,5,2,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [1,7,6,2,5,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => [1,7,6,2,5,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => [1,7,6,3,2,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => [1,7,6,2,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => [1,7,6,4,3,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => [1,7,6,4,2,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => [1,7,6,2,4,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => [1,7,6,3,2,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => [1,7,6,2,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [1,7,2,6,5,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => [1,7,2,6,5,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => [1,7,2,6,4,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => [1,7,3,2,6,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => [1,7,3,2,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [1,7,2,3,6,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => [1,7,4,3,2,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [1,7,4,2,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => [1,7,3,2,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => [1,7,5,4,3,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => [1,7,5,4,2,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => [1,7,5,2,4,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => [1,7,5,3,2,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => [1,7,5,2,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => [1,7,2,5,4,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => [1,7,3,2,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => [1,7,4,3,2,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => [1,7,4,2,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => [1,7,3,2,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => [2,1,7,6,5,3,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => [2,1,7,6,3,5,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => [2,1,7,6,4,3,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => [2,1,7,6,3,4,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => [2,1,7,3,6,5,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => [2,1,7,3,6,4,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => [2,1,7,4,3,6,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => [2,1,7,3,4,6,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => [2,1,7,5,4,3,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => [2,1,7,5,3,4,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => [2,1,7,3,5,4,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => [2,1,7,4,3,5,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => [2,1,7,3,4,5,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => [1,2,7,6,5,3,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => [1,2,7,6,3,5,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => [1,2,7,6,4,3,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => [1,2,7,6,3,4,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => [1,2,7,3,6,5,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => [1,2,7,3,6,4,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => [1,2,7,4,3,6,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => [1,2,7,3,4,6,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => [1,2,7,5,4,3,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => [1,2,7,5,3,4,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => [1,2,7,3,5,4,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => [1,2,7,4,3,5,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => [3,2,1,7,6,4,5] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => [3,2,1,7,4,6,5] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => [3,2,1,7,5,4,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => [3,2,1,7,4,5,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => [3,1,2,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => [3,1,2,7,6,4,5] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => [3,1,2,7,4,6,5] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => [3,1,2,7,5,4,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => [3,1,2,7,4,5,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => [1,3,2,7,6,4,5] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => [1,3,2,7,4,6,5] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => [1,3,2,7,5,4,6] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => [1,3,2,7,4,5,6] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => [2,1,3,7,6,4,5] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => [2,1,3,7,4,6,5] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => [2,1,3,7,5,4,6] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => [2,1,3,7,4,5,6] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => [1,2,3,7,6,4,5] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => [1,2,3,7,4,6,5] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => [1,2,3,7,5,4,6] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => [4,3,2,1,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => [4,3,1,2,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => [4,3,1,2,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => [4,1,3,2,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => [4,1,3,2,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => [4,2,1,3,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => [4,2,1,3,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => [4,1,2,3,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => [4,1,2,3,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 4
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => [1,4,3,2,7,5,6] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 4
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => [1,4,2,3,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 4
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => [1,4,2,3,7,5,6] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 4
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => [2,1,4,3,7,6,5] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 4
[[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => [2,1,4,3,7,5,6] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 4
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
[[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => [3,2,1,4,7,5,6] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
[[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => [3,1,2,4,7,6,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
[[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => [3,1,2,4,7,5,6] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => [1,3,2,4,7,5,6] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => [2,1,3,4,7,6,5] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => [2,1,3,4,7,5,6] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => [5,4,3,1,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => [5,4,1,3,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => [5,4,2,1,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => [5,4,1,2,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => [5,1,4,3,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => [5,1,4,2,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => [5,2,1,4,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => [5,1,2,4,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => [5,3,2,1,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => [5,3,1,2,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => [5,1,3,2,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => [5,2,1,3,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => [5,1,2,3,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 5
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => [1,5,4,2,3,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 5
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => [1,5,2,4,3,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 5
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => [1,5,3,2,4,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 5
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 5
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => [2,1,5,4,3,7,6] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => [2,1,5,3,4,7,6] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => [3,2,1,5,4,7,6] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 5
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 5
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => [4,3,1,2,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 5
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => [4,1,3,2,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 5
[[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => [4,2,1,3,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 5
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 5
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 5
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 5
[[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 5
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5
[[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => [3,2,1,4,5,7,6] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 5
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 5
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5
[[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [6,5,4,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => [6,5,4,1,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [6,5,4,2,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [6,5,4,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => [6,5,1,4,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => [6,5,1,4,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => [6,5,2,1,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [6,5,1,2,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [6,5,3,2,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [6,5,3,1,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [6,5,1,3,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [6,5,2,1,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [6,5,1,2,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => [6,1,5,4,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => [6,1,5,4,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [6,1,5,2,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => [6,1,5,3,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => [6,1,5,2,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => [6,2,1,5,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => [6,2,1,5,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [6,1,2,5,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => [6,1,2,5,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => [6,3,2,1,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [6,3,1,2,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => [6,1,3,2,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => [6,2,1,3,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [6,1,2,3,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [6,4,3,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [6,4,3,1,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => [6,4,1,3,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [6,4,2,1,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [6,4,1,2,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [6,1,4,3,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => [6,1,4,2,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => [6,2,1,4,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [6,1,2,4,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [6,3,2,1,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [6,3,1,2,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [6,1,3,2,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [6,2,1,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => [1,6,5,4,2,3,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [1,6,5,2,4,3,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => [1,6,5,3,2,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [1,6,5,2,3,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [1,6,2,5,4,3,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [1,6,2,5,3,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [1,6,3,2,5,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [1,6,2,3,5,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [1,6,4,3,2,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [1,6,4,2,3,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [1,6,2,4,3,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [1,6,3,2,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 6
[[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => [2,1,6,5,3,4,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 6
[[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => [2,1,6,3,5,4,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 6
[[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => [2,1,6,4,3,5,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 6
[[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => [2,1,6,3,4,5,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 6
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [1,2,6,5,3,4,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [1,2,6,3,5,4,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [1,2,6,4,3,5,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6
[[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => [3,2,1,6,4,5,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6
[[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => [3,1,2,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6
[[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => [3,1,2,6,4,5,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [1,3,2,6,4,5,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => [2,1,3,6,5,4,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 6
[[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => [2,1,3,6,4,5,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 6
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 6
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 6
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 6
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => [4,3,1,2,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 6
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => [4,1,3,2,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 6
[[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => [4,2,1,3,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 6
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 6
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [1,4,2,3,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 6
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 6
[[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => [3,2,1,4,6,5,7] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 6
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 6
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 6
[[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 6
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [5,4,3,1,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => [5,4,1,3,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [5,4,2,1,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [5,4,1,2,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => [5,1,4,3,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => [5,1,4,2,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => [5,2,1,4,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [5,1,2,4,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [5,3,2,1,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [5,3,1,2,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [5,1,3,2,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [5,2,1,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [1,5,4,2,3,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [1,5,2,4,3,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [1,5,3,2,4,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => [2,1,5,4,3,6,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 6
[[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => [2,1,5,3,4,6,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 6
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 6
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 6
[[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => [3,2,1,5,4,6,7] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 6
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 6
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 6
[[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 6
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [4,3,1,2,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [4,1,3,2,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [4,2,1,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 6
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 6
[[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 6
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 6
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 6
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => [1,8,7,6,5,4,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => [1,8,7,6,5,2,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => [1,8,7,6,5,3,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => [1,8,7,6,5,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => [1,8,7,6,2,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,6,5,8,7,4,3,2] => [1,8,7,6,3,2,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => [1,8,7,6,4,3,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,6,7,5,8,4,3,2] => [1,8,7,6,4,2,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,5,7,6,8,4,3,2] => [1,8,7,6,2,4,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,6,5,7,8,4,3,2] => [1,8,7,6,3,2,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,5,6,7,8,4,3,2] => [1,8,7,6,2,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,4,8,7,6,5,3,2] => [1,8,7,2,6,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,4,7,8,6,5,3,2] => [1,8,7,2,6,5,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,4,6,8,7,5,3,2] => [1,8,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,4,6,7,8,5,3,2] => [1,8,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,5,4,7,8,6,3,2] => [1,8,7,3,2,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,4,5,8,7,6,3,2] => [1,8,7,2,3,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,4,5,7,8,6,3,2] => [1,8,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,6,5,4,8,7,3,2] => [1,8,7,4,3,2,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,5,6,4,8,7,3,2] => [1,8,7,4,2,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,5,4,6,8,7,3,2] => [1,8,7,3,2,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,4,5,6,8,7,3,2] => [1,8,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,7,6,5,4,8,3,2] => [1,8,7,5,4,3,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [1,6,5,7,4,8,3,2] => [1,8,7,5,3,2,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[.,[[[.,.],.],.]],.]]] => [1,5,6,7,4,8,3,2] => [1,8,7,5,2,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,4,7,6,5,8,3,2] => [1,8,7,2,5,4,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,4,6,7,5,8,3,2] => [1,8,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,5,4,7,6,8,3,2] => [1,8,7,3,2,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,4,5,7,6,8,3,2] => [1,8,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,6,5,4,7,8,3,2] => [1,8,7,4,3,2,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,5,6,4,7,8,3,2] => [1,8,7,4,2,3,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,5,4,6,7,8,3,2] => [1,8,7,3,2,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,4,5,6,7,8,3,2] => [1,8,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,3,8,7,6,5,4,2] => [1,8,2,7,6,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,3,6,8,7,5,4,2] => [1,8,2,7,6,3,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,3,7,6,8,5,4,2] => [1,8,2,7,6,4,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,3,6,7,8,5,4,2] => [1,8,2,7,6,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,3,5,8,7,6,4,2] => [1,8,2,7,3,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,3,6,5,8,7,4,2] => [1,8,2,7,4,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,3,5,6,8,7,4,2] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,3,7,6,5,8,4,2] => [1,8,2,7,5,4,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,3,6,7,5,8,4,2] => [1,8,2,7,5,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,3,5,7,6,8,4,2] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,3,6,5,7,8,4,2] => [1,8,2,7,4,3,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,3,5,6,7,8,4,2] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => [1,8,3,2,7,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,4,3,7,8,6,5,2] => [1,8,3,2,7,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,4,3,7,6,8,5,2] => [1,8,3,2,7,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,3,4,8,7,6,5,2] => [1,8,2,3,7,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,3,4,7,8,6,5,2] => [1,8,2,3,7,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,3,4,7,6,8,5,2] => [1,8,2,3,7,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,5,4,3,8,7,6,2] => [1,8,4,3,2,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,5,4,3,7,8,6,2] => [1,8,4,3,2,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,4,5,3,8,7,6,2] => [1,8,4,2,3,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,4,5,3,7,8,6,2] => [1,8,4,2,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,3,5,4,8,7,6,2] => [1,8,2,4,3,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,3,5,4,7,8,6,2] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,4,3,5,7,8,6,2] => [1,8,3,2,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,3,4,5,8,7,6,2] => [1,8,2,3,4,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,3,4,5,7,8,6,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => [1,8,5,4,3,2,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,5,6,4,3,8,7,2] => [1,8,5,4,2,3,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,5,4,6,3,8,7,2] => [1,8,5,3,2,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,4,5,6,3,8,7,2] => [1,8,5,2,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,3,5,6,4,8,7,2] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => [1,8,3,2,5,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,5,4,3,6,8,7,2] => [1,8,4,3,2,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,4,5,3,6,8,7,2] => [1,8,4,2,3,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,4,3,5,6,8,7,2] => [1,8,3,2,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,3,4,5,6,8,7,2] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,7,6,5,4,3,8,2] => [1,8,6,5,4,3,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,6,7,5,4,3,8,2] => [1,8,6,5,4,2,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,6,5,7,4,3,8,2] => [1,8,6,5,3,2,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,4,6,7,5,3,8,2] => [1,8,6,2,5,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,5,4,7,6,3,8,2] => [1,8,6,3,2,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,5,6,4,7,3,8,2] => [1,8,6,4,2,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,4,6,5,7,3,8,2] => [1,8,6,2,4,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,5,4,6,7,3,8,2] => [1,8,6,3,2,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,4,5,6,7,3,8,2] => [1,8,6,2,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,3,6,7,5,4,8,2] => [1,8,2,6,5,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,3,5,7,6,4,8,2] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,3,6,5,7,4,8,2] => [1,8,2,6,4,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,3,5,6,7,4,8,2] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,4,3,6,7,5,8,2] => [1,8,3,2,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,3,4,7,6,5,8,2] => [1,8,2,3,6,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,3,4,6,7,5,8,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,3,5,4,7,6,8,2] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,3,4,5,7,6,8,2] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,6,5,4,3,7,8,2] => [1,8,5,4,3,2,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,5,6,4,3,7,8,2] => [1,8,5,4,2,3,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,5,4,6,3,7,8,2] => [1,8,5,3,2,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,3,5,6,4,7,8,2] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,4,3,6,5,7,8,2] => [1,8,3,2,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,3,4,6,5,7,8,2] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,5,4,3,6,7,8,2] => [1,8,4,3,2,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,4,5,3,6,7,8,2] => [1,8,4,2,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,3,5,4,6,7,8,2] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => [1,8,3,2,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,3,4,5,6,7,8,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [2,1,7,8,6,5,4,3] => [2,1,8,7,6,5,3,4] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [2,1,6,8,7,5,4,3] => [2,1,8,7,6,3,5,4] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [2,1,7,6,8,5,4,3] => [2,1,8,7,6,4,3,5] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => [2,1,8,7,6,3,4,5] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [2,1,5,8,7,6,4,3] => [2,1,8,7,3,6,5,4] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => [2,1,8,7,3,6,4,5] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [2,1,6,5,8,7,4,3] => [2,1,8,7,4,3,6,5] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [2,1,5,6,8,7,4,3] => [2,1,8,7,3,4,6,5] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [2,1,7,6,5,8,4,3] => [2,1,8,7,5,4,3,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [2,1,6,7,5,8,4,3] => [2,1,8,7,5,3,4,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [2,1,5,7,6,8,4,3] => [2,1,8,7,3,5,4,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [2,1,6,5,7,8,4,3] => [2,1,8,7,4,3,5,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [2,1,5,6,7,8,4,3] => [2,1,8,7,3,4,5,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [2,1,4,8,7,6,5,3] => [2,1,8,3,7,6,5,4] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [2,1,4,7,8,6,5,3] => [2,1,8,3,7,6,4,5] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [2,1,4,6,8,7,5,3] => [2,1,8,3,7,4,6,5] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [2,1,4,7,6,8,5,3] => [2,1,8,3,7,5,4,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [2,1,4,6,7,8,5,3] => [2,1,8,3,7,4,5,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [2,1,5,4,8,7,6,3] => [2,1,8,4,3,7,6,5] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [2,1,5,4,7,8,6,3] => [2,1,8,4,3,7,5,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [2,1,4,5,8,7,6,3] => [2,1,8,3,4,7,6,5] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [2,1,6,5,4,8,7,3] => [2,1,8,5,4,3,7,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [2,1,5,6,4,8,7,3] => [2,1,8,5,3,4,7,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [2,1,4,6,5,8,7,3] => [2,1,8,3,5,4,7,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [2,1,5,4,6,8,7,3] => [2,1,8,4,3,5,7,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [2,1,7,6,5,4,8,3] => [2,1,8,6,5,4,3,7] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [2,1,5,7,6,4,8,3] => [2,1,8,6,3,5,4,7] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => [2,1,8,6,4,3,5,7] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [2,1,4,6,7,5,8,3] => [2,1,8,3,6,4,5,7] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => [2,1,8,4,3,6,5,7] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [2,1,6,5,4,7,8,3] => [2,1,8,5,4,3,6,7] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [2,1,5,6,4,7,8,3] => [2,1,8,5,3,4,6,7] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [2,1,4,5,6,7,8,3] => [2,1,8,3,4,5,6,7] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,8,7,6,5,4,3] => [1,2,8,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,2,7,8,6,5,4,3] => [1,2,8,7,6,5,3,4] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,2,6,8,7,5,4,3] => [1,2,8,7,6,3,5,4] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,2,7,6,8,5,4,3] => [1,2,8,7,6,4,3,5] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => [1,2,8,7,6,3,4,5] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,2,5,8,7,6,4,3] => [1,2,8,7,3,6,5,4] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,2,6,5,8,7,4,3] => [1,2,8,7,4,3,6,5] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,2,5,6,8,7,4,3] => [1,2,8,7,3,4,6,5] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,2,7,6,5,8,4,3] => [1,2,8,7,5,4,3,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,2,5,7,6,8,4,3] => [1,2,8,7,3,5,4,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,2,5,6,7,8,4,3] => [1,2,8,7,3,4,5,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => [1,2,8,3,7,6,5,4] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,2,4,7,8,6,5,3] => [1,2,8,3,7,6,4,5] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,2,4,6,8,7,5,3] => [1,2,8,3,7,4,6,5] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,2,4,7,6,8,5,3] => [1,2,8,3,7,5,4,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,2,4,6,7,8,5,3] => [1,2,8,3,7,4,5,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,2,5,4,8,7,6,3] => [1,2,8,4,3,7,6,5] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,2,5,4,7,8,6,3] => [1,2,8,4,3,7,5,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,2,4,5,8,7,6,3] => [1,2,8,3,4,7,6,5] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,2,4,6,5,8,7,3] => [1,2,8,3,5,4,7,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,2,5,4,6,8,7,3] => [1,2,8,4,3,5,7,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,2,4,5,6,8,7,3] => [1,2,8,3,4,5,7,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,2,7,6,5,4,8,3] => [1,2,8,6,5,4,3,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,2,6,5,7,4,8,3] => [1,2,8,6,4,3,5,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,2,5,6,7,4,8,3] => [1,2,8,6,3,4,5,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,2,4,7,6,5,8,3] => [1,2,8,3,6,5,4,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,2,4,6,7,5,8,3] => [1,2,8,3,6,4,5,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,2,5,4,7,6,8,3] => [1,2,8,4,3,6,5,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,2,4,5,7,6,8,3] => [1,2,8,3,4,6,5,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,2,6,5,4,7,8,3] => [1,2,8,5,4,3,6,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,2,5,6,4,7,8,3] => [1,2,8,5,3,4,6,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,2,4,6,5,7,8,3] => [1,2,8,3,5,4,6,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => [1,2,8,4,3,5,6,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,2,4,5,6,7,8,3] => [1,2,8,3,4,5,6,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,3,2,8,7,6,5,4] => [1,3,2,8,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,3,2,7,8,6,5,4] => [1,3,2,8,7,6,4,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,3,2,6,8,7,5,4] => [1,3,2,8,7,4,6,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,3,2,7,6,8,5,4] => [1,3,2,8,7,5,4,6] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,3,2,6,7,8,5,4] => [1,3,2,8,7,4,5,6] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,3,2,5,7,8,6,4] => [1,3,2,8,4,7,5,6] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,3,2,6,5,8,7,4] => [1,3,2,8,5,4,7,6] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,3,2,5,6,8,7,4] => [1,3,2,8,4,5,7,6] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,3,2,7,6,5,8,4] => [1,3,2,8,6,5,4,7] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,3,2,6,7,5,8,4] => [1,3,2,8,6,4,5,7] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,3,2,5,7,6,8,4] => [1,3,2,8,4,6,5,7] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,3,2,6,5,7,8,4] => [1,3,2,8,5,4,6,7] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,3,2,5,6,7,8,4] => [1,3,2,8,4,5,6,7] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [2,1,3,8,7,6,5,4] => [2,1,3,8,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [2,1,3,7,8,6,5,4] => [2,1,3,8,7,6,4,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [2,1,3,6,8,7,5,4] => [2,1,3,8,7,4,6,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [2,1,3,7,6,8,5,4] => [2,1,3,8,7,5,4,6] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [2,1,3,6,7,8,5,4] => [2,1,3,8,7,4,5,6] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [2,1,3,5,8,7,6,4] => [2,1,3,8,4,7,6,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [2,1,3,5,7,8,6,4] => [2,1,3,8,4,7,5,6] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [2,1,3,6,5,8,7,4] => [2,1,3,8,5,4,7,6] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [2,1,3,5,6,8,7,4] => [2,1,3,8,4,5,7,6] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [2,1,3,7,6,5,8,4] => [2,1,3,8,6,5,4,7] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [2,1,3,6,7,5,8,4] => [2,1,3,8,6,4,5,7] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [2,1,3,5,7,6,8,4] => [2,1,3,8,4,6,5,7] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [2,1,3,6,5,7,8,4] => [2,1,3,8,5,4,6,7] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [2,1,3,5,6,7,8,4] => [2,1,3,8,4,5,6,7] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => [1,2,3,8,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,2,3,7,8,6,5,4] => [1,2,3,8,7,6,4,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => [1,2,3,8,7,4,6,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,2,3,7,6,8,5,4] => [1,2,3,8,7,5,4,6] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,2,3,6,7,8,5,4] => [1,2,3,8,7,4,5,6] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,2,3,5,8,7,6,4] => [1,2,3,8,4,7,6,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,2,3,5,7,8,6,4] => [1,2,3,8,4,7,5,6] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,2,3,6,5,8,7,4] => [1,2,3,8,5,4,7,6] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,2,3,5,6,8,7,4] => [1,2,3,8,4,5,7,6] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,2,3,7,6,5,8,4] => [1,2,3,8,6,5,4,7] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,2,3,6,7,5,8,4] => [1,2,3,8,6,4,5,7] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,2,3,5,7,6,8,4] => [1,2,3,8,4,6,5,7] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => [1,2,3,8,5,4,6,7] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => [1,2,3,8,4,5,6,7] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,4,3,2,8,7,6,5] => [1,4,3,2,8,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => [1,4,3,2,8,6,5,7] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,4,3,2,6,7,8,5] => [1,4,3,2,8,5,6,7] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,3,4,2,8,7,6,5] => [1,4,2,3,8,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,3,4,2,7,8,6,5] => [1,4,2,3,8,7,5,6] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,3,4,2,6,8,7,5] => [1,4,2,3,8,5,7,6] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,3,4,2,7,6,8,5] => [1,4,2,3,8,6,5,7] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,3,4,2,6,7,8,5] => [1,4,2,3,8,5,6,7] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => [2,1,4,3,8,7,5,6] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => [2,1,4,3,8,5,7,6] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,6,5,7] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,5,6,7] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,4,3,8,7,6,5] => [1,2,4,3,8,7,6,5] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,2,4,3,7,8,6,5] => [1,2,4,3,8,7,5,6] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,2,4,3,6,8,7,5] => [1,2,4,3,8,5,7,6] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,2,4,3,7,6,8,5] => [1,2,4,3,8,6,5,7] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,5,6,7] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,3,2,4,8,7,6,5] => [1,3,2,4,8,7,6,5] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,3,2,4,6,8,7,5] => [1,3,2,4,8,5,7,6] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,3,2,4,7,6,8,5] => [1,3,2,4,8,6,5,7] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,5,6,7] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [2,1,3,4,8,7,6,5] => [2,1,3,4,8,7,6,5] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [2,1,3,4,7,8,6,5] => [2,1,3,4,8,7,5,6] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [2,1,3,4,6,8,7,5] => [2,1,3,4,8,5,7,6] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [2,1,3,4,7,6,8,5] => [2,1,3,4,8,6,5,7] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,5,6,7] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,8,7,6,5] => [1,2,3,4,8,7,6,5] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,2,3,4,7,8,6,5] => [1,2,3,4,8,7,5,6] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,2,3,4,6,8,7,5] => [1,2,3,4,8,5,7,6] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => [1,2,3,4,8,6,5,7] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,5,6,7] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,5,4,3,2,8,7,6] => [1,5,4,3,2,8,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,4,5,3,2,8,7,6] => [1,5,4,2,3,8,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,4,5,3,2,7,8,6] => [1,5,4,2,3,8,6,7] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,3,5,4,2,8,7,6] => [1,5,2,4,3,8,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,3,5,4,2,7,8,6] => [1,5,2,4,3,8,6,7] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,4,3,5,2,8,7,6] => [1,5,3,2,4,8,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,4,3,5,2,7,8,6] => [1,5,3,2,4,8,6,7] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,3,4,5,2,8,7,6] => [1,5,2,3,4,8,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,3,4,5,2,7,8,6] => [1,5,2,3,4,8,6,7] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [2,1,5,4,3,8,7,6] => [2,1,5,4,3,8,7,6] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,2,5,4,3,8,7,6] => [1,2,5,4,3,8,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,2,5,4,3,7,8,6] => [1,2,5,4,3,8,6,7] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,2,4,5,3,8,7,6] => [1,2,5,3,4,8,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,2,4,5,3,7,8,6] => [1,2,5,3,4,8,6,7] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,3,2,5,4,8,7,6] => [1,3,2,5,4,8,7,6] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,6,7] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [2,1,3,5,4,8,7,6] => [2,1,3,5,4,8,7,6] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,5,4,8,7,6] => [1,2,3,5,4,8,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,6,7] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,4,3,2,5,8,7,6] => [1,4,3,2,5,8,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 5
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,4,3,2,5,7,8,6] => [1,4,3,2,5,8,6,7] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 5
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,3,4,2,5,8,7,6] => [1,4,2,3,5,8,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 5
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,3,4,2,5,7,8,6] => [1,4,2,3,5,8,6,7] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 5
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [2,1,4,3,5,8,7,6] => [2,1,4,3,5,8,7,6] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,6,7] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,2,4,3,5,8,7,6] => [1,2,4,3,5,8,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,6,7] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,3,2,4,5,8,7,6] => [1,3,2,4,5,8,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 5
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,6,7] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 5
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [2,1,3,4,5,8,7,6] => [2,1,3,4,5,8,7,6] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,6,7] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,8,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,6,5,4,3,2,8,7] => [1,6,5,4,3,2,8,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,5,6,4,3,2,8,7] => [1,6,5,4,2,3,8,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,5,4,6,3,2,8,7] => [1,6,5,3,2,4,8,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
[[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,4,5,6,3,2,8,7] => [1,6,5,2,3,4,8,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,3,5,6,4,2,8,7] => [1,6,2,5,3,4,8,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
[[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,4,5,3,6,2,8,7] => [1,6,4,2,3,5,8,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
[[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,3,5,4,6,2,8,7] => [1,6,2,4,3,5,8,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,3,4,5,6,2,8,7] => [1,6,2,3,4,5,8,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => [2,1,6,5,3,4,8,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => [2,1,6,3,5,4,8,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => [2,1,6,4,3,5,8,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => [2,1,6,3,4,5,8,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,2,4,5,6,3,8,7] => [1,2,6,3,4,5,8,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,3,2,6,5,4,8,7] => [1,3,2,6,5,4,8,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 6
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [2,1,3,6,5,4,8,7] => [2,1,3,6,5,4,8,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 6
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [2,1,3,5,6,4,8,7] => [2,1,3,6,4,5,8,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 6
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,2,3,6,5,4,8,7] => [1,2,3,6,5,4,8,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 6
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,2,3,5,6,4,8,7] => [1,2,3,6,4,5,8,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 6
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,3,4,2,6,5,8,7] => [1,4,2,3,6,5,8,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 6
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 6
[[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 6
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 6
[[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,4,5,3,2,6,8,7] => [1,5,4,2,3,6,8,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 6
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,3,5,4,2,6,8,7] => [1,5,2,4,3,6,8,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 6
[[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,4,3,5,2,6,8,7] => [1,5,3,2,4,6,8,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 6
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,3,4,5,2,6,8,7] => [1,5,2,3,4,6,8,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 6
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [2,1,5,4,3,6,8,7] => [2,1,5,4,3,6,8,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 6
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [2,1,4,5,3,6,8,7] => [2,1,5,3,4,6,8,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 6
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,2,5,4,3,6,8,7] => [1,2,5,4,3,6,8,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 6
[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,2,4,5,3,6,8,7] => [1,2,5,3,4,6,8,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 6
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [2,1,3,5,4,6,8,7] => [2,1,3,5,4,6,8,7] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 6
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 6
[[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,4,3,2,5,6,8,7] => [1,4,3,2,5,6,8,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 6
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,3,4,2,5,6,8,7] => [1,4,2,3,5,6,8,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 6
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 6
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 6
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 6
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,7,6,5,4,3,2,8] => [1,7,6,5,4,3,2,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => [1,7,6,5,4,2,3,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,5,7,6,4,3,2,8] => [1,7,6,5,2,4,3,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,6,5,7,4,3,2,8] => [1,7,6,5,3,2,4,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,5,4,7,6,3,2,8] => [1,7,6,3,2,5,4,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,5,6,4,7,3,2,8] => [1,7,6,4,2,3,5,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,4,6,5,7,3,2,8] => [1,7,6,2,4,3,5,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,5,4,6,7,3,2,8] => [1,7,6,3,2,4,5,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,4,5,6,7,3,2,8] => [1,7,6,2,3,4,5,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,3,7,6,5,4,2,8] => [1,7,2,6,5,4,3,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,3,5,7,6,4,2,8] => [1,7,2,6,3,5,4,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,3,6,5,7,4,2,8] => [1,7,2,6,4,3,5,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,3,5,6,7,4,2,8] => [1,7,2,6,3,4,5,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,3,4,6,7,5,2,8] => [1,7,2,3,6,4,5,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,3,5,4,7,6,2,8] => [1,7,2,4,3,6,5,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,4,3,5,7,6,2,8] => [1,7,3,2,4,6,5,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,3,4,5,7,6,2,8] => [1,7,2,3,4,6,5,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,6,5,4,3,7,2,8] => [1,7,5,4,3,2,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,5,4,6,3,7,2,8] => [1,7,5,3,2,4,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,4,5,6,3,7,2,8] => [1,7,5,2,3,4,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,3,6,5,4,7,2,8] => [1,7,2,5,4,3,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,3,5,6,4,7,2,8] => [1,7,2,5,3,4,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,4,3,6,5,7,2,8] => [1,7,3,2,5,4,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,3,4,6,5,7,2,8] => [1,7,2,3,5,4,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,5,4,3,6,7,2,8] => [1,7,4,3,2,5,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,4,5,3,6,7,2,8] => [1,7,4,2,3,5,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,3,5,4,6,7,2,8] => [1,7,2,4,3,5,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [1,4,3,5,6,7,2,8] => [1,7,3,2,4,5,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,3,4,5,6,7,2,8] => [1,7,2,3,4,5,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [2,1,7,6,5,4,3,8] => [2,1,7,6,5,4,3,8] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [2,1,6,7,5,4,3,8] => [2,1,7,6,5,3,4,8] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [2,1,5,6,7,4,3,8] => [2,1,7,6,3,4,5,8] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [2,1,4,6,7,5,3,8] => [2,1,7,3,6,4,5,8] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [2,1,4,5,6,7,3,8] => [2,1,7,3,4,5,6,8] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,2,7,6,5,4,3,8] => [1,2,7,6,5,4,3,8] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,2,6,5,7,4,3,8] => [1,2,7,6,4,3,5,8] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,2,5,6,7,4,3,8] => [1,2,7,6,3,4,5,8] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,2,4,6,7,5,3,8] => [1,2,7,3,6,4,5,8] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,2,4,5,7,6,3,8] => [1,2,7,3,4,6,5,8] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,2,5,6,4,7,3,8] => [1,2,7,5,3,4,6,8] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,2,4,6,5,7,3,8] => [1,2,7,3,5,4,6,8] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,2,5,4,6,7,3,8] => [1,2,7,4,3,5,6,8] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,2,4,5,6,7,3,8] => [1,2,7,3,4,5,6,8] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,3,2,7,6,5,4,8] => [1,3,2,7,6,5,4,8] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,3,2,6,7,5,4,8] => [1,3,2,7,6,4,5,8] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,3,2,5,7,6,4,8] => [1,3,2,7,4,6,5,8] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,3,2,6,5,7,4,8] => [1,3,2,7,5,4,6,8] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,3,2,5,6,7,4,8] => [1,3,2,7,4,5,6,8] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,7,6,5,4,8] => [1,2,3,7,6,5,4,8] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 7
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,2,3,6,7,5,4,8] => [1,2,3,7,6,4,5,8] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 7
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,2,3,5,7,6,4,8] => [1,2,3,7,4,6,5,8] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 7
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,2,3,6,5,7,4,8] => [1,2,3,7,5,4,6,8] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 7
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,2,3,5,6,7,4,8] => [1,2,3,7,4,5,6,8] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 7
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 7
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => [1,4,2,3,7,5,6,8] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 7
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,2,4,3,6,7,5,8] => [1,2,4,3,7,5,6,8] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 7
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,3,2,4,7,6,5,8] => [1,3,2,4,7,6,5,8] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 7
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [2,1,3,4,6,7,5,8] => [2,1,3,4,7,5,6,8] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 7
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,2,3,4,7,6,5,8] => [1,2,3,4,7,6,5,8] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 7
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,5,6,8] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 7
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,5,4,3,2,7,6,8] => [1,5,4,3,2,7,6,8] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,4,5,3,2,7,6,8] => [1,5,4,2,3,7,6,8] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,3,5,4,2,7,6,8] => [1,5,2,4,3,7,6,8] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,4,3,5,2,7,6,8] => [1,5,3,2,4,7,6,8] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,3,4,5,2,7,6,8] => [1,5,2,3,4,7,6,8] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [2,1,5,4,3,7,6,8] => [2,1,5,4,3,7,6,8] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 7
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,2,4,5,3,7,6,8] => [1,2,5,3,4,7,6,8] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 7
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 7
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 7
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,4,3,2,5,7,6,8] => [1,4,3,2,5,7,6,8] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 7
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,3,4,2,5,7,6,8] => [1,4,2,3,5,7,6,8] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 7
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 7
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 7
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,6,5,4,3,2,7,8] => [1,6,5,4,3,2,7,8] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 7
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,5,4,6,3,2,7,8] => [1,6,5,3,2,4,7,8] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 7
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,3,5,6,4,2,7,8] => [1,6,2,5,3,4,7,8] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 7
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,4,3,6,5,2,7,8] => [1,6,3,2,5,4,7,8] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 7
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,5,4,3,6,2,7,8] => [1,6,4,3,2,5,7,8] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 7
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,4,5,3,6,2,7,8] => [1,6,4,2,3,5,7,8] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 7
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,3,5,4,6,2,7,8] => [1,6,2,4,3,5,7,8] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 7
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,4,3,5,6,2,7,8] => [1,6,3,2,4,5,7,8] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 7
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,3,4,5,6,2,7,8] => [1,6,2,3,4,5,7,8] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 7
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [2,1,5,4,6,3,7,8] => [2,1,6,4,3,5,7,8] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 7
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,2,6,5,4,3,7,8] => [1,2,6,5,4,3,7,8] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 7
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,2,5,6,4,3,7,8] => [1,2,6,5,3,4,7,8] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 7
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,2,4,6,5,3,7,8] => [1,2,6,3,5,4,7,8] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 7
[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [1,2,5,4,6,3,7,8] => [1,2,6,4,3,5,7,8] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 7
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,2,4,5,6,3,7,8] => [1,2,6,3,4,5,7,8] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 7
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,3,2,6,5,4,7,8] => [1,3,2,6,5,4,7,8] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 7
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,3,2,5,6,4,7,8] => [1,3,2,6,4,5,7,8] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 7
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [2,1,3,5,6,4,7,8] => [2,1,3,6,4,5,7,8] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 7
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,2,3,6,5,4,7,8] => [1,2,3,6,5,4,7,8] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 7
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,2,3,5,6,4,7,8] => [1,2,3,6,4,5,7,8] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 7
[[[[[.,.],[[.,.],.]],[.,.]],.],.] => [1,3,4,2,6,5,7,8] => [1,4,2,3,6,5,7,8] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 7
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 7
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 7
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 7
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,5,4,3,2,6,7,8] => [1,5,4,3,2,6,7,8] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 7
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,4,5,3,2,6,7,8] => [1,5,4,2,3,6,7,8] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 7
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,3,5,4,2,6,7,8] => [1,5,2,4,3,6,7,8] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 7
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,4,3,5,2,6,7,8] => [1,5,3,2,4,6,7,8] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 7
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,3,4,5,2,6,7,8] => [1,5,2,3,4,6,7,8] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 7
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [2,1,5,4,3,6,7,8] => [2,1,5,4,3,6,7,8] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 7
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [2,1,4,5,3,6,7,8] => [2,1,5,3,4,6,7,8] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 7
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,2,5,4,3,6,7,8] => [1,2,5,4,3,6,7,8] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 7
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,2,4,5,3,6,7,8] => [1,2,5,3,4,6,7,8] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 7
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 7
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [2,1,3,5,4,6,7,8] => [2,1,3,5,4,6,7,8] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,4,3,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 7
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,3,4,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 7
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
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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:
1,1 2,1,2 5,2,2,5 14,5,4,5,14 42,14,10,10,14,42 132,42,28,25,28,42,132
F2=1+q
F3=2+q+2 q2
F4=5+2 q+2 q2+5 q3
F5=14+5 q+4 q2+5 q3+14 q4
F6=42+14 q+10 q2+10 q3+14 q4+42 q5
F7=132+42 q+28 q2+25 q3+28 q4+42 q5+132 q6
Description
The sum of the semi-lengths of tunnels before a valley of a Dyck path.
For each valley v in a Dyck path D there is a corresponding tunnel, which
is the factor Tv=si…sj of D where si is the step after the first intersection of D with the line y=ht(v) to the left of sj. This statistic is
∑v(jv−iv)/2.
For each valley v in a Dyck path D there is a corresponding tunnel, which
is the factor Tv=si…sj of D where si is the step after the first intersection of D with the line y=ht(v) to the left of sj. This statistic is
∑v(jv−iv)/2.
Map
inverse
Description
Sends a permutation to its inverse.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
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.
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